Page 25 realized assigns to each state the probability if and the probability zero otherwise (i.e. the probability of ω conditional on . As an example, if τ i ( ω ) = ω for all then player i has full information about the state of nature. Alternatively, if and for each player i the probability measure p i is a product measure on Ω and τ i ( ω ) = ω i then the players' signals are independent and player i does not learn from his signal anything about the other players' information. As in a strategic game, each player cares about the action profile; in addition he may care about the state of nature. Now, even if he knows the action taken by every other player in every state of nature, a player may be uncertain about the pair ( a , ω ) that will be realized given any action that he takes, since he has imperfect information about the state of nature. Therefore we include in the model a profile of preference relations over lotteries on A × Ω (where, as before, ). To summarize, we make the following definition.
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This note was uploaded on 09/10/2011 for the course DEFR 090234589 taught by Professor Vinh during the Spring '10 term at Aarhus Universitet, Aarhus.