We develop a framework for studying the introduction of a new payment method in a controlled laboratory environment, where consumers (buyers)
and merchants (sellers) can learn to coordinate their adoption decisions over time. The underlying game exhibits network adoption effects as
emphasized by the theoretical literature. We elicit players’ beliefs about the adoption decisions of the other side of the market so that we
can directly test for network effects. We investigate how the additional fixed cost of adopting the new payment method, relative to its savings
on per transaction costs, affects merchant’s decisions to adopt the new payment method and how that in turn affects buyer’s adoption decisions.
We find that a low fixed cost favors quick adoption of the new payment method by all participants, while for a sufficiently high fixed cost,
merchants gradually learn to reject the new payment method. We also find strong evidence of network effects and that the fixed costs are
important for the strong response of seller acceptance decisions to buyer adoption decisions. An evolutionary learning model provides a good
characterization of the dynamic adjustment paths found in our experimental data.
Bargaining is widely used in monetary, labor and finance models to determine terms of trade. The chosen bargaining solution can matter for welfare
analysis, for example when agents are liquidity constrained. Here we report on an experiment in which buyers and sellers engage in semi-structured
bargaining to determine the terms of trade with the aim of evaluating the empirical relevance of two bargaining solutions, the generalized Nash
bargaining solution and Kalai’s proportional bargaining solution. These bargaining solutions predict different outcomes when buyers are constrained
in their money holdings. We first use the case when the buyer is not liquidity constrained to estimate the bargaining power parameter, which we find
to be equal to 1/2. Then, imposing liquidity constraints on buyers, we find strong evidence in support of the Kalai proportional solution. Our
findings have policy implications, e.g., for the welfare cost of inflation in search-theoretic models of money.
Credit default swaps (CDS) played an important role in the financial crisis of 2008. Here, we provide the first controlled experiment analyzing CDS
pricing in a bond market subject to default risk. We further use the laboratory as a testbed to analyze CDS regulation. Our results show that the
regulation achieves the goal of increasing the use of CDS for hedging purposes while reducing the use of CDS for speculation. This success does not
come at the expense of lower initial public offering (IPO) prices for the bonds or worse pricing of bonds or CDS in the secondary market.
Tax deferred accounts (TDAs) are an increasingly popular method of saving for retirement, and have become common across many developed countries.
Nevertheless, it is unclear whether TDAs actually improve a lifecycle savings behavior and retirement preparedness because it is difficult to
perform a counterfactual analysis. Households always have other means of savings so there is no guarantee that a TDA, with its inflexible restriction
that funds cannot be drawn until retirement, will improve lifecycle savings and lifetime utility. In this paper we resort to laboratory experiments to
study the effects of TDAs and we compare experimental treatments where subjects have access to TDAs with treatments where they do not, and we are also
careful to consider the tax consequences of our different treatments as well. We find that the presence of TDAs substantially improves a household's
lifecycle savings behavior, making them better prepared for retirement, and it has a small positive but insignificant effect on lifetime utility.
We report on an experiment where subjects play an indefinitely repeated prisoner’s dilemma game against robot opponents known to play the Grim
trigger strategy. The game’s continuation probability is varied affecting whether cooperation can be rationalized. We find that overall first round
cooperation is higher than predicted and increases in the continuation probability. However, some subjects defect after cooperating, perhaps
anticipating the end of a supergame and others cooperate after defecting, which is harder to rationalize. The latter type of error decreases
in a measure of cognition, suggesting that cognition is important for the successful implementation of strategies.
A growing body of evidence suggests that assets included in market indexes trade at a premium relative to excluded assets. Here we look for evidence
of such an index inclusion premium in a carefully controlled laboratory experiment. Our environment involves three assets and an Exchange Traded Fund
(ETF) index asset. We model Authorized Participants (APs) as bots that create and redeem ETF shares by scanning the order books of the underlying
assets. In one treatment, all three assets are included in the ETF index asset. In a second treatment, one of the three assets is excluded from the
ETF index and is replaced by a second unit of one of the included assets; the included and excluded assets have identical fundamental values enabling
a clean test of whether there exists an index inclusion premium. In a further variant of the excluded asset treatment, short-selling is allowed. We
find that inclusion of an asset in the ETF index results in a substantial price premium. This is due to investors' strong demand for the ETF asset
and use of a buy-and-hold strategy that reduces the tradeable supply of the assets that underlie the ETF asset and increases their price. Short-selling
helps to alleviate the supply problem, but given the strong demand for the ETF asset, the inclusion premium persists.
We explore how information ambiguity and traders’ attitudes toward ambiguity affect expectations and asset prices under three different market institutions.
Specifically, we test the prediction of Epstein and Schneider (2008) that information ambiguity will lead market prices to overreact to bad news and to
underreact to good news. We find that such an asymmetric reaction exists and is strongest in individual prediction markets. It occurs to a lesser extent
in single price call markets. It is weakest of all in double auction markets, where buyers’ asymmetric reaction to good/bad news is cancelled out by the
opposite asymmetric reaction of sellers.
We report on an experiment testing the empirical relevance of least squares (LS) learning, a common way of modelling how individuals
learn a rational expectations equilibrium (REE). Subjects are endowed with the correct perceived law of motion (PLM) for a price level variable they are
seeking to forecast, but do not know the true parameterization of that PLM. Instead, they must choose and can adjust the parameters of this PLM over
50 periods. Consistent with the E-stability of the REE in the model studied, 93.1% of subjects achieve convergence to the REE in terms of their price
level predictions. However, only 20.3% of subjects can be characterized as least squares learners via the adjustments they make to the parameterization
of the PLM over time. We also find that subjects' parameter estimates are more accurate when there is greater variance in the independent variable of the
model. We consider several alternatives to least squares learning and find evidence that many subjects employ a simple satisficing approach.
We provide a direct, experimental test of the buffer stock model of savings behavior. We use a three-period intertemporal model of consumption/savings
decisions where liquidity in the second period is constrained (and, thus, borrowing is not possible). We contrast behavior in this constrained version
of the model with an unconstrained version where there is no liquidity constraint. A second treatment variable is the variance of the stochastic income
process, resulting in a 2×2 experimental design. We test the comparative statics predictions of the model and find that, in contrast to these
predictions, the liquidity constraint does not increase savings in the first period of the constrained model relative to the first period of the unconstrained
model. However, we find strong support for all the other comparative statics predictions of the model, e.g., the impact of a higher variance of income on
savings behavior and differences between period 1 and period 2 savings. In further analyses, we find that we can rationalize the departures we observe
from model predictions by some combination of debt aversion, heterogeneity in cognitive abilities and/or learning.
Stock splits and reverse splits often result in short-term abnormal returns even though such split events do not change any fundamental factors affecting
the valuation of the firm. In this paper we report on an experiment designed to better understand market reactions to stock splits and reverse splits.
In one treatment, two assets have increasing fundamental values, and one asset is subject to a 2-for-1 share split while the other asset is not. In a
second treatment, the fundamental values of both assets are decreasing, and one asset is subject to a 1-for-2 reverse split while the other asset is not.
We find that in both cases, share prices do not fully adjust to changes in fundamental values per share following a split announcement. We provide evidence
that the less than complete adjustment of share prices to splits or reverse splits can be attributed to heterogeneity in the cognitive abilities of traders.
We provide a model of group sorting or polarization based on group identity alone. In our model, agents differ from one another in terms of an observable
binary group identity. Groups may also differ in terms of the distribution of abilities (types) but the true distribution is uncertain, so agents have to
form beliefs about that distribution in making both investment and location decisions. Each agent's ability is private information, whereas group identity
is publicly observable. Agents have no preferences or special facilities for interacting with members of their own group. In this environment, we show that,
in equilibrium, agents endogenously sort themselves according to their group identity to two different locations under rational belief updating, and we
identify conditions under which the society becomes completely polarized with members of each group rationally choosing to congregate in distinct locations.
