CONVEXITY IN STOCHASTIC COOPERATIVE SITUATIONS

Judith Timmer (), Peter Borm and Stef Tijs
Additional contact information
Judith Timmer: Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands
Stef Tijs: Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands

International Game Theory Review (IGTR), 2005, vol. 07, issue 01, 25-42

Abstract: This paper introduces a new model concerning cooperative situations in which the payoffs are modeled by random variables. We analyze these situations by means of cooperative games with random payoffs. Special attention is paid to three types of convexity, namely coalitional-merge, individual-merge and marginal convexity. The relations between these types are studied and in particular, as opposed to their deterministic counterparts for TU games, we show that these three types of convexity are not equivalent. However, all types imply that the core of the game is nonempty. Sufficient conditions on the preferences are derived such that the Shapley value, defined as the average of the marginal vectors, is an element of the core of a convex game.

Keywords: Cooperative games; random variables; preferences; convexity; Subject Classification: 91A12 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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Related works:
Working Paper: Convexity in stochastic cooperative situations (2005)
Working Paper: Convexity in Stochastic Cooperative Situations (2000)
Working Paper: Convexity in Stochastic Cooperative Situations (2000)
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DOI: 10.1142/S0219198905000387

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