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Decentralized Coalition-Proof Pure Nash Equilibrium: Existence And Uniquenesse

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  • Yohan Pelosse

    (Humanities and Social Sciences, Swansea University)

Abstract

This paper explores some sufficient conditions for the existence and uniqueness of a pure-strategy Nash equilibrium (PSNE) in a class of finite dimensional convex games which do not admit a global strictly concave potential function a la Neyman (1997) and fails the global ’diagonal strict concavity’ conditions of Rosen (1965). We show that applying a ’mixture’ of these well-known regularity conditions inside and across the ’local games’ played within and between some (disjoint) subsets of players (’coalitions) guarantee the existence and uniqueness of a PSNEwhen the game is linearly aggregative inside the coalitions. This PSNE is also the unique correlated equilibriumof the ’partitioned’ strategic game played across the coalitions. When the partitioned game is quasi-aggregative and exhibits ’strategic complementarities’, we obtain the existence of a unique PSNE which has the additional property to be coalition-proof across the coalitions of players. This result suggests the existence of a rich class of games which may admit these ’decentralized coalition-proof ’Nash equilibria as a weakened version of the coalition-proof Nash equilibriumof Bernheim et al. (1987).

Suggested Citation

  • Yohan Pelosse, 2024. "Decentralized Coalition-Proof Pure Nash Equilibrium: Existence And Uniquenesse," Working Papers 2024-09, Swansea University, School of Management.
    • Handle: RePEc:swn:wpaper:2024-09
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    File URL: https://rahwebdav.swan.ac.uk/repec/pdf/WP2024-09.pdf
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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