We study indefinitely-lived assets in experimental markets and find that the traded prices of these assets are on average about 40% of the risk
neutral fundamental value. Neither uncertainty about the value of total dividend payments nor horizon uncertainty about the duration of trade can
account for this low traded price, while the temporal resolution of payoff uncertainty plays a crucial role. We show that an Epstein and Zin (1989)
recursive preference specification together with probability weighting can rationalize the low traded prices observed in our indefinite-horizon
asset markets, while risk attitudes do not play such an important role.
The beauty contest game (BCG) serves as a core framework for demonstrating behavioral non-equilibrium patterns such as focal points and level-k reasoning.
We introduce a new version of the BCG that removes the bounded choice interval and thus eliminates iterative elimination of dominated strategies. We further
add correlated idiosyncratic signals that can serve as (equilibrium) coordination devices. We find that choices in these new versions of the BCG are closer
to equilibrium as compared with the standard BCG. Indeed, we show how variations in the design of BCGs can greatly affect the use of focal points and
We provide some theory and experimental evidence on contests with entry fees. In our setup, players must simultaneously decide whether or not to pay a
fee to enter a contest and on the amount they wish to bid should they choose to enter the contest. In a general n-bidder game, we show that
the addition of contest entry fees increases the contest designer's expected revenue and that there is a unique revenue maximizing entry fee. In an
experimental test of this theory we vary both the entry fee and the number of bidders. We find over-bidding for all entry fees and bidder group sizes,
n. We also find under-participation in the contest for low entry fees and over-participation for higher entry fees. Overall, the revenue
maximizing entry fee for the contest designer is found to be greater than the theoretically optimal entry fee. We offer some possible explanations
for these departures from theoretical predictions.
We report on an experiment comparing two institutions for determining spending on public goods. Two parties bargain over how to divide a dollar between
a public and two private accounts, one for each party. Each party attaches a different weight to the public good, either high or low, and there is some
probabilistic persistence over time as to which party makes a proposal. Under discretion, the status quo default allocation to the public account (in
the event of disagreement) is zero while under a mandatory rule it is equal to the level that was last agreed upon. The mandatory rule thus creates a
relationship between current decisions and future payoffs, and our experiment tests the theoretical prediction that the efficient level of public good
is provided under the mandatory rule while the level of public good funding is at a sub-optimal level under the discretionary rule. We find that proposers
(particularly high types) tend to contribute significantly more to the public account under the mandatory institution than under the discretionary rule,
and that the dynamic patterns of adjustment to the public account are largely consistent with theoretical predictions.
Click on the title to download a pdf file of the paper.
We extend the beauty contest game to two dimensions: each player chooses two numbers to be as close as possible to certain target values, which are
linear functions of the averages of the two number choices. One of the targets depends on the averages of both numbers, making the choices interrelated.
We report on an experiment where we vary the eigenvalues of the associated two-dimensional linear system and find that subjects can learn the Pareto-optimal
Nash Equilibrium of the system if both eigenvalues are stable and cannot learn it if both eigenvalues are unstable. Interestingly, subjects can also learn
it if the system has the saddlepath property -- with one stable and one unstable eigenvalue –- but only if the one unstable eigenvalue is negative. We
show theoretically that our results cannot be explained by homogeneous level-k models where all agents apply the same level k depth of
reasoning to their choices, including the naïve learning model. However, our results can be explained by a mixed cognitive-levels model,
including the adaptive learning model. We also run a horserace between many models used in the literature with the winner being a simple mixed model with
levels 0, 1, and equilibrium reasoning.
We explore the celebrated Friedman rule for optimal monetary policy in the context of a laboratory economy based on the Lagos-Wright model. The
rule that Friedman proposed can be shown to be optimal in a wide variety of different monetary models, including the Lagos-Wright model. However,
we are not aware of any prior empirical evidence evaluating the welfare consequences of the Friedman rule. We explore two implementations of the
Friedman rule in the laboratory. The first is based on a deflationary monetary policy where the money supply contracts to offset time discounting.
The second implementation pays interest on money removing the private marginal cost from holding money. We explore the welfare consequences of
these two theoretically equivalent implementations of the Friedman Rule and compare results with two other policy regimes, a constant money supply regime
and another regime advocated by Friedman, where the supply of money grows at a constant k-percent rate. We find that, counter to theory,
the Friedman rule is not welfare improving, performing no better than a constant money regime. By one welfare measure, we find that the k-percent
money growth rate regime performs best.
This paper discusses how macroeconomics can and already has begun to make use of controlled experimental methods to address the assumptions and predictions of
macroeconomic models as well as to evaluate the impacts of macroeconomic policy interventions. Specifc issues addressed include rational expectations and
alternatives, intertemporal optimization with an application to household consumption and savings decisions and the efficacy of various monetary policies.
We compare two fixed-prize mechanisms for funding public goods, an all-pay auction and a lottery, where public good provision can only occur if the
participants’ contributions equal or exceed the fixed-prize value. We show that the provisional nature of the fixed- prize means that efficiency and
endowment conditions must both be satisfied to assure positive public good provision. Our main finding is that provisional fixed-prize lotteries can
outperform provisional fixed-prize all-pay auctions in terms of public good provision when endowments are large relative to prize values. We test these
predictions in a labora- tory experiment where we vary the number of participants, the marginal per capita return (mpcr) on the public good, and the
mechanism for awarding the prize, either a lottery or an all-pay auction. Consistent with the theory, we find that the mpcr matters for contribution
amounts under the lottery mechanism. However, inconsistent with the theory, bids are significantly higher than predicted and there is no significant
difference in the level of public good provision under either provisional, fixed-prize mechanism. We consider sev- eral different modifications to
our framework that might help to explain these departures from theoretical predictions.
We examine how exchange traded funds (ETFs) affect asset pricing, and trade volume in a laboratory asset market. We focus on behavior in secondary
markets with or without ETF assets and whether there is zero or negative correlation in asset dividends. In the latter case, the diversification
benefits of ETFs are most salient. We find that when the dividends are negatively correlated, ETFs reduce mispricing without decreasing trading volume.
When dividends are uncorrelated, the ETF has no impact on these same measures. Thus, our findings suggest that ETFs do not harm, and may in fact improve,
price discovery and liquidity in asset markets.
We propose a model of how social norms change in response to the evolution of privately held preferences. Our aim is to rationalize the tendency for
individuals who hold minority preferences to take actions favored by the majority. We do this using a game involving a tension between a desire to act
according to one's underlying preferences and a desire to conform to the majority opinion. In an experimental setting, we find that even after a majority
of the population shares what was previously an unpopular minority opinion, members of the new majority are slow to change their behavior. The timing
and speed with which behavior transitions to match new, majority-held opinions depends on the size of the reward for conformity. When the rewards for
conformity are low, the transition is gradual, with considerable periods of costly public disagreement. When the rewards for conformity are high, transitions
are slow to start but conclude rapidly once they begin.
We demonstrate the possibility of conducting synchronous, repeated, multi-game economic decision-making experiments with hundreds of subjects in-person
or remotely with live streaming using entirely mobile platforms. Our experiment provides important proof-of-concept that such experiments are not only
possible, but yield recognizable results as well as new insights, blurring the line between laboratory and field experiments. Specifically, our findings
from 8 different experimental economics games and tasks replicate existing results from traditional laboratory experiments despite the fact that subjects
play those games/task in a specific order and regardless of whether the experiment was conducted in person or remotely. We further leverage our large
subject population to study the effect of large (N=100) versus small (N=10) group sizes on behavior in three of the scalable games that we study.
While our results are largely consistent with existing findings for small groups, increases in group size are shown to matter for the robustness of
We report on an experiment that distinguishes between rational social learning and behavioral information source bias. Subjects are asked to
correctly guess the current binary state of the world. Differently from other social learning studies, subjects must choose between receiving a
private, noisy signal about the current state or observing the past guesses of other subjects in the prior period. Our design varies the persistence of
the state across time, which affects whether private or social information is optimal. Thus our design enables us to separate subjects who choose
information optimally from those who excessively use either social information (``herd animals'') or private information (``lone wolves'').
We find sizable proportions of both behavioral types.
