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Nonsymmetric Values of Nonatomic and Mixed Games

Author

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  • Ori Haimanko

    () (CORE, Voie du Roman Pays 34, B-1348 Louvain-la-Neuve, Belgium)

Abstract

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.

Suggested Citation

  • Ori Haimanko, 2000. "Nonsymmetric Values of Nonatomic and Mixed Games," Mathematics of Operations Research, INFORMS, vol. 25(4), pages 591-605, November.
  • Handle: RePEc:inm:ormoor:v:25:y:2000:i:4:p:591-605
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    File URL: http://dx.doi.org/10.1287/moor.25.4.591.12120
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