Convexity In Stochastic Cooperative Situations
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.
Volume (Year): 07 (2005)
Issue (Month): 01 ()
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- Ruud Hendrickx & Judith Timmer & Peter Borm, 2002.
"A note on NTU convexity,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 31(1), pages 29-37.
- Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
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