k-convexn-person games and their cores |
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Authors: | T S H Driessen |
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Institution: | 1. Department of Mathematics, Catholic University, Nijmegen, The Netherlands
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Abstract: | For any natural numbersk andn, the subclass ofk-convexn-person games is introduced. In casek=n, the subclass consists of the convexn-person games. Ak-convexn-person game is characterized in several ways in terms of the core and certain marginal worth vectors. The marginal worth vectors of a game are described in terms of an upper bound for the core and the corresponding gap function. It is shown that thek-convexity of ann-person gamev is equivalent to - all marginal worth vectors ofv belong to the core ofv; or
- the core ofv is the convex hull of the set consisting of all marginal worth vectors ofv; or
- the extreme points of the core ofv are exactly the marginal worth vectors ofv.
Examples ofk-convexn-person games are also treated. |
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Keywords: | |
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