Set-valued solution concepts using interval-type payoffs for interval games
Uncertainty is a daily presence in the real world. It affects our decision making and may have influence on cooperation. Often uncertainty is so severe that we can only predict some upper and lower bounds for the outcome of our actions, i.e., payoffs lie in some intervals. A suitable game theoretic model to support decision making in collaborative situations with interval data is that of cooperative interval games. Solution concepts that associate with each cooperative interval game sets of interval allocations with appealing properties provide a natural way to capture the uncertainty of coalition values into the players’ payoffs. In this paper, some set-valued solution concepts using interval payoffs, namely the interval core, the interval dominance core and the interval stable sets for cooperative interval games, are introduced and studied. The main results contained in the paper are a necessary and sufficient condition for the non-emptiness of the interval core of a cooperative interval game and the relations between the interval core, the interval dominance core and the interval stable sets of such a game.
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- Suijs, J.P.M. & Borm, P.E.M. & De Waegenaere, A.M.B. & Tijs, S.H., 1995.
"Cooperative games with stochastic payoffs,"
1995-88, Tilburg University, Center for Economic Research.
- repec:ner:tilbur:urn:nbn:nl:ui:12-78432 is not listed on IDEAS
- repec:ner:tilbur:urn:nbn:nl:ui:12-167605 is not listed on IDEAS
- repec:ebl:ecbull:v:3:y:2003:i:9:p:1-8 is not listed on IDEAS
- Judith Timmer & Peter Borm & Stef Tijs, 2005.
"Convexity In Stochastic Cooperative Situations,"
International Game Theory Review (IGTR),
World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 25-42.
- repec:spr:compst:v:69:y:2009:i:1:p:99-109 is not listