We examine the connection between discrete-time models of financial markets and the celebrated Black--Scholes--Merton (BSM) continuous-time model in which ''markets are complete." Suppose that (a) the probability law of a sequence of discrete-time models converges to the law of the BSM model and...

We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback-Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman (1990)'s...

We use an evolutionary model to determine which misperceptions can persist. Every period, a new generation of agents use their subjective models and the data generated by the previous generation to update their beliefs, and models that induce better actions become more prevalent. An equilibrium...

We de.ne and analyze a strategic topology on types in the Harsanyi-Mertens-Zamir universal type space, where two types are close if their strategic behavior is similar in all strategic situations. For a .xed game and action de.ne the distance be-tween a pair of types as the diþerence between...

We study learning and information acquisition by a Bayesian agent whose prior belief is misspecified in the sense that it assigns probability 0 to the true state of the world. At each instant, the agent takes an action and observes the corresponding payoff, which is the sum of a fixed but...

We study models of learning in games where agents with limited memory use social information to decide when and how to change their play. When agents only observe the aggregate distribution of payoffs and only recall information from the last period, aggregate play comes close to Nash...

We examine games played by a single large player and a large number of opponents who are small, but not anonymous. If the play of the small players is observed with noise, and if the number of actions the large player controls is bounded independently of the number of small players, then as the...

We define and analyze a "strategic topology'' on types in the Harsanyi-Mertens-Zamir universal type space, where two types are close if their strategic behavior is similar in all strategic situations. For a fixed game and action define the distance between a pair of types as the difference...