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Linear criterion for testing the extremity of an exact game based on its finest min-representation.
- Source :
-
International Journal of Approximate Reasoning . Oct2018, Vol. 101, p49-68. 20p. - Publication Year :
- 2018
-
Abstract
- A game-theoretical concept of an exact (cooperative) game corresponds to the notion of a discrete coherent lower probability, used in the context of imprecise probabilities. The collection of (suitably standardized) exact games forms a pointed polyhedral cone and the paper is devoted to the recognition of extreme rays of that cone, whose generators are called extreme exact games . We give a necessary and sufficient condition for an exact game to be extreme. Our criterion leads to solving a simple linear equation system determined by a certain min-representation of the game. It has been implemented on a computer and a web-based platform for testing the extremity of an exact game is available, which works with a modest number of variables. The paper also deals with different min-representations of a fixed exact game μ , which can be compared with the help of the concept of a tightness structure (of a min-representation) introduced in the paper. The collection of tightness structures (of min-representations of μ ) is shown to be a finite lattice with respect to a refinement relation. We give a method to obtain a min-representation with the finest tightness structure, which construction comes from the coarsest standard min-representation of μ given by the (complete) list of vertices of the core (polytope) of μ . The newly introduced criterion for exact extremity is based on the finest tightness structure. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0888613X
- Volume :
- 101
- Database :
- Academic Search Index
- Journal :
- International Journal of Approximate Reasoning
- Publication Type :
- Periodical
- Accession number :
- 131452171
- Full Text :
- https://doi.org/10.1016/j.ijar.2018.06.007