We report on an experiment examining whether individuals can solve a simple signal extraction problem of the type found in models with imperfect
information. In one treatment, subjects must form point predictions based on observing both public and private signals, while in another they receive
the same information but must decide on the weight to attach to each signal, which then determines their point prediction. We find that, at the
aggregate level, signal extraction provides a good characterization of subjects' behavior in both treatments, but at the individual level, there is
considerable heterogeneity in subjects' ability to perform signal extraction.
We implement a repeated version of the Barro-Gordon monetary policy game in the laboratory and ask whether reputation serves as a substitute for
commitment, enabling the central bank to achieve the efficient Ramsey equilibrium and avoid the inefficient, time-inconsistent one-shot Nash equilibrium.
We find that reputation is a poor substitute for commitment. We then explore whether central bank cheap talk, policy transparency, both cheap talk and
policy transparency or economic transparency or committees of central bankers yield improvements in the direction of the Ramsey equilibrium under the
discretionary policy regime. Our findings suggest that these mechanisms have only small or transitory effects on welfare. Surprisingly, the real effects
of supply shocks are better mitigated by a commitment regime than by any discretionary policy. Thus, we find that there is no trade-off between
flexibility and credibility.
We study a sequence of “double-slit” experiments designed to perform repeated measurements of an attribute in a large pool of subjects using Amazon’s
Mechanical Turk. Our findings contrast the prescriptions of decision theory in novel and interesting ways. The response to an identical sequel measurement
of the same attribute can be at significant variance with the initial measurement. Furthermore, the response to the sequel measurement depends on whether
the initial measurement has taken place. In the absence of the initial measurement, the sequel measurement reveals additional variability, leading to
a multimodal frequency distribution which is largely absent if the first measurement has taken place.
We model and experimentally evaluate the trade-off between innovation and imitation commonly faced by firms and individuals. Innovation involves
searching for a high payoff opportunity, but paying a cost to do so. Imitation involves avoiding the search cost and copying the most successful
payoff opportunity uncovered thus far. We formulate a novel model of sequential innovation versus imitation decisions made by a group of n
regret minimizing agents. We analyze the consequences of complete versus incomplete information about the distribution of payoffs from innovation
on agent's decisions. We then study these predictions in a laboratory experiment where we find evidence in support of our theoretical predictions.
We document heterogeneity of rationality and bias in information acquisition in a social learning experiment, where subjects, prior to
guessing an unknown binary state of the world, must choose between receiving a private signal or seeing social information containing
the guesses made by previous subjects in the sequence, rather than observing both pieces of information as in the classic design of Anderson and
Holt (1997). By requiring subjects to make this information choice at different points in the sequence, our within-subject design allows us to
separate biased from optimal information choices. Overall, the majority of subjects exhibit a suboptimal bias in favor of choosing social rather
than private information, consistent with underestimating both mistakes made by other subjects and the frequency of uninformative social information.
Furthermore, a substantial minority behave according to a refined equilibrium prediction, while some subjects consistently choose
social information and others consistently choose private information.
We design and report on the first laboratory experiment exploring the role of interbank network structure and premature liquidation
costs for the likelihood of a financial contagion. The laboratory provides the control necessary to understand the role played by
interbank network configurations and liquidation costs for the fragility of the financial system. Specifically, we study the
likelihood of financial contagion in complete and incomplete networks of banks that are linked in terms of interbank deposits as
in the model of Allen and Gale (2000) and we further vary the cost of premature liquidation. Subjects play the role of depositors
who must decide whether or not to withdraw their funds from their interconnected banks. We find that when liquidation costs are
high, a complete network structure enabling efficient risk sharing is significantly less vulnerable to financial contagions than
an incomplete network structure. However, when liquidation costs are low, network structure does not matter as much for the frequency
of financial contagions. We conclude that low liquation costs or a more complete network structure can be viewed as substitutes for
reducing the frequency of financial contagions.
We report on a series of economic decision-making experiments exploring how individuals make lifecycle consumption and saving plans when they
face different income profiles, representing different pension replacement rates. We aim to assess whether variations in pension replacement
rates might aid or hinder individuals' ability to make good lifecycle consumption and saving plans. We find that pension replacement rates
matter for subjects' experimental payoffs and consumption behavior. In particular, our treatment with a 100% pension replacement rate yields
the highest experimental payoff, and more subjects in this treatment choose the status quo strategy of consuming endowments in every period.
We show that a model of rational inattention is useful for explaining subjects' responses to different pension replacement rates.
Correlated equilibrium (Aumann 1974, 1987) is an important generalization of the Nash equilibrium concept for multiplayer non-cooperative games.
In a correlated equilibrium, players rationally condition their strategies on realizations of a common external randomization device and, as a
consequence, can achieve payoffs that Pareto dominate any of the game's Nash equilibria. In this paper we explore whether such correlated equilibria
can be learned over time using an evolutionary learning model where agents do not start with any knowledge of the distribution of random draws
made by the external randomization device. Furthermore, we validate our learning algorithm findings by comparing the end behavior of simulations
of our algorithm with both the correlated equilibrium of the game and the behavior of human subjects that play that same game. Our results suggest
that the evolutionary learning model is capable of learning the correlated equilibria of these games in a manner that approximates well the learning
behavior of human subjects and that our findings are robust to changes in the specification and parameterization of the model.
We propose a classroom experiment implementing a simple version of a New Keynesian model suitable for courses in intermediate
macroeconomics and money and banking. Students play as either the central bank or members of the private sector. The central
banker sets interest rates to meet either twin objectives for inflation and the output gap or to meet only an inflation target.
In both settings, private sector agents are concerned with correctly forecasting the inflation rate. We show that an experiment
implementing this setup is feasible and yields results that enhance understanding of the New Keynesian model of monetary policy.
We propose alternative versions where the central bank is replaced by a policy rule and we provide suggestions for discussing
the experimental results with students.
We implement a dynamic asset pricing experiment in the spirit of Lucas (1978) with storable assets and non-storable cash. In the first treatment,
we impose diminishing marginal returns to cash to incentivize consumption smoothing across periods. We find that subjects use the asset to smooth
consumption, although the asset trades at a discount relative to the risk-neutral fundamental price. This under-pricing is a departure from the
asset price "bubbles" observed in the large experimental asset pricing literature originating with Smith et al. (1988) and can be rationalized
by considering subjects' risk aversion with respect to uncertain money earnings. In a second treatment, with no induced motivation for trade
à la the Smith et al. design, we find that the asset trades at a premium relative to its expected value and that shareholdings are highly
concentrated. Elimination of asset price uncertainty in additional experimental treatments serves to reinforce the same observations, and suggests
that speculative behavior explains the departure of prices from fundamental value in the absence of a consumption-smoothing motive for asset trades.
An important feature of bond markets is the relationship between the IPO price and the probability that the issuer defaults. On the one hand,
the default probability affects the IPO price. On the other hand, IPO prices affect the default probability. It is a priori unclear whether
agents can competitively price such assets and our paper is the first to explore this question. We do so using laboratory experiments. We
develop two flexible bond market models that are easily implemented in the laboratory. We find that subjects learn to price the bonds well
after only a few repetitions.
We report on an experiment examining behavior and equilibrium selection in two similar, infinitely repeated games, Stag Hunt and Prisoner's Dilemma
under anonymous random matching. We are interested in the role that historical precedents may play for equilibrium selection between these two repeated
games. We find that a precedent for efficient play in the repeated Stag Hunt game does not carry over to the repeated Prisoner's Dilemma game
despite the possibility that efficient play can be sustained as an equilibrium of the indefinitely repeated game. Similarly, a precedent for
inefficient play in the repeated Prisoner's Dilemma game does not extend to the repeated Stag Hunt game. We conclude that equilibrium selection
between similar repeated games may have less to do with historical precedents and might instead depend more on strategic considerations associated
with the different payoffs of these similar repeated games.
We report on experimental evidence rationalizing the use of heterogeneous agent models. We provide compelling evidence that subjects in laboratory
experiments often behave in ways that depart from the rational choice ideal. Further, these subjects' heuristic approaches often differ from one another
in distinct, classifiable ways. It follows that models of heterogeneous, boundedly rational agents can often deliver predictions that are a
better fit to the experimental data at both the micro and the macro levels of analysis than can rational-choice, single-actor models.
