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Twin relationships in Parsimonious Games: some results

Author

Listed:
  • Flavio Pressacco

    (DIES - DIES - Dept. of Economics and Statistics - Università degli Studi di Udine - University of Udine [Italie])

  • Giacomo Plazzotta

    (Department of Mathematics [Imperial College London] - Imperial College London)

  • Laura Ziani

    (DIES - DIES - Dept. of Economics and Statistics - Università degli Studi di Udine - University of Udine [Italie])

Abstract

In a vintage paper concerning Parsimonious games, a subset of constant sum homogeneous weighted majority games, Isbell introduced a twin relationship based on transposition properties of the incidence matrices upon minimal winning coalitions of such games. A careful investigation of such properties allowed the discovery of some results on twin games presented in this paper. In detail we show that a) twin games have the same minimal winning quota and b) each Parsimonious game admits a unique balanced lottery on minimal winning coalitions, whose probabilities are given by the individual weights of its twin game.

Suggested Citation

  • Flavio Pressacco & Giacomo Plazzotta & Laura Ziani, 2014. "Twin relationships in Parsimonious Games: some results," Working Papers hal-00950076, HAL.
    • Handle: RePEc:hal:wpaper:hal-00950076
    Note: View the original document on HAL open archive server: https://hal.science/hal-00950076
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    References listed on IDEAS

    as
    1. Montero, Maria & Vidal-Puga, Juan J., 2011. "Demand bargaining and proportional payoffs in majority games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 395-408, March.
    2. Maria Montero, 2008. "Proportional Payoffs in Majority Games," Discussion Papers 2008-03, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
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