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The Partnered Core of a Game with Side Payments

Author

Listed:
  • Philip J. Reny

    () (Department of Economics, University of Chicago)

  • Eyal Winter

    () (Center for the Study of Rationality, Hebrew University)

  • Myrna Wooders

    () (Department of Economics, Vanderbilt University)

Abstract

An outcome of a game is partnered if there are no asymmetric dependencies between any two players. For a cooperative game, a payoff is in the partnered core of the game if it is partnered, feasible and cannot be improved upon by any coalition of players. We show that the relative interior of the core of a game with side payments is contained in the partnered core. For quasi-strictly convex games the partnered core coincides with the relative interior of the core. When there are no more than three partnerships, the sums of the payoffs to partnerships are constant across all core payoffs. When there are no more than three players, the partnered core satisfies additional properties.

Suggested Citation

  • Philip J. Reny & Eyal Winter & Myrna Wooders, 2009. "The Partnered Core of a Game with Side Payments," Vanderbilt University Department of Economics Working Papers 0917, Vanderbilt University Department of Economics.
  • Handle: RePEc:van:wpaper:0917
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    References listed on IDEAS

    as
    1. Yakar Kannai & Myrna H. Wooders, 2000. "A Further Extension of the KKMS Theorem," Mathematics of Operations Research, INFORMS, vol. 25(4), pages 539-551, November.
    2. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    3. Stef Tijs & Anne van den Nouweland & Bhaskar Dutta, 1998. "Link formation in cooperative situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 245-256.
    4. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 419-427.
    5. Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May.
    6. Reny, Philip J. & Holtz Wooders, Myrna, 1996. "The Partnered Core of a Game without Side Payments," Journal of Economic Theory, Elsevier, vol. 70(2), pages 298-311, August.
    7. Bennett, Elaine & Zame, William R, 1988. "Bargaining in Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(4), pages 279-300.
    8. Myrna Holtz Wooders, 1992. "Large Games and Economies With Effective Small Groups," Discussion Paper Serie B 215, University of Bonn, Germany, revised Aug 1992.
    9. Philip Reny & Eyal Winter & Myrna Wooders, 2012. "The partnered core of a game with side payments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 521-536, July.
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    12. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
    13. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "The Partnered Core of an Economy and the Partnered Competitive Equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 143-152, August.
    14. Dutta, Bhaskar & Mutuswami, Suresh, 1997. "Stable Networks," Journal of Economic Theory, Elsevier, vol. 76(2), pages 322-344, October.
      • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
    15. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 185-187.
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    More about this item

    Keywords

    Partnership; core; cooperative game; convex game; separating collections of sets; minimal partnership; coalition structure games; partitioning games; kernel;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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