The Proportional Value of a Cooperative Game

Barry Feldman

No 1140, Econometric Society World Congress 2000 Contributed Papers from Econometric Society

Abstract: The proportional value is the unique strictly consistent TU and NTU value which, in two-player TU games, gives players equal proportional gains from cooperation. Strict consistency means consistency with respect to the Hart and Mas-Colell (1989) reduced game. The proportional value is a nonlinear analog of the Shapley (1953) value in TU games and the egalitarian value (Kalai and Samet (1985)) in NTU games. It is derived from a ratio potential similar to the Hart and Mas-Colell (1989) diference potential. The propor- tional value is monotonic and is in the core of a log-convex game. It is also the unique equilibrium payoff configuration in a variation of the noncooperative bargaining game of Hart and Mas-Colell (1996) where players' probabilities of participation at any point in the game are proportional to their expected payoff at that time. Thus, it is a model of endogenous power in cooperative games. Application to cost allocation problems is considered.

Date: 2000-08-01
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Citations: View citations in EconPapers (9)

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