Nonsymmetric values of nonatomic and mixed games

This paper presents a new unifying approach to the study of nonsymmetric (or quasi-) values of 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) γ attaching to each player a distribution function of [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 γ. Each player's payoff is defined as his marginal contribution to the coalition of players that have arrived earlier. Under certain conditions on a path, different subspaces of mixed games (pNA, pM, bv′FL) are shown to be in the domain of the path value. The family of path values turns out to be very wide - we show that on pNA, pM and their subspaces the path values are essentially the basic construction blocks (extreme points) of quasi-values.