The proportional value of a cooperative game
by
Barry Feldman
Ibbotson Associates

The proportional value is the unique strictly consistent TU and NTU value that, 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) difference potential. The proportional 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.

This presentation will consider a "dual theory of value" - translation covariant or scale covariant, but not both at the same time - as an alternative to the current consensus that NTU value should be embody both properties.

Date received: July 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cafl-45.