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An Ordinal Shapley Value for Economic Environments

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  • David Pérez-Castrillo
  • David Wettstein

Abstract

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (T U ) games. We show a solution exists, and call it an Ordinal Shapley value (OSV ). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapley value for T U games, we construct a weighted OSV as well.

Suggested Citation

  • David Pérez-Castrillo & David Wettstein, 2003. "An Ordinal Shapley Value for Economic Environments," Working Papers 26, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:26
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    References listed on IDEAS

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    1. Koji Yokote, 2017. "Weighted values and the core in NTU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 631-654, August.
    2. Yildirim, Huseyin, 2007. "Proposal power and majority rule in multilateral bargaining with costly recognition," Journal of Economic Theory, Elsevier, vol. 136(1), pages 167-196, September.
    3. de Clippel, Geoffroy & Pérez-Castrillo, David & Wettstein, David, 2012. "Egalitarian equivalence under asymmetric information," Games and Economic Behavior, Elsevier, vol. 75(1), pages 413-423.
    4. David Pérez-Castrillo & David Wettstein, 2005. "Implementation of the Ordinal Shapley Value for a three-agent economy," Economics Bulletin, AccessEcon, vol. 3(48), pages 1-8.
    5. 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.
    6. Alon, Shiri & Lehrer, Ehud, 2019. "Competitive equilibrium as a bargaining solution: An axiomatic approach," Games and Economic Behavior, Elsevier, vol. 118(C), pages 60-71.
    7. Sun, Chaoran, 2022. "Bidding against a Buyout: Implementing the Shapley value and the equal surplus value," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    8. Vidal-Puga, Juan, 2015. "A non-cooperative approach to the ordinal Shapley–Shubik rule," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 111-118.
    9. Vidal-Puga, Juan, 2013. "A non-cooperative approach to the ordinal Shapley rule," MPRA Paper 43790, University Library of Munich, Germany.

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    More about this item

    Keywords

    Non-transferable utility games; shapley value; ordinal shapley value; consistency; fairness;
    All these keywords.

    JEL classification:

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

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