Our focus in this chapter is on experimental studies developed to address questions in macroeconomics and finance.
We report on an experiment exploring whether and how subjects may learn to use a correlation device to coordinate on a correlated equilibrium of
the Battle of the Sexes game which Pareto dominates the mixed-strategy Nash equilibrium of that game. We consider a direct correlation device with
messages phrased in terms of players' actions as well as an indirect device with a priori meaningless messages. According to the revelation principle,
it does not matter whether the correlation device is direct or indirect so long as it implements a correlated equilibrium. However, we find that
subjects had an easier time coordinating on the efficient correlated equilibrium with a direct rather than an indirect device. Nevertheless,
subjects were able to learn to use the indirect device to better coordinate their play. We further find that, when paired with a fixed partner,
subjects utilized history-contingent strategies (e.g., "alternation") as a coordinating device and were more likely to ignore the correlation
device in this setting; the fixed-matching protocol can thus serve as a substitute for a correlation device in achieving an efficient coordination
We consider a model where two players compete for n items having different common values in a Blotto game. Players must decide how to allocate
their common budgets across all n items. The winner of each item is determined stochastically using a lottery mechanism which yields a unique
equilibrium in pure strategies. We analyze behavior under two competing payoff objectives found in the Blotto games literature that have not been
previously compared: (i) players aim to maximize their total expected payoff and (ii) players maximize the probability of winning a majority value of
all n items. We report results from an experiment where subjects face both payoff objectives and we find support for the differing theoretical
The Condorcet jury model with costless but informative signals about the true state of the world predicts that the efficiency of group
decision-making increases unambiguously with the group size. However, if signal acquisition is made an endogenous and costly decision, then rational
voters have disincentives to purchase information as the group size becomes larger. We investigate the extent to which human subjects recognize this
trade-off between better information aggregation and greater incentives to free-ride in a laboratory experiment where we vary the group size, the cost
of information acquisition and the precision of signals. We find that the theory predicts well in the case of precise signals. However, when signals
are imprecise, free-riding incentives appear to be much weaker as there is a pronounced tendency for subjects to over-acquire information relative to
equilibrium predictions. We rationalize the latter finding using a quantal response equilibrium that allows for risk aversion
This chapter surveys laboratory experiments addressing macroeconomic phenomena. The first part focuses on experimental tests of the
microfoundations of macroeconomic models discussing laboratory studies of intertemporal consumption/savings decisions, time (in)consistency of
preferences and rational expectations. Part two explores coordination problems of interest to macroeconomists and mechanisms for resolving these
problems. Part three looks at experiments in specific macroeconomic sectors including monetary economics, labor economics, international economics as
well-as large scale, multi-sector models that combine several sectors simultaneously. The final section addresses experimental tests of
macroeconomic policy issues.
We study how group size affects cooperation in an infinitely repeated n-player Prisoner’s Dilemma (PD) game. In each repetition of the game, groups
of size n ≤ M are randomly and anonymously matched from a fixed population of size M to play the n-player PD stage game. We provide conditions for
which the contagious strategy (Kandori, 1992) sustains a social norm of cooperation among all M players. Our main finding is that if agents are sufficiently
patient, a social norm of society-wide cooperation becomes easier to sustain under the contagious strategy as n increases toward M. In an experiment
where the population size M is fixed and conditions identified by our theoretical analysis hold, we find strong evidence that cooperation rates are
higher with larger group sizes than with smaller group sizes in treatments where each subject interacts with M-1 robot players who follow the
contagious strategy. When the number of human subjects increases in the population, the cooperation rates decrease significantly, indicating that
it is the strategic uncertainty among the human subjects that hinders cooperation.
Adaptive and eductive learning are two widely used ways of modeling the process by which agents learn a rational expectation equilibrium (REE).
In this paper we report on an experiment where we exploit differences in the conditions under which adaptive and eductive learning converge to
REE so as to investigate which approach provides the better description of the learning behavior of human subjects. Our results suggest that
the path by which the system converges appears to be a mixture of both adaptive and eductive learning model predictions.
We explore the effect of fixed versus dynamic group membership on public good provision.
In a novel experimental design, we modify the traditional voluntary contribution mechanism (VCM) by
periodically replacing old members of a group with new members over time. Under this dynamic, overlapping
generations matching protocol we find that average contributions experience significantly less decay over time
relative to a traditional VCM environment with fixed group membership. These findings suggest that the
traditional pattern of contribution and decay seen in many public goods experiments may not accurately
reflect behavior in groups with changing membership, as is the case in many real-world environments.
We explore real time, adaptive nonlinear learning dynamics in stochastic
macroeconomic systems. Rather than linearizing nonlinear Euler equations where expectations
play a role around a steady state, we instead approximate the nonlinear expected values using
the method of parameterized expectations. Further we suppose that these approximated expectations
are updated in real time as new data become available. We argue that this method of real-time
parameterized expectations learning provides a plausible alternative to real-time adaptive
learning dynamics under linearized versions of the same nonlinear system.
This paper investigates behavior in finitely repeated simultaneous and sequential-move prisoner's dilemma games when there is one-sided incomplete
information and signaling about players' concerns for fairness, specifically, their preferences regarding "inequity aversion." In this environment,
we show that only a pooling equilibrium can be sustained, in which a player type who is unconcerned about fairness initially cooperates in order to
disguise himself as a player type who is concerned about fairness. This disguising strategy induces the uninformed player to cooperate in all periods
of the repeated game, including the final period, at which point the player type who is unconcerned about fairness takes the opportunity to defect,
i.e., he "backstabs" the uninformed player. Despite such last-minute defection, our results show that the introduction of incomplete information can
actually result in a Pareto improvement under certain conditions. We connect the predictions of this "backstabbing" equilibrium with the frequently
observed decline in cooperative behavior in the final period of finitely-repeated experimental games.
We report results from a laboratory experiment exploring the extent to which individuals can solve a deterministic, intertemporal
lifecycle consumption optimization problem and the effect of revealing social information on past average consumption amounts; as
all individuals have identical induced preferences and lifetime incomes, such social information could be useful in solving for the optimal consumption path.
Instead, we find that the provision of social information on past average levels of consumption results in a greater deviation of consumption from both the unconditional
and the conditionally optimal paths. We find some improvement in consumption planning relative to the conditional optimum when social concerns (external habits) are explicitly
incorporated into subject's period utility functions as in external habit formation preference specifications. Our results on the effects of social information on
consumption behavior may help to explain the phenomenon of over-consumption and under-saving that has been observed in many developed countries in recent decades as
social information on the behavior of others has become more readily available.
We study a micro-founded search model of exchange in the laboratory. Using a within subjects design, we consider exchange behavior with and without
an intrinsically worthless token object. While these tokens have no redemption value, like fiat money they may foster greater exchange and welfare via the
coordinating role of having prices of goods in terms of tokens. We find that welfare is indeed improved by the presence of tokens provided that the economy starts
with a supply of such tokens. In economies that operate for some time without tokens, the later surprise introduction of tokens does not serve to improve welfare.
We also explore the impact of announced changes in the economy-wide stock of tokens (fiat money) on prices. Consistent with the quantity theory of money, we find
that increases in the stock of money (tokens) have no real effects and mainly result in proportionate changes to prices. However, the same finding
does not hold for decreases in the stock of money.
We study the Lagos and Wright (2005) model of monetary exchange in the laboratory. With a finite population of sufficiently patient agents, this
model has a unique monetary equilibrium and a continuum of non-monetary gift exchange equilibria, some of which Pareto dominate the monetary equilibrium.
We find that subjects avoid the gift-exchange equilibria in favor of the monetary equilibrium. We also study versions of the model without money
where all equilibria involve non-monetary gift-exchange. We find that welfare is higher in the model with money than without money, suggesting
that money plays a role as an efficiency enhancing coordination device.
