A nonatomic game involving incomplete information and general ambiguity attitudes

Abstract

We consider a nonatomic game involving incomplete information. On top of a player’s own action and the joint distribution of other players’ traits and actions, also influencing the player’s return is a state of the world that incorporates uncertain factors external to all players. Non-exact knowledge about the latter is embedded in a player’s signal. When other players adopt strategies that amount to signal-based action distributions, a given player’s action would be guided by her own preference on the vector made up of the distributions on returns that she anticipates to encounter under all potential states allowed by her signal. There can be two equilibrium notions; namely, the action- and distribution-based ones that depend on whether a player controls individual actions or merely their distributions. Besides the existence of equilibria, we also study relationships between the two equilibrium notions for various special cases. Furthermore, the nonatomic game is shown to approximate its finite counterparts.