DECENTRALIZED COALITION-PROOF PURE NASH EQUILIBRIUM: EXISTENCE AND UNIQUENESSE

Yohan Pelosse ()
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Yohan Pelosse: Humanities and Social Sciences, Swansea University

No 2024-09, Working Papers from Swansea University, School of Management

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).

JEL-codes: C72 C92 D83 (search for similar items in EconPapers)
Pages: 9 pages
Date: 2024-12-13
New Economics Papers: this item is included in nep-gth and nep-mic
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