Equity Equilibrium for Cooperative Games

Matthew Van Essen

No 2024-04, Working Papers from University of Tennessee, Department of Economics

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.

Keywords: Cooperative Games; Equity Equilibrium; Kernel; Shapley Value; Computation of Cooperative Solutions (search for similar items in EconPapers)
JEL-codes: C92 D82 D9 H41 Q51 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2024-11
New Economics Papers: this item is included in nep-gth
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