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The Possibility of Impossible Stairways and Greener Grass

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  • Voorneveld, M.

    (Tilburg University, Center for Economic Research)

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 coordina- tion 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.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-62.

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Date of creation: 2007
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Handle: RePEc:dgr:kubcen:200762

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Web page: http://center.uvt.nl

Related research

Keywords: coordination games; dominant strategies; payoff-dominance; nonexistence of equi- librium; tail events;

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  1. Basu Kaushik, 1994. "Group Rationality, Utilitarianism, and Escher's Waterfall," Games and Economic Behavior, Elsevier, vol. 7(1), pages 1-9, July.
  2. Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Milchtaich, Igal, 2004. "Random-player games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 353-388, May.
  4. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  5. Gary S. Becker & Kevin M. Murphy, 1986. "A Theory of Rational Addiction," University of Chicago - George G. Stigler Center for Study of Economy and State 41, Chicago - Center for Study of Economy and State.
  6. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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