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Unformatted text preview: Nau: Game Theory 1 Updated 12/12/11 CMSC 498T, Game Theory 9. Other things Dana Nau University of Maryland Nau: Game Theory 2 Updated 12/12/11 The Price of Anarchy In the Prisoners dilemma, recall that (C,C) is the action profile that provides the best outcome for everyone If we assume each payer acts to maximize his/her utility without regard to the other, we get (D,D) By choosing (C,C), each player could have gotten 3 times as much Lets generalize best outcome for everyone C D C 3, 3 0, 5 D 5, 0 1, 1 C D C 3, 3 0, 5 D 5, 0 1, 1 Nau: Game Theory 3 Updated 12/12/11 The Price of Anarchy Social welfare function : a function w ( s ) that measures the players welfare, given a strategy profile s , e.g., Utilitarian function: w ( s ) = average expected utility Egalitarian function: w ( s ) = minimum expected utility Social optimum : benevolent dictator chooses s * that optimizes w s * = arg max s w ( s ) Anarchy : no dictator; every player selfishly tries to optimize his/her own expected utility, disregarding the welfare of the other players...
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 Fall '11
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