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Consistency, Monotonicity and Implementation of Egalitarian Shapley Values

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Author Info

  • René van den Brink

    ()
    (VU University, Amsterdam)

  • Yukihiko Funaki

    ()
    (Waseda University, Tokyo, Japan)

  • Yuan Ju

    ()
    (Keele University, Keele, UK)

Abstract

One of the main issues in economics is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide tools that make it possible to study this trade-off in a consistent way by providing three types of results on egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, we show that all these solutions satisfy the same reduced game consistency. Second, we characterize this class of solutions using monotonicity properties. Finally, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 07-062/1.

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Date of creation: 24 Aug 2007
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Handle: RePEc:dgr:uvatin:20070062

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Web page: http://www.tinbergen.nl

Related research

Keywords: Shapley value; Equal division solution; Egalitarian Shapley value; Reduced Game Consistency; Monotonicity; Implementation;

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References

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  1. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer, vol. 28(4), pages 685-703, June.
  2. Ju, Y. & Wettstein, D., 2006. "Implementing Cooperative Solution Concepts: A Generalized Bidding Approach," Discussion Paper 2006-42, Tilburg University, Center for Economic Research.
  3. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation for Research in Economics, Yale University.
  4. René van den Brink & Yukihiko Funaki, 2004. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for Cooperative Games with Transferable Utility," Tinbergen Institute Discussion Papers 04-136/1, Tinbergen Institute.
  5. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
  6. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  7. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  9. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer, vol. 15(4), pages 567-582.
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Citations

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Cited by:
  1. Emilio Calvo & Esther Gutiérrez, 2012. "Weighted Solidarity Values," Discussion Papers in Economic Behaviour 0212, University of Valencia, ERI-CES.

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