This paper introduces games of incomplete information in which the number, as well as the identity, of the participating players is determined by chance. The participation of certian players may not be independent of the participation of others, and hence the very fact that a particular player was chosen to play may give that player a clue as to the number and the identity of the other players chosen. However, players have to choose their strategies before the identity of the other players is fully revealed to them and thus, effectively, before they know whether or not they will take part in the game. Pure-strategy, mix-strategy, and correlated equilibria of random-player games are defined. These definitions extend the corresponding definitions for finite games, Bayesian games with consistent beliefs, and Poisson games-all of which can be seen as special cases of random-player games. Sufficient conditions for the existence of pure and mixed-strategy equilibria are given.