Bayesian Games

So far, the number of agents, the actions available to each agent, and the payoffs have all been assumed to be common knowledge among the agents. Note that this is true even of imperfect-information games; the actual moves of agents are not common knowledge, but the game itself is. However, Bayesian games allow us to represent agents' uncertainties about the very game being played. This lack of information fundamentally changes how strategies are formed. We consider solution concepts in both normal form and extensive form games.

Elements

1. 3.5.aBayes–Nash Equilibrium

   The ability to compute and select best responses with respect to beliefs about the other agents' strategies, and can update these beliefs based on observed strategies.

2. 3.5.bSubgame–Perfect Bayes–Nash Equilibrium soon

   The ability to compute and select a strategy that satisfies the following: (1) (Bayes–Nash Equilibrium) The strategy maximizes their expected utility, given their beliefs about the other agents' types and strategies, and given the strategies of the other agents. (2) (Subgame Perfection) The strategy constitutes a Bayes–Nash Equilibrium not just for the whole game, but for every subgame of the game. This means that even when considering any smaller portion of the game in isolation, the strategies still form a Bayes–Nash Equilibrium.