Uncertainty About Payoffs: Bayesian Games

Abstract

All of the game forms discussed so far assumed that all players know what game is being played. Specifically, the number of players, the actions available to each player, and the payoff associated with each action vector, have all been assumed to be common knowledge among the players. Note that this is true even of imperfect-information games; the actual moves of agents are not common knowledge, but the game itself is. In contrast, Bayesian games, or games of incomplete information, allow us to represent players’ uncertainties about the very game being played.¹ This uncertainty is represented as a probability distribution over a set of possible games. We make two assumptions.