Non-Symmetric Values of Non-Atomic and Mixed Games

Ori Haimanko

This paper presents a new unifying approach to the study of nonsymmetric (or quasi-) valuesof nonatomic and mixed games. A family of path values is defined, using an appropriate generalization of Mertens diagonal formula. A path value possesses the following intuitive description: consider a function (path) gamma attaching to each player a distribution function on [0; 1]. We think of players as arriving randomly and independently to a meeting when the arrival time of a player is distributed according to gamma. Each player’s payoff is defined as his marginal contribution to thecoalition of players that have arrived earlier.Under certain conditions on a path, different subspaces of mixed games (pNA; pM; bv'FL) areshown to be in the domain of the path value. The family of path values turns out to be verywide - we show that on pNA;pM and their subspaces the path values are essentially the basicconstruction blocks (extreme points) of quasi-values.

March, 1998
Published in: 
Mathematics of Operations Research 25 (2000), 591-605