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Equity Equilibrium for Cooperative Games

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Abstract

We introduce a unifying stability concept to cooperative game theorythe equity equilibrium. A central authority selects an outcome of the game to enforce and evaluates its stability using a collection of functions called a complaint system.These complaints are used to identify the grievances against and the concessions to each player. Equity equilibrium occurs when an individually rational payo¤ con guration balances the grievances and concessions of each player. We establish the existence of equity equilibrium for any valid complaint system and under any coalition structure. Next, we show that equity equilibrium under speci c complaint systems characterizes the kernel, the Shapley value, and the generalized Nash bargaining solution of a cooperative game. We show how simplicial algorithms can be employed for computing any type of equity equilibrium. This approach is illustrated with an example from the Tennessee Valley Authority.

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  • Matt Van Essen, 2024. "Equity Equilibrium for Cooperative Games," Working Papers 2024-04, University of Tennessee, Department of Economics.
    • Handle: RePEc:ten:wpaper:2024-04
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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. 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).
    3. Serrano, Roberto, 1997. "Reinterpreting the Kernel," Journal of Economic Theory, Elsevier, vol. 77(1), pages 58-80, November.
    4. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, December.
    5. 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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    More about this item

    Keywords

    Cooperative Games; Equity Equilibrium; Kernel; Shapley Value; Computation of Cooperative Solutions;
    All these keywords.

    JEL classification:

    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • Q51 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Valuation of Environmental Effects

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