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A comparison of the average prekernel and the prekernel

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  • Serrano, Roberto
  • Shimomura, Ken-Ichi

Abstract

We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is approximated by the set of equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average prekernel as the unique solution that satisfies a set of Nash-like axioms for two-person games, and versions of average consistency and its converse for multilateral settings

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  • Serrano, Roberto & Shimomura, Ken-Ichi, 2005. "A comparison of the average prekernel and the prekernel," UC3M Working papers. Economics we055827, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:we055827
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    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. Serrano, Roberto, 1997. "Reinterpreting the Kernel," Journal of Economic Theory, Elsevier, vol. 77(1), pages 58-80, November.
    8. Serrano, Roberto & Shimomura, Ken-Ichi, 1998. "Beyond Nash Bargaining Theory: The Nash Set," Journal of Economic Theory, Elsevier, vol. 83(2), pages 286-307, December.
    9. Guni Orshan & Federico Valenciano & José M. Zarzuelo, 2003. "The Bilateral Consistent Prekernel, the Core, and NTU Bankruptcy Problems," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 268-282, May.
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    11. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667, Elsevier.
    12. Orshan, Gooni & Zarzuelo, Jose M., 2000. "The Bilateral Consistent Prekernel for NTU Games," Games and Economic Behavior, Elsevier, vol. 32(1), pages 67-84, July.
    13. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
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    Cited by:

    1. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    2. Serrano, Roberto & Shimomura, Ken-Ichi, 2006. "A comparison of the average prekernel and the prekernel," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 288-301, December.
    3. Vincent Iehlé, 2004. "Transfer rate rules and core selections in NTU games," Economics Bulletin, AccessEcon, vol. 3(42), pages 1-10.
    4. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    5. repec:dau:papers:123456789/89 is not listed on IDEAS
    6. Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores (revised version)," UFAE and IAE Working Papers 678.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).

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