STRONG NASH IMPLEMENTATION AND ECONOMIC APPLICATIONS

MISE EN ŒUVRE SELON L’EQUILIBRE DE NASH FORT ET APPLICATIONS ECONOMIQUES

Mohamed Bouchta (), Ahmed Doghmi () and Abderrahmane Ziad
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Mohamed Bouchta: National Institute of Statistics and Applied Economics,Madinat Al Irfane, Rabat Institutes, 10100 Rabat, Morocco
Ahmed Doghmi: National Institute of Statistics and Applied Economics,Madinat Al Irfane, Rabat Institutes, 10100 Rabat, Morocco

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Abstract: Strong Nash implementation is a challenging problem for which there is no similar theorem to that of Maskin (1977/1999) for Nash implementation with simple conditions, which involves a wide range of applications. In this paper, we explore the origins of Maskin's theorem (1979) in this context. We assume that there exists at least one pair of agents who are associated with specific alternatives, which we refer to as separately exclusive alternatives. A pair of agents with separately exclusive alternatives is one where each agent prefers their own alternative over the other agent's alternative, and for each agent, all other agents in society prefer any socially chosen alternative over their respective alternatives. We show that when there are at least three agents, all social choice correspondences satisfying a strong version of Maskin monotonicity and unanimity can be implemented in Nash equilibria. We apply our findings to finite fair allocation problems in matching markets, to infinite fair allocation problems with single-peaked preferences, to efficient sharing Rules for a commonly owned technology and coalitional games.

Keywords: Implementation Strong Nash equilibrium Fair allocation problems. JEL classification: C72 D71; Implementation; Strong Nash equilibrium; Fair allocation problems. JEL classification: C72; D71 (search for similar items in EconPapers)
Date: 2025-04-26
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