Abstract
A multi-choice game is a generalization of a cooperative game in which each player has several activity levels. Cooperative 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bondareva ON (1963) Certain applications of the methods of linear programming to the theory of cooperative games (In Russian). Problemy Kibernetiki 10:119–139
Chih-Ru Hsiao, Raghavan TES (1993) Shapley value for multi-choice cooperative games (I). Games and Economic Behavior 5:240–256
Curiel I, Derks J, Tijs S (1989) On balanced games and games with committee control. OR Spektrum 11:83–88
Derks JJM (1987) Decomposition of games with non-empty cores into veto-controlled simple games. OR Spektrum 9:81–85
Derks JJM (1991) On polyhedral cones of cooperative games. PhD Dissertation University of Limburg The Netherlands
Ford LR, Fulkerson DR (1956) Maximal flow through a network. Canad J of Math 8:399–404
Ichiishi T (1983) Game theory for economic analysis. Academic press New York
Kalai E, Zemel E (1982) Totally balanced games and games of flow. Math of Oper Res 7:476–479
Neumann J von, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press Princeton New Jersey
Nouweland A. van den (1993) Games and graphs in economic situations. PhD Dissertation Tilburg University The Netherlands
Roth A (1976) Subsolutions and the supercore of cooperative games. Math Oper Res 1:43–49
Shapley LS (1967) On balanced sets and cores. Nav Res Log Quart 14:453–460
Shapley LS (1971) Cores of convex games. Int J of Game Theory 1:11–26
Weber RJ (1988) Probabilistic values for games. In: Roth AE (Ed.) The Shapley value. Cambridge University Press Cambridge 101–119
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van den Nouweland, A., Tijs, S., Potters, J. et al. Cores and related solution concepts for multi-choice games. ZOR - Methods and Models of Operations Research 41, 289–311 (1995). https://doi.org/10.1007/BF01432361
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01432361