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The Shapley Value as a von Neumann-Morgenstern Utility


  • Roth, Alvin

    (Illinois University)


The Shapley value is shown to be avon Neumann-Morgenstern utility function. The concept of strategic risk is introduced, and it is shown that the Shapley value of agame equals its utility if and only if the underlying preferences are neutral to both ordinary and strategic risk.

Suggested Citation

  • Roth, Alvin, 2012. "The Shapley Value as a von Neumann-Morgenstern Utility," Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 6, pages 1-9.
  • Handle: RePEc:rnp:ecopol:1279

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    References listed on IDEAS

    1. Roth, Alvin E, 1978. "The Nash Solution and the Utility of Bargaining," Econometrica, Econometric Society, vol. 46(3), pages 587-594, May.
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    1. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    2. Maria Montero & Martin Sefton & Ping Zhang, 2008. "Enlargement and the balance of power: an experimental study," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(1), pages 69-87, January.
    3. van den Brink, René & Pintér, Miklós, 2015. "On axiomatizations of the Shapley value for assignment games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 110-114.
    4. André Casajus, 2010. "Another characterization of the Owen value without the additivity axiom," Theory and Decision, Springer, vol. 69(4), pages 523-536, October.
    5. Ehud Kalai & Roger B. Myerson, 1977. "Values of Games Without Sidepayments," Discussion Papers 267, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    7. Casajus, André & Yokote, Koji, 2017. "Weak differential marginality and the Shapley value," Journal of Economic Theory, Elsevier, vol. 167(C), pages 274-284.
    8. René van den Brink & Robert P. Gilles, 2003. "Explicit and Latent Authority in Hierarchical Organizations," Tinbergen Institute Discussion Papers 03-102/1, Tinbergen Institute.
    9. Rene (J.R.) van den Brink & Osman Palanci & S. Zeynep Alparslan Gok, 2017. "Interval Solutions for Tu-games," Tinbergen Institute Discussion Papers 17-094/II, Tinbergen Institute.
    10. Ismail M.S., 2014. "The equivalence between two-person symmetric games and decision problems," Research Memorandum 023, Maastricht University, Graduate School of Business and Economics (GSBE).
    11. Manfred Holler & Hannu Nurmi, 2010. "Measurement of power, probabilities, and alternative models of man," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(5), pages 833-847, August.
    12. Murali Agastya, 2008. "On choosing which game to play when ignorant of the rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(2), pages 297-308, February.
    13. Victor Aguiar & Roland Pongou & Jean-Baptiste Tondji, 2016. "Measuring and Decomposing the Distance to the Shapley Wage Function with Limited Data," Working Papers 1613e, University of Ottawa, Department of Economics.
    14. Casajus, André, 2014. "The Shapley value without efficiency and additivity," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 1-4.
    15. Casajus, André, 2014. "Potential, value, and random partitions," Economics Letters, Elsevier, vol. 125(2), pages 164-166.
    16. Committee, Nobel Prize, 2012. "Alvin E. Roth and Lloyd S. Shapley: Stable allocations and the practice of market design," Nobel Prize in Economics documents 2012-1, Nobel Prize Committee.
    17. Bourheneddine Ben Dhaou & Abderrahmane Ziad, 2015. "The Free Solidarity Value," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201508, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    18. Swanenberg, A.J.M., 1981. "Rationing and price dynamics in a simple market-game," Research Memorandum 43559370-0b7a-4bd0-87ed-6, Tilburg University, School of Economics and Management.
    19. Norman Kleinberg & Jeffrey Weiss, 2013. "On membership and marginal values," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 357-373, May.
    20. Casajus, André & Tutić, Andreas, 2013. "Nash bargaining, Shapley threats, and outside options," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 262-267.
    21. Trockel, Walter, 1996. "A Walrasian approach to bargaining games," Economics Letters, Elsevier, vol. 51(3), pages 295-301, June.
    22. Flores Díaz, Ramón Jesús & Molina, Elisenda & Tejada, Juan, 2013. "The Shapley group value," DES - Working Papers. Statistics and Econometrics. WS ws133430, Universidad Carlos III de Madrid. Departamento de Estadística.
    23. Ehud Kalai & Roger B. Myerson, 1977. "Linear Functionals of Convex Sets with Applications to Economics," Discussion Papers 272, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    24. Orlova, Ekaterina & Hubert, Franz, 2014. "Network Access and Market Power," Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100474, Verein für Socialpolitik / German Economic Association.
    25. Federico Valenciano & Annick Laruelle, 2003. "Potential, Value And Probability," Working Papers. Serie AD 2003-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).


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