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Supermodular Social Games

By Ludovic Renou

Abstract

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.strategic-form games, social games, supermodularity, Nash equilibrium, existence

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  1. A social equilibrium existence theorem,
  2. (2004). Equilibria in constrained bimatrix games,
  3. (1979). Equilibrium Points in Nonzero-Sum n-Person Submodular Games,
  4. (1954). Existence of an equilibrium for a competitive economy,
  5. (1978). Minimizing a Submodular Function on a Lattice,
  6. (1998). Supermodularity and Complementarity,

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