We report on an experiment comparing compulsory and voluntary voting institutions in a voting game with common preferences. Rational choice
theory predicts sharp differences in voter behavior between these two institutions. If voting is compulsory, then voters may find it rational
to vote insincerely, i.e., against their private information. If voting is voluntary so that abstention is allowed, then sincere voting in accordance
with a voter's private information is always rational while participation may become strategic. We find strong support for these theoretical predictions in
our experimental data. Moreover, voters adapt their decisions to the voting institution in place in such a way as to make the group decision accuracy differences
between the two voting institutions negligible. The latter finding may serve to rationalize the co-existence of compulsory and voluntary voting
institutions in nature.
We consider implementation issues regarding two mechanisms that have been used to increase voter turnout in elections: fines and lotteries. We focus
on the amount of the fine or lottery prize needed to achieve full participation. We then propose a combined, self-financing mechanism by which the
fines imposed on non-participants are used to finance the prize that is awarded by lottery to one of the individuals choosing to participate in
voting. We argue that this combined mechanism has some advantages over the other two mechanisms and merits consideration.
Rational Expectations (RE) models have two crucial dimensions: (i) agents on average correctly forecast future prices given all available information,
and (ii) given expectations, agents solve optimization problems and these solutions in turn determine actual price realizations. Experimental tests
of such models typically focus on only one of these two dimensions. In this paper we consider both forecasting and optimization decisions in an
experimental cobweb economy. We report results from four experimental treatments: (1) subjects form forecasts only, (2) subjects determine quantity
only (solve an optimization problem), (3) they do both and (4) they are paired in teams and one member is assigned the forecasting role while the
other is assigned the optimization task. All treatments converge to Rational Expectation Equilibrium (REE), but at different speeds. We observe that
performance is the best in treatment 1 and worst in the treatment 3. We further find that most subjects use adaptive rules to forecast prices. Given
a price forecast, subjects are less likely to make conditionally optimal production decisions in treatment 3 where the forecast is made by themselves,
than in treatment 4 where the forecast is made by the other member of their team, which suggests that "two heads are better than one" in finding REE.
Can a social norm of trust and reciprocity emerge among strangers? We investigate this question by examining
behavior in an experiment where subjects repeatedly play a two-player binary "trust" game. Players are
randomly and anonymously paired with one another in each period. The main questions addressed are whether
a social norm of trust and reciprocity emerges under the most extreme information restriction (anonymous
community-wide enforcement) or whether trust and reciprocity require additional, individual-specific
information about a player's past history of play and whether that information must be provided freely
or at some cost. In the absence of such reputational information, we find that a social norm of trust and
reciprocity is difficult to sustain. The provision of reputational information on past individual decisions
significantly increases trust and reciprocity, with longer histories yielding the best outcomes. Importantly,
we find that making reputational information available at a small cost may also lead to a significant
improvement in trust and reciprocity, despite the fact that most subjects do not choose to purchase
We experimentally examine equilibrium refinements in static and dynamic binary choice games of complete information with
strategic complementarities known as "entry" games. Our aim is to assess the predictive power of two different equilibrium
selection principles. In static entry games, we test the theory of global games as an equilibrium selection device.
This theory posits that players play games of complete information as if they were playing a related global game of incomplete
information. In dynamic entry games, individuals decide not only whether to enter but also when to enter. Once entry occurs
it is irreversible. The number of people who have already entered is part of the state description, and individuals can
condition their decisions on that information. If the state variable does not indicate that entry is dominated, the efficient
subgame perfect equilibrium prediction calls for all players to enter. Further, if there is a cost of delay, entry should
occur immediately, thereby eliminating the coordination problem. This subgame perfect entry threshold in the dynamic game
will generally differ from the global game threshold in static versions of the same entry game. Nevertheless, our experimental
findings suggest that observed entry thresholds in both static and dynamic versions of the same entry game are surprisingly
similar. The mean entry threshold in the static game lies below the global game equilibrium threshold while the mean entry
threshold in the dynamic game lies above the efficient subgame perfect equilibrium threshold. An important implication of this
finding is that if one were to observe only the value of the state variable and the number of people who enter by the end of
the game one could not determine whether the static or the dynamic game had been played.
This paper investigates how the introduction of social preferences affects players' equilibrium behavior in both the
one-shot and the infinitely repeated version of the Prisoner's Dilemma game. We show that fairness concerns operate
as a "substitute" for time discounting in the infinitely repeated game, as fairness helps sustain cooperation for
lower discount factors. In addition, such cooperation can be supported under larger parameter values if players are
informed about each others' social preferences than if they are uninformed. Finally, our results help to identify
conditions under which cooperative behavior observed in recent experimental repeated games can be rationalized using
time preferences alone (patience) or a combination of time and social preferences (fairness).
Research on decision-making strategies among younger and older adults suggests that older adults may be more risk
averse than younger people in the case of potential losses. These results mostly come from experimental studies
involving gambling paradigms. Since these paradigms involve substantial demands on memory and learning, differences
in risk aversion or other features of decision making attributed to age may in fact reflect age-related declines
in cognitive abilities. In the current study, older and younger adults completed a simpler, paired lottery choice
task used in the experimental economics literature to elicit risk aversion. A similar approach was used to elicit
participants' discount rates. The older adult group was more risk averse than the younger (p<0.05) and had a
higher discount rate (15.6-21.0 percent versus 10.3-15.5 percent, p<0.01), indicating lower expected utility from future
income. Risk aversion and implied discount rates were weakly correlated. It may be valuable to investigate developmental
changes in neural correlates of decision making across the lifespan.
We explore whether competitive outcomes arise in an experimental
implementation of a market game, introduced by Shubik (1972). Market
games obtain Pareto inferior (strict) Nash equilibria, in which some or
possibly all markets are closed. We find that subjects do not coordinate on
autarkic Nash equilibria, but favor more efficient Nash equilibria in which
all markets are open. As the number of subjects participating in the market
game increases, the Nash equilibrium they achieve approximates the
associated competitive equilibrium of the underlying economy. Motivated by
these findings, we provide a theoretical argument for why evolutionary
forces can lead to competitive outcomes in market games.
We explore determinacy and expectational stability (learnability) of rational expectations equilibrium (REE)
in "New Keynesian" (NK) models that include capital. Using a consistent calibration across three different
models--labor only, firm-specific capital, or an economy-wide rental market for capital, we provide a clear
picture of when REE is determinate and learnable and when it is not under a variety of monetary policy
rules. Our findings make a case for greater optimism concerning the use of such rules in NK models with
capital. While Bullard and Mitra's (2002, 2007) findings for the labor-only NK model do not always extend
to models with capital, we show that determinate and learnable REE can be achieved in NK models with capital
if there is (i) plausible capital adjustment costs, (ii) some weight given to output in the policy rule and/or
iii) a policy of interest rate smoothing.
Some issues are raised with regard to conducting economic decision-making experiments in
virtual worlds. The issues are illustrated via a visit to an experimental laboratory on Second
Life. Some suggestions for addressing these issues are proposed.
We report results from an experiment that explores the empirical validity of correlated
equilibrium, an important generalization of Nash equilibrium. Specifically, we examine the conditions under
which subjects playing the game of Chicken will condition their behavior on private third-party recommendations
drawn from publicly announced distributions. We find that when recommendations are given, behavior differs
from both a mixed-strategy Nash equilibrium and behavior without recommendations. In particular, subjects
typically follow recommendations if and only if (1) those recommendations derive from a correlated equilibrium
and (2) that correlated equilibrium is payoff-enhancing relative to the available Nash equilibria.
We investigate conditions under which self-organized criticality (SOC) arises in
a version of a dynamic entry game. In the simplest version of the game, there is
a single location -- a pool -- and one agent is exogenously dropped into the pool
every period. Payoffs to entrants are positive as long as the number of agents in
the pool is below a critical level. If an agent chooses to exit, he cannot re-enter,
resulting in a future payoff of zero. Agents in the pool decide simultaneously each
period whether to stay in or not. We characterize the symmetric mixed strategy
equilibrium of the resulting dynamic game. We then introduce local interactions
between agents that occupy neighboring pools and demonstrate that, under our payoff
structure, local interaction effects are necessary and sufficient for SOC and for an
associated power law to emerge. Thus, we provide an explicit game-theoretic model of
the mechanism through which SOC can arise in a social context with forward looking agents.
