Random-player games

This paper introduces general games with incomplete information in which the number, as well as the types or identities, of the participating players are determined by chance and might not be known to the players when they make their choices of actions. In these games, the selection of the number and types of players is modeled as a finite point process on a suitable type space. Definitions of pure-strategy, mixed-strategy, and correlated equilibria in random-player games are given, extending the corresponding ones for finite games, Bayesian games, and games with population uncertainty, which may all be considered as special cases of random-player games.