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The proportional ordinal Shapley solution for pure exchange economies

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  • Pérez-Castrillo, David
  • Sun, Chaoran

Abstract

We define the proportional ordinal Shapley (the POSh) solution, an ordinal concept for pure exchange economies in the spirit of the Shapley value. Our construction is inspired by Hart and Mas-Colell's (1989) characterization of the Shapley value with the aid of a potential function. The POSh exists and is unique and essentially single-valued for a fairly general class of economies. It satisfies individual rationality, anonymity, and properties similar to the null-player and null-player out properties in transferable utility games. The POSh is immune to agents' manipulation of their initial endowments: It is not D-manipulable and does not suffer from the transfer paradox. Moreover, we characterize the POSh through a Harsanyi's (1959) system of dividends and, when agents' preferences are homothetic, through a weighted balanced contributions property à la Myerson (1980).

Suggested Citation

  • Pérez-Castrillo, David & Sun, Chaoran, 2022. "The proportional ordinal Shapley solution for pure exchange economies," Games and Economic Behavior, Elsevier, vol. 135(C), pages 96-109.
    • Handle: RePEc:eee:gamebe:v:135:y:2022:i:c:p:96-109
    DOI: 10.1016/j.geb.2022.06.001
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    More about this item

    Keywords

    Shapley value; Exchange economy; Ordinal solution; Potential;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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