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Nash oligarchies

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  • Rachmilevitch, Shiran

Abstract

A bargaining solution is a Nash oligarchy if there exists a set of players O, the oligarchy, such that in every bargaining problem every player outside O is allocated his disagreement payoff, and the oligarchs share the surplus according to the |O|-person Nash solution. The Nash bargaining solution corresponds to the case where O contains all players, and dictatorial solutions correspond to singleton Os. I show that a solution satisfies three standard axioms together with a condition that balances utilitarianism and egalitarianism if and only if it is a Nash oligarchy. Strengthening the condition implies that the oligarchy contains at most two players. Strengthening it further implies a dictatorship.

Suggested Citation

  • Rachmilevitch, Shiran, 2025. "Nash oligarchies," Journal of Mathematical Economics, Elsevier, vol. 117(C).
    • Handle: RePEc:eee:mateco:v:117:y:2025:i:c:s0304406825000102
    DOI: 10.1016/j.jmateco.2025.103093
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    More about this item

    Keywords

    Bargaining; Egalitarianism; Nash solution; Oligarchies; Utilitarianism;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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