Mark Voorneveld: Dept. of Economics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, SE-113 83 Stockholm, Sweden
Abstract: In classical game theory, players have finitely many actions and evaluate outcomes of mixed strategies using a von Neumann-Morgenstern utility function. Allowing a larger, but countable, player set introduces a host of phenomena that are impossible in finite games. Firstly, in coordination games, all players have the same preferences: switching to a weakly dominant action makes everyone at least as well off as before. Nevertheless, there are coordination games where the best outcome occurs if everyone chooses a weakly dominated action, while the worst outcome occurs if everyone chooses the weakly dominant action. Secondly, the location of payoff-dominant equilibria behaves capriciously: two coordination games that look so much alike that even the consequences of unilateral deviations are the same may nevertheless have disjoint sets of payoff-dominant equilibria. Thirdly, a large class of games has no (pure or mixed) Nash equilibria. Following the proverb ``the grass is always greener on the other side of the hedge'', greener-grass games model constant discontent: in one part of the strategy space, players would rather switch to its complement. Once there, they'd rather switch back.
15 pages, August 28, 2007
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