Nonsymmetric values of nonatomic and mixed games
(2000) Mathematics of operations research — Vol. 25, n° 4, p. 591-605 (2000)
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- 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) 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 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.
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Haimanko, O. (2000). Nonsymmetric values of nonatomic and mixed games. Mathematics of operations research, 25(4), 591-605. https://doi.org/10.1287/moor.25.4.591.12120 (Original work published 2000)