Charities often devise fund-raising strategies that exploit natural human competitiveness in
combination with the desire for public recognition. We explore whether institutions promoting
competition can affect altruistic giving - even when possibilities for public acclaim are minimal.
In a controlled laboratory experiment based on a sequential "dictator game," we find that subjects
tend to give more when placed in a generosity tournament, and tend to give less when placed in
an earnings tournament - even if there is no award whatsoever for winning the tournament. Further
we find that subjects' experimental behavior correlates with their responses to a post-experiment
questionnaire, particularly questions addressing altruistic and rivalrous behavior. Based on this
evidence, we argue that behavior in our experiment is driven, in part, by innate competitive motives.
We experimentally study decentralized organizational learning.
Our objective is to understand how learning members of an organization cope with the
confounding effects of the simultaneous learning of others. Rather than inferring or
postulating some heuristic organizational learning behavior, we experimentally test the optimal
learning predictions of a stylized, rational agent model of organizational learning due
to Blume and Franco (2007). This model provides sharp testable predictions as to how
learning members of an organization might cope with the simultaneous learning of others
as a function of fundamental variables that characterize an organization, e.g., the firm
size and the discounting of future payoffs. While the problem of learning while others are
learning is quite difficult, we find support for the comparative static predictions of the
unique symmetric equilibrium of the model.
We report results from an experiment that examines play
in an indefinitely repeated, two-player Prisoner's Dilemma game. Each experimental
session involves N subjects and a sequence of indefinitely repeated games. The main
treatment consists of whether agents are matched in fixed pairings or matched randomly
in each indefinitely repeated game. Within the random matching treatment, we elicit
player's strategies and beliefs or vary the information that players have about their
opponents. Contrary to a theoretical possibility suggested by Kandori (1992), a
cooperative norm does not emerge in the treatments where players are matched randomly.
On the other hand, in the fixed pairings treatment, the evidence suggests that a
cooperative norm does emerge as players gain more experience.
We examine how groups of agents form trading networks in the presence of idiosyncratic
risk and the possibility of contagion. Specifically, four agents play a two-stage finite
repeated game. In the first stage, the network structure is endogenously determined
through a noncooperative proposal game. In the second stage, agents play multiple rounds
of a coordination game against all of their chosen `neighbors' after the realization of a
payoff relevant shock. While parsimonious, our four agent environment is rich enough to
capture all of the important interaction structures in the networks literature: bilateral
(marriage), local interaction, star, and uniform matching. Consistent with our theory,
marriage networks are the most frequent and stable network structures in our experiments.
We find that payoff efficiency is around 90 percent of the ex-ante, payoff dominant
strategies and the distribution of network structures is significantly different from
that which would result from random play.
We report results from a laboratory experiment testing the basic hypothesis
imbedded in various rational voter models that there is a direct correlation between the
strength of an individual's belief that his/her vote will be pivotal and the likelihood
that individual incurs the cost to vote. This belief is typically unobservable. In one
of our experimental treatments we elicit these subjective beliefs using a proper scoring
rule that induces truthful revelation of beliefs. This allows us to directly test the pivotal
voter model. We find that a higher subjective probability of being pivotal increases the
likelihood that an individual votes, but the probability thresholds used by subjects are
not as crisp as the theory would predict. There is some evidence that individuals learn over
time to adjust their beliefs to be more consistent with the historical frequency of pivotality.
However, many subjects keep substantially overestimating their probability of being pivotal.
Many internet auction sites implement ascending-bid, second-price auctions.
Empirically, last-minute or "late" bidding is frequently observed in "hard-close"
but not in "soft-close" versions of these auctions. In this paper, we introduce
an independent private-value repeated internet auction model to explain this
observed difference in bidding behavior. We use finite automata to model the
repeated auction strategies. We report results from simulations involving
populations of artificial bidders who update their strategies via a genetic
algorithm. We show that our model can deliver late or early bidding behavior,
depending on the auction closing rule in accordance with the empirical evidence.
Among other findings, we observe that hard-close auctions raise less revenue
than soft-close auctions. We also investigate interesting properties of the
evolving strategies and arrive at some conclusions regarding both auction
designs from a market design point of view.
Charitable contributions are frequently made over time. Donors are free to
contribute whenever they wish and as often as they want, and are frequently
updated on the level of contributions by others. A dynamic structure enables
donors to condition their contribution on that of others, and, as Schelling
(1960) suggested, it may establish trust thereby increasing charitable
giving. Marx and Matthews (2000) build on Schelling's insight and show that
multiple contribution rounds may secure a provision level that cannot be
achieved in the static, one-shot setting, but only if there is a discrete,
positive payoff jump upon completion of the project. We examine these two
hypotheses experimentally using static and dynamic public good games. We
find that contributions are indeed higher in the dynamic than in the static
game. However, in contrast to the predictions, the increase in contributions
in the dynamic game does not depend critically on the existence of a
completion benefit jump or on whether players can condition their decisions
on the behavior of other members of their group.
We examine the stability of equilibrium in sunspot-driven
real business cycle (RBC) models under adaptive learning. We show that
a general, reduced form of this class of models can admit rational expectations
equilibria that are both indeterminate and stable under adaptive learning.
Indeterminacy of equilibrium allows for the possibility that non-fundamental
"sunspot" variable realizations can serve as the main driving
force of the model, and several researchers have put forward calibrated
structural models where sunspot shocks play such a role. We show analytically
how the structural restrictions that researchers have imposed on this
type of model lead to reduced form systems where equilibrium is indeterminate
but always unstable under adaptive learning. Our findings provide a possible
resolution of the "stability puzzle" identified by Evans and
We examine the expectational stability (E--stability) of rational
expectations equilibrium in the "New Keynesian" model where monetary policy is
optimally derived and interest rate stabilization is added to the central bank's
traditional objectives of inflation and output stabilization. We consider both the
case where the central bank lacks a commitment technology and the case of full
commitment. We show that for both cases, optimal policy rules yield rational
expectations equilibria that are E-stable for a wide range of empirically plausible
parameter values. These findings stand in contrast to Evans and Honkapohja's
(2003ab, 2006) findings for optimal monetary policy rules in environments where
interest rate stabilization is not a central bank objective.
We examine the role of central bank transparency when the
private sector is modeled as adaptive learners. In our model, transparent policies
enable the private sector to adopt correctly specified models of inflation and
output while intransparent policies do not. In the former case, the private sector
learns the rational expectations equilibrium while in the latter case it learns a
restricted perceptions equilibrium. These possibilities arise regardless of whether
the central bank operates under commitment or discretion. We provide conditions under
which the policy loss from transparency is lower (higher) than under intransparency,
allowing us to assess the value of transparency when agents are learning.
We report the results of an experiment in which subjects
play games against changing opponents. In one treatment, "senders" send
"receivers" messages indicating intended actions in that round, and receivers
observe senders' previous-round actions (when matched with another receiver).
In another treatment, the receiver additionally observes the sender's previous-round
message to the previous opponent, enabling him to determine whether the sender had
lied. We find that allowing multiple signals leads to better outcomes when signals
are aligned (all pointing to the same action), but worse outcomes when
signals are crossed. Also, senders' signals tend to be truthful, though the
degree of truthfulness depends on the game and treatment, and receivers' behavior
combines elements of pay-off maximization and reciprocity.
The paper analyzes dollarization in the sense of asset
substitution, where a foreign currency competes with local assets, especially
domestic capital, as a store of value, the impact of dollarization on
capital accumulation and output, and why economies remain dollarized long
after a successful inflation stabilization. We relate this dollarization
hysteresis to a financial intermediation failure that happens during high
inflation. We show that in dollarized countries, inflation stabilization
policies may not have any effect on domestic capital accumulation, thus
preventing such policies from stimulating growth, i.e., dollarized
economies are vulnerable to "dollarization traps."
