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Cores and related solution concepts for multi-choice games. (English) Zbl 0837.90133

Summary: A multi-choice game is a generalization of a cooperative game in which each player has several activity levels. Cooperating games form a subclass of the class of multi-choice games.
This paper extends some solution concepts for cooperative games to multi- choice games. In particular, the notions of core, dominance core and Weber set are extended. Relations between cores and dominance cores and between cores and Weber sets are extensively studied. A class of flow games is introduced and relations with non-negative games with non-empty cores are investigated.

MSC:

91A12 Cooperative games
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[1] Bondareva ON (1963) Certain applications of the methods of linear programming to the theory of cooperative games (In Russian). Problemy Kibernetiki 10:119-139 · Zbl 1013.91501
[2] Chih-Ru Hsiao, Raghavan TES (1993) Shapley value for multi-choice cooperative games (I). Games and Economic Behavior 5:240-256 · Zbl 0795.90092 · doi:10.1006/game.1993.1014
[3] Curiel I, Derks J, Tijs S (1989) On balanced games and games with committee control. OR Spektrum 11:83-88 · Zbl 0678.90102 · doi:10.1007/BF01746002
[4] Derks JJM (1987) Decomposition of games with non-empty cores into veto-controlled simple games. OR Spektrum 9:81-85 · Zbl 0625.90099 · doi:10.1007/BF01732642
[5] Derks JJM (1991) On polyhedral cones of cooperative games. PhD Dissertation University of Limburg The Netherlands
[6] Ford LR, Fulkerson DR (1956) Maximal flow through a network. Canad J of Math 8:399-404 · Zbl 0073.40203 · doi:10.4153/CJM-1956-045-5
[7] Ichiishi T (1983) Game theory for economic analysis. Academic press New York · Zbl 0522.90104
[8] Kalai E, Zemel E (1982) Totally balanced games and games of flow. Math of Oper Res 7:476-479 · Zbl 0498.90030 · doi:10.1287/moor.7.3.476
[9] Neumann J von, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press Princeton New Jersey · Zbl 0063.05930
[10] Nouweland A. van den (1993) Games and graphs in economic situations. PhD Dissertation Tilburg University The Netherlands · Zbl 0795.90094
[11] Roth A (1976) Subsolutions and the supercore of cooperative games. Math Oper Res 1:43-49 · Zbl 0457.90095 · doi:10.1287/moor.1.1.43
[12] Shapley LS (1967) On balanced sets and cores. Nav Res Log Quart 14:453-460 · doi:10.1002/nav.3800140404
[13] Shapley LS (1971) Cores of convex games. Int J of Game Theory 1:11-26 · Zbl 0222.90054 · doi:10.1007/BF01753431
[14] Weber RJ (1988) Probabilistic values for games. In: Roth AE (Ed.) The Shapley value. Cambridge University Press Cambridge 101-119
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