Monotonicity and dummy free property for multi-choice cooperative games |
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Authors: | C -R Hsiao T E S Raghavan |
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Institution: | 1. Department of Mathematics, Soochow University, Taipei, Taiwan ROC 2. Department of Mathematics, Statistics and Computer Science, The University of Illinois at Chicago, Box 4348, 60680, Chicago, Illinois, USA
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Abstract: | Given a coalition of ann-person cooperative game in characteristic function form, we can associate a zero-one vector whose non-zero coordinates identify the players in the given coalition. The cooperative game with this identification is just a map on such vectors. By allowing each coordinate to take finitely many values we can define multi-choice cooperative games. In such multi-choice games we can also define Shapley value axiomatically. We show that this multi-choice Shapley value is dummy free of actions, dummy free of players, non-decreasing for non-decreasing multi-choice games, and strictly increasing for strictly increasing cooperative games. Some of these properties are closely related to some properties of independent exponentially distributed random variables. An advantage of multi-choice formulation is that it allows to model strategic behavior of players within the context of cooperation.Partially funded by the NSF grant DMS-9024408 |
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