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Beyond dominance and Nash: Ranking equilibria by critical mass

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  • Kalai, Adam Tauman
  • Kalai, Ehud

Abstract

Strategic interactions pose central issues that are not adequately explained by the traditional concepts of dominant strategy equilibrium (DSE), Nash equilibrium (NE), and their refinements. A comprehensive analysis of equilibrium concepts within the von Neumann-Nash framework of n-person optimization reveals a decreasing hierarchy of n nested concepts ranging from DSE to NE. These concepts are defined by the “critical mass,” the number of players needed to adopt and sustain the play of a strategy profile as an equilibrium. In games with n>2 players, the n−2 intermediate concepts explain strategic issues in large social systems, implementation, decentralization, as well as replication studied in economics, operations management, and political games.

Suggested Citation

  • Kalai, Adam Tauman & Kalai, Ehud, 2024. "Beyond dominance and Nash: Ranking equilibria by critical mass," Games and Economic Behavior, Elsevier, vol. 144(C), pages 378-394.
    • Handle: RePEc:eee:gamebe:v:144:y:2024:i:c:p:378-394
    DOI: 10.1016/j.geb.2024.01.011
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