Characterizing Pure-strategy Equilibria in Large Games

In this paper, we divide the players of a large game into countable different groups and assume that each player’s payoff depends on her own action and the distribution of actions in each of the subgroups. Focusing on the interaction between Nash equilibria and the best response correspondence of the players, we characterize the pure-strategy equilibria in three settings of such large games, namely large games with countable actions, large games with countable homogeneous groups of players and large games with an atomless Loeb agent space. Furthermore, we also present a counterexample showing that a similar characterization result does not hold for large games under a more general setting.