A Bayesian game gives players private information about their types, a probability model for that information, and strategies depending on the player's own type. A private-value auction with uncertain other valuations is a Bayesian game.
A Bayesian Nash equilibrium consists of type-dependent strategies such that every type maximizes its conditional expected payoff given the other players' strategies and the type distribution. It is a Nash equilibrium in the strategic description whose actions are whole contingent strategy functions. Auction incentive comparisons can test a deviation by imitating another type's equilibrium bid.
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A Bayesian game is a type of game in game theory that incorporates incomplete information about certain aspects of the game, particularly the preferences or types of the players. In a Bayesian game, players have private information that is not known to the other players, and this information can affect their strategies and payoffs. Key features of Bayesian games include: 1. **Types**: Each player has a type, typically representing their preferences or payoffs.