Reasoning about knowledge
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The Bayesian approach to non-cooperative game theory, pioneered by Bernheim [6] and Pearce [15], views games as Bayesian decision problems in the sense of Savage, where the uncertainty faced by the players is the strategy choices of their opponents. Accordingly it is assumed that each player has a prior over the strategy sets of the other players. But each player is also uncertain about the others' priors, and so must have a prior over the set of priors, and so on. So we need some representation of this infinite hierarchy of beliefs for the players, and this has been provided by the work of Mertens and Zamir [14]. In their construction of a 'universal type space', each state of the world describes not only the strategy choices but also the (first-order) beliefs of the players. These first- order beliefs over the space in turn generate second-order beliefs, that is, beliefs about others' first-order beliefs, and so on.