Macroeconomic Dynamics, 2, 1998, 141–155. Printed in the United States of America. ARTICLES LEARNING IN BAYESIAN GAMES BY BOUNDED RATIONAL PLAYERS II: NONMYOPIA KONSTANTINOS SERFES AND NICHOLAS C. YANNELIS University of Illinois at Urbana–Champaign We generalize results of earlier work on learning in Bayesian games by allowing players to make decisions in a nonmyopic fashion. In particular, we address the issue of nonmyopic Bayesian learning with an arbitrary number of bounded rational players, i.e., players who choose approximate best-response strategies for the entire horizon (rather than the current period). We show that, by repetition, nonmyopic bounded rational players can reach a limit full-information nonmyopic Bayesian Nash equilibrium (NBNE) strategy. The converse is also proved: Given a limit full-information NBNE strategy, one can find a sequence of nonmyopic bounded rational plays that converges to that strategy. Keywords: Bayesian Game, Nash Equilibrium, Nonmyopia, Bayesian Learning, Bounded Rationality 1. INTRODUCTION The issue of myopic Bayesian learning by a finite number of bounded rational players has been addressed by Koutsougeras and Yannelis (1994). Recently, Kim and Yannelis (1997b) extended that work by allowing the number of bounded rational players to be arbitrary, i.e., any finite or infinite set or a continuum. Here, we drop the myopia assumption and allow the players to be nonmyopic i.e., to make decisions by taking into account the future. In particular, the description of the model is as follows: Let (˜, F, μ) be a probability measure space interpreted as the set of states of the world. Let T denote the time horizon and A the set of players.A repeated Bayesian game (or a repeated game with differential information) is a sequence of games {G t : t ∈ T } such that for each t , G t ={( F t α , X t α , u α , q α ) : α ∈ A}, where 1. F t α denotes the private information of agent α in period t , 2. X t α (ω) is the set of actions available to agent α in period t when the state is ω, 3. u α (ω, ·) : 5 α∈A X t α (ω) → R is the utility function of agent α, 4. q α is the prior of agent α [q α is a density function, or Radon-Nikodym derivative, such that, R ω∈˜ q α (ω) d μ(ω) = 1]. Address correspondence to: Nicholas C. Yannelis, Department of Economics, University of Illinois at Urbana– Champaign, Champaign IL 61820, USA; e-mail: nyanneli@uiuc.edu. c  1998 Cambridge University Press 1365-1005/98 $9.50 141