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Mollifier Representation in Non-Constant-Sum Games

Author

Listed:
  • H. Andrew Michener
  • Greg B. Macheel
  • Charles G. Depies
  • Chris A. Bowen

    (Department of Sociology, University of Wisconsin—Madison)

Abstract

This article reports an experimental test that juxtaposes the von Neumann-Morgenstern characteristic function v(S) against the homomollifier function h(S) proposed by Charnes et al. (1978). The test was conducted in the context of 5-person cooperative sidepayment non-constant-sum games with nonempty core. Experimental results show that payoff predictions by various solution concepts (the Shapley value, the nucleolus, the 2-center) computed from the homomollifier are more accurate than predictions by the same solutions computed from the characteristic function. Supplementary analyses of data show that the payoff function x(S) is more closely approximated by the homomollifier h(S) than by the characteristic function v(S). These findings are interpreted as indicating that the homomollifier is more useful than the characteristic function for purposes of predicting payoffs in non-constant-sum games.

Suggested Citation

  • H. Andrew Michener & Greg B. Macheel & Charles G. Depies & Chris A. Bowen, 1986. "Mollifier Representation in Non-Constant-Sum Games," Journal of Conflict Resolution, Peace Science Society (International), vol. 30(2), pages 361-382, June.
    • Handle: RePEc:sae:jocore:v:30:y:1986:i:2:p:361-382
    DOI: 10.1177/0022002786030002007
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    References listed on IDEAS

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    1. J. Keith Murnighan & Alvin E. Roth, 1977. "The Effects of Communication and Information Availability in an Experimental Study of a Three-Person Game," Management Science, INFORMS, vol. 23(12), pages 1336-1348, August.
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    3. Michael Maschler, 1963. "The Power of a Coalition," Management Science, INFORMS, vol. 10(1), pages 8-29, October.
    4. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August.
    6. Richard Spinetto, 1974. "The Geometry of Solution Concepts for N-Person Cooperative Games," Management Science, INFORMS, vol. 20(9), pages 1292-1299, May.
    7. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
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    Cited by:

    1. H. Michener & Daniel Myers, 1998. "An Empirical Comparison of Probabilistic Coalition Structure Theories in 3-Person Sidepayment Games," Theory and Decision, Springer, vol. 45(1), pages 37-82, August.

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