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Supermodular social games


  • Ludovic Renou

    (University of Adelaide, School of Economics)


A social game is a generalization of a strategic-form game, in which not only the payoff of each player depends upon the strategies chosen by their opponents, but also their set of admissible strategies. Debreu (1952) proves the existence of a Nash equilibrium in social games with continuous strategy spaces. Recently, Polowczuk and Radzik (2004) have proposed a discrete counterpart of Debreu's theorem for two-person social games satisfying some ``convexity properties'. In this note, we define the class of supermodular social games and give an existence theorem for this class of games.

Suggested Citation

  • Ludovic Renou, 2005. "Supermodular social games," Game Theory and Information 0502002, EconWPA.
  • Handle: RePEc:wpa:wuwpga:0502002
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    References listed on IDEAS

    1. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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    Strategic-form games; social games; supermodularity; Nash equilibrium; existence.;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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