gametheory4 - Bayesian Games How do we incorporate into...

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Bayesian Games How do we incorporate into game theory the uncer- tainty players face about the characteristics of other players (their payo®s, what they know about our pay- o®s, etc.)? We can model incomplete information by letting na- ture select the players' characteristics. This frame- work allows a player to know her own \type" but not the other players' types. The payo® function is now ¼ i ( s i ;s ¡ i i ), where μ i is player i 's type. The joint probability distribution, which allows correlation, is given by F ( μ 1 ; :::; μ n ). It is assumed that this distribution is common knowl- edge ,eventhoughtherea l izat iono fthe μ 's is not. Afu l lspe c ca t fp la y e r i 's strategy must take into account that di®erent types will make di®erent choices. A strategy is a decision rule, s i ( μ i ).
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To solve the game, we think of the players planning their decision rules at a stage before they observe their types. A Bayesian Nash equilibrium is a N.E. in the game of choosing decision rules.
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gametheory4 - Bayesian Games How do we incorporate into...

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