We use two different nonparametric methods to determine whether there were
multiple regimes in U.S. monetary policy over the period 1955--2003. We model
monetary policy using two different versions of Taylor's rule for the
nominal interest rate target. By contrast with parametric tests for regime
changes, the nonparametric methods we use allow the data to determine
the dimensions on which to split the sample for purposes of estimating the
coefficients of the Taylor rule. We find evidence for a few structural
breaks and consistent agreement between our two nonparametric methods on the
dating of those breaks.
This chapter examines the relationship between agent-based
modeling and economic decision-making experiments with paid human subjects.
Both approaches exploit controlled "laboratory" conditions as a means
of isolating the sources of aggregate phenomena. Research findings from
laboratory studies of human subject behavior have inspired studies using
artificial agents in "computational laboratories" and vice versa. In certain
cases, both methods have been used to examine the same phenomenon. The
focus of this chapter is on the use of agent-based models to explain experimental
findings. We point out synergies between the two methodologies that have
been exploited as well as promising new possibilities.
We examine whether a simple agent--based model can generate
asset price bubbles and crashes of the type observed in a series of laboratory
asset market experiments beginning with the work of Smith, Suchanek and
Williams (1988). We follow the methodology of Gode and Sunder (1993, 1997)
and examine the outcomes that obtain when populations of zero--intelligence
(ZI) budget constrained, artificial agents are placed in the various laboratory
market environments that have given rise to price bubbles. We have to
put more structure on the behavior of the ZI-agents in order to address
features of the laboratory asset bubble environment. We show that our
model of "near--zero--intelligence" traders, operating in the
same double auction environments used in several different laboratory
studies, generates asset price bubbles and crashes comparable to those
observed in laboratory experiments and can also match other, more subtle
features of the experimental data.
We show that extrinsic or non-fundamental uncertainty
influences markets in a controlled environment. This work provides the
first direct evidence of sunspot equilibria. These equilibria require
a common understanding of the semantics of the sunspot variable, and they
appear to be sensitive to the flow of information. Sunspots always occur
in a closed-book call market, but they happen only occasionally in a double
auction, where infra-marginal bids and offers are observable.
A recent literature on the economics of conflict has
provided conditions under which an "anarchic" outcome may come
to serve as an equilibrium for an economy, as well as conditions under
which a "dictator" or "government agent" is empowered
to make collective action choices that enable the economy to achieve a
Pareto superior equilibrium. This paper reports results from a laboratory
experiment designed to test the predictions of this theory. We find that
in the absence of any government, groups of subjects choose forecasts
and actions that lie within a neighborhood of the predicted anarchic equilibrium,
where some players choose to be producers, while others choose to be predators.
The introduction of the government agent, charged with maximizing the
consumption of producers, enables the subject groups to achieve nearly
perfect coordination on a Pareto superior Nash equilibrium, where the
fraction of time devoted to defense is high, but predation is eliminated.
Previous data from experiments on market entry games,
N-player games where each player faces a choice between entering a market
and staying out, appear inconsistent with either mixed or pure Nash equilibria.
Here we show that, in this class of game, learning theory predicts sorting,
that is, in the long run, agents play a pure strategy equilibrium with
some agents permanently in the market, and some permanently out. We conduct
experiments with a larger number of repetitions than in previous work
in order to test this prediction. We find that when subjects are given
minimal information, only after close to 100 periods do subjects begin
to approach equilibrium. In contrast, with full information, subjects
learn to play a pure strategy equilibrium relatively quickly. However,
the information which permits rapid convergence, revelation of the individual
play of all opponents, is not predicted to have any effect by existing
models of learning.
This paper studies adaptive behavior in a simple coordination
game that Van Huyck, Cook and Battalio (1994) have investigated in a controlled
laboratory setting with human subjects. We consider how populations of
artificially intelligent agents play the same game. The computational
approach that we adopt provides us with much greater flexibility in the
experimental design than is possible with experiments involving human
subjects. We use genetic programming techniques developed by Koza (1992,
1994) to model how players might learn over time. These genetic programming
techniques have certain advantages over other artificial intelligence
techniques that have been applied to economic models, for example, genetic
algorithms. We find that the pattern of behavior generated by our population
of artificially intelligent players is remarkably similar to that followed
by human subjects who played the same game. In particular, we find that
a steady state that is theoretically unstable under a myopic best-response
learning dynamic turns out to be stable under our genetic-programming-based
learning system, in accordance with Van Huyck et al.'s finding using human
subjects. We conclude that genetic programming techniques may serve as
a plausible and inexpensive selection criterion in environments with multiple
The paper presents a simulation of the dynamics of impersonal
trust. It shows how a "trust and reciprocate" norm can emerge
and stabilize in populations of conditional cooperators. The norm, or
behavioral regularity, is not to be identified with a single strategy.
It is instead supported by several conditional strategies that vary in
the frequency and intensity of sanctions.
Since Griliches (1969), researchers have been intrigued
by the idea that physical capital and skilled labor are relatively more
complementary than physical capital and unskilled labor. In this paper
we consider the cross-country evidence for capital-skill complementarity
using a time-series, cross-section panel of 73 developed and less developed
countries over a 25 year period. We focus on three empirical issues. First,
what is the best specification of the aggregate production technology
to address the capital-skill complementarity hypothesis. Second, how should
we measure skilled labor? Finally, is there any cross-country evidence
in support of the capital-skill complementarity hypothesis? Our main finding
is that we find some support for the capital-skill complementarity hypothesis
in our macro panel dataset.
This is a comment on the paper "Adaptive Learning
and Monetary Policy Design" by George W. Evans and Seppo Honkapohja
that was prepared for the FRB-Cleveland/JMCB conference, "Recent
Developments in Monetary Macroeconomics" hosted by the Federal Reserve
Bank of Cleveland in November 2002.
This paper reports results from an experiment that examines
whether an intrinsically worthless, `token' object serves as a medium
of exchange in a laboratory implementation of Kiyotaki and Wright's search
model of money. The theory admits Nash equilibria in which the token object
is or is not used as a medium of exchange. We find that subjects nearly
always offer to trade for the token object when such a trade lowers their
storage costs. However, subjects frequently refuse to offer to trade the
token object for more costly-to-store goods when the theory predicts they
should make such trades. View
the raw data from this experiment.
This paper reports results from an experiment designed
to compare cheap talk and observation of past actions. We consider three
games and explain why cheap talk or observation is likely to be more effective
for achieving good outcomes in each game. We find that both cheap talk
and observation make cooperation and coordination more likely and increase
payoffs, relative to our control treatment. The relative success of cheap
talk versus observation depends on the game, in accordance with our predictions.
We also find that players' signals are informative, and that signal receivers
condition their actions on the signal they receive.
We propose the use of a new technique--symbolic
regression--as a method for inferring the strategies that are being
played by subjects in economic decision making experiments. We begin by
describing symbolic regression and our implementation of this technique
using genetic programming. We provide a brief overview of how our algorithm
works and how it can be used to uncover simple data generating functions
that have the flavor of strategic rules. We then apply symbolic regression
using genetic programming to experimental data from the ultimatum game.
We discuss and analyze the strategies that we uncover using symbolic regression
and we conclude by arguing that symbolic regression techniques should
at least complement standard regression analyses of experimental data.
We introduce adaptive learning behavior into a general
equilibrium lifecycle economy with capital accumulation. Agents form forecasts
of the rate of return to capital assets using least squares autoregressions
on past data. We show that, in contrast to the perfect foresight dynamics,
the dynamical system under learning possesses equilibria that are characterized
by persistent excess volatility in returns to capital. We explore a quantitative
case for these learning equilibria. We use an evolutionary search algorithm
to calibrate a version of the system under learning and show that this
system can generate data that matches some features of the time series
data for U.S. stock returns and per capita consumption. We argue that
this finding provides support for the hypothesis that the observed excess
volatility of asset returns can be explained by changes in investor expectations
against a background of relatively small changes in fundamental factors.
This paper suggests a new approach to solving the one-sector
stochastic growth model using the method of parameterized expectations.
The approach is to employ a "global" genetic algorithm search
for the parameters of the expectation function followed by a "local"
gradient-descent optimization method to ensure fine-tuning of the approximated
solution. We use this search procedure in combination with either polynomial
or neural network specifications for the expectation function. We find
that our approach yields highly accurate solutions in the case where an
exact analytic solution exists as well as in cases where no closed-form
solution exists. Our results further suggest that neural network specifications
for the expectation function may be preferred to the more commonly used
This paper employs an artificial agent-based, computational
approach to understanding and designing laboratory environments in which
to study and test Kiyotaki and Wright's (1989) search model of money.
The behavioral rules of the artificial agents are modeled on the basis
of prior evidence from human subject experiments. Simulations of the artificial
agent-based model are conducted in two new versions of the Kiyotaki-Wright
environment and yield some testable predictions. These predictions are
examined using data from new human subject experiments. The results are
encouraging and suggest that artificial agent-based modeling may be a
useful device for both understanding and designing human subject experiments.
Many growth models assume that aggregate output is generated
by a Cobb-Douglas production function. In this article we question the
empirical relevance of this specification. We use a panel of 82 countries
over a 28-year period to estimate a general constant-elasticity-of-substitution
(CES) production function specification. We find that for the entire sample
of countries we can reject the Cobb-Douglas specification. When we divide
our sample of countries up into several subsamples, we find that physical
capital and human capital adjusted labor are more substitutable in the
richest group of countries and are less substitutable in the poorest group
of countries than would be implied by a Cobb-Douglas specification.
This paper presents experimental results from an analysis
of two similar games, the repeated ultimatum bargaining game and the repeated
best-shot game. The experiments examine how the amount and content of
information given to players affects the evolution of play in the two
games. In one experimental treatment, subjects in both games observe not
only their own actions and payoffs, but also those of one randomly chosen
pair of players in the just-completed round of play. In the other treatment,
subjects in both games observe only their own actions and payoffs. We
present evidence suggesting that observation of other players' actions
and payoffs affects the evolution of play in both games relative to the
case of no observation. Moreover, the effect of observation on learning
is different in the two games. In the ultimatum game, players who observe
the actions and payoffs of others tend to deviate further from the subgame
perfect equilibrium strategy over time than players who observe only their
own actions and payoffs. In contrast, in the best-shot game, players who
observe the actions and payoffs of others tend to play closer to the subgame
perfect equilibrium strategy over time than players who observe only their
own actions and payoffs. We conclude that providing players with additional
information need not hasten the rate at which they learn to play subgame
perfect equilibrium strategies. Rather, our findings support the conclusion
of Prasnikar and Roth (1992) that the incentives players face off the
equilibrium path strongly influence how behavior evolves over time.
Kiyotaki and Wright (1989) developed a simple dynamic
model of an exchange economy in which one or more commodities are used
as media of exchange. In this paper, we report findings from an experiment
that implements the Kiyotaki-Wright model. We consider whether the equilibrium
predictions of the Kiyotaki-Wright model are robust to the dynamics created
by out-of-equilibrium play. In particular, we examine whether individuals
placed in the Kiyotaki-Wright environment learn over time to adopt the
same commodities as media of exchange as the model implies will be used
in equilibrium. We find that subjects have a strong tendency to play "fundamental"
rather than "speculative strategies even in environments where speculative
strategies would lead to higher payoffs. We examine some possible motivations
for subjects' trading behavior and we find that subjects are mainly motivated
by their own past payoff experience as opposed to being motivated by the
marketability concerns that the theory suggests are important.
We study a general equilibrium system where agents have
heterogeneous beliefs concerning realizations of possible outcomes. The
actual outcomes feed back into beliefs thus creating a complicated nonlinear
system. Beliefs are updated via a genetic algorithm learning process which
we interpret as representing communication among agents in the economy.
We are able to illustrate a simple principle: genetic algorithms can be
implemented so that they represent pure learning effects (i.e. beliefs
updating based on realizations of endogenous variables in an environment
with heterogeneous beliefs). Agents optimally solve their maximization
problem at each date given their beliefs at each date. We report the results
of a set of computational experiments in which we find that our population
of artificial adaptive agents is usually able to coordinate their beliefs
so as to achieve the Pareto superior rational expectations equilibrium
of the model.
Empirical tests of macroeconomic and monetary theories
are typically conducted using non-experimental field data provided by
government agencies. Modern theories, however, have increasingly imposed
restrictions on individual behavior that are not embodied in any available
field data. An alternative method for testing such theories is to conduct
controlled laboratory experiments with paid human subjects. This article
provides a critical survey of recent papers that have used laboratory
methods to test modern monetary-theory predictions. While the survey focuses
on the results obtained from these laboratory studies, I also provide
some justification for the experimental methodology and discuss experimental
We study a general equilibrium model where the multiplicity
of stationary periodic perfect foresight equilibria is pervasive. We investigate
the extent to which agents can learn to coordinate on stationary perfect
foresight cycles. The example economy, taken from J.M. Grandmont (1985),
is a two period, endowment overlapping generations model with fiat money,
where consumption in the first and second periods of life are not necessarily
gross substitutes. Depending on the value of a preference parameter, the
limiting backward (direction of time reversed) perfect foresight dynamics
are characterized by steady state, periodic or chaotic trajectories for
real money balances. We relax the perfect foresight assumption and examine
how a population of artificial, heterogeneous adaptive agents might learn
in such an environment. These artificial agents optimize given their forecast
of future prices, and they use forecast rules that are consistent with
steady state or periodic trajectories for prices. The agents' forecast
rules are updated by a genetic algorithm. We find that the population
of artificial adaptive agents is able to eventually coordinate on steady
state and low-order cycles, but not on the higher-order periodic equilibria
that exist under the perfect foresight assumption.
We study adaptive learning behavior in a sequence of
n-period endowment overlapping generations economies, where n refers to
the number of periods in agents' lifetimes. Agents initially have heterogeneous
beliefs and seek to form multi-step ahead consumption plans based on forecasts
of future prices. Agents learn in every period by forming new consumption
plans and by emulating the consumption plans of other agents. Computational
experiments with artificial adaptive agents are conducted. In these experiments,
the heterogeneous population of artificial agents nearly always learns
over time to form consumption plans that are consistent with perfect foresight
knowledge of future prices. The model of learning and emulation that we
develop is also used to study transition dynamics from one stationary
perfect foresight equilibrium to another.
We report and compare results from several different
versions of an experimental interactive guessing game first studied by
Nagel (1995), which we refer to as the 'beauty contest' game following
Keynes (1936). In these games, groups of subjects are repeatedly asked
to simultaneously guess a real number in the interval [0,100] that they
believe will be closest to 1/2 times either the median, mean, or maximum
of all numbers chosen. In all three versions of the beauty contest game,
the unique Nash equilibrium is for all subjects to announce zero. We find
that convergence to this equilibrium is fastest in the 1/2-median game
and slowest in the 1/2-maximum game and we offer an explanation for the
findings. We also use our experimental data to test a simple model of
adaptive learning behavior.
This paper develops the first model in which, consistent
with the empirical evidence, the transition from stagnation to economic
growth is a very long endogenous process. The model has one steady state
with a low and stagnant level of income per capita and another steady
state with a high level of income per capita. Both of these steady states
are locally stable under the perfect foresight assumption. We relax the
perfect foresight assumption and introduce learning into this environment.
Learning acts as an equilibrium selection criterion and provides an interesting
transition dynamic between steady states. We find that for sufficiently
low initial values of human capital--values that would tend to characterize
pre-industrial countries--the system under learning spends a long period
of time (an epoch ) in the neighborhood of the low income steady state
before finally transitioning to a neighborhood of the high income steady
state. We argue that this kind of transition dynamic provides a good characterization
of the economic growth and development patterns that have been observed
This paper examines disequilibrium adaptive learning
behavior in an overlapping generations model with fiat money. Agents are
concerned with forming correct forecasts of future inflation. If they
use a disequilibrium, adaptive forecast rule, it is shown that they will
eventually learn to believe in a nonstationary, nonunique perfect foresight
equilibrium. The nonstationary equilibrium isolated by the adaptive learning
process can be used to explain the sluggish adjustment of the price level
to monetary disturbances as documented in the work of C.A. Sims (1989).