In this talk, Reny will present his paper in which he and co-author Roger Myerson extend Kreps and Wilson's concept of sequential equilibrium to games where the sets of actions that players can choose and the sets of signals that players may observe are infinite. A strategy profile is a conditional epsilon-equilibrium if, for any player and for any of his positive probability signal events outside a uniformly unlikely set, the player's conditional expected utility would be within epsilon of the best that the player could achieve by deviating. Perfect conditional epsilon-equilibria are defined by testing conditional epsilon-rationality also under nets of small perturbations of the players' strategies and of nature's probability function that can make any finite collection of signals have positive probability. Every perfect conditional epsilon-equilibrium strategy profile is a subgame perfect epsilon-equilibrium and admits a finitely consistent conditional belief system that makes it sequentially epsilon-rational. Nature's perturbations can produce equilibria that seem unintuitive and so we consider two ways to limit the effects of those perturbations, using topologies on nature's states and on players' actions.