Symmetric versus asymmetric equilibria in symmetric supermodular games

Abstract

This paper investigates the general properties of symmetric n-player supermodular games with complete-lattice action spaces. In particular, we examine the extent to which all pure strategy Nash equilibria tend to be symmetric for the general case of multi-dimensional strategy spaces. As asymmetric equilibria are possible even for strictly supermodular games, we investigate whether some symmetric equilibrium would always Pareto dominate all asymmetric equilibria. While this need not hold in general, we identify different sufficient conditions, each of which guarantees that such dominance holds: 2-player games with scalar action sets, uni-signed externalities, identical interests, and superjoin payoffs. Various illustrative examples are provided. Finally, some economic applications are discussed.

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Correspondence to Rabah Amir.

Additional information

The first version of this paper was completed while M. Jakubczyk and M. Knauff were visiting junior scholars at CORE, Louvain-la-Neuve, Belgium, financed through the Marie-Curie Early Stage Training program of the European Union (under contract no HPMT-CT-2001-00327), which is hereby gratefully acknowledged. The presentation of the revised version of this paper has benefitted from detailed and careful suggestions by two anonymous referees and William Thomson (as editor) of this Journal.

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Amir, R., Jakubczyk, M. & Knauff, M. Symmetric versus asymmetric equilibria in symmetric supermodular games. Int J Game Theory 37, 307–320 (2008). https://doi.org/10.1007/s00182-008-0118-5

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Keywords

  • Strategic complementarity
  • Endogenous heterogeneity
  • Symmetry breaking
  • Doubly symmetric games
  • Superjoin payoffs

JEL Classification

  • C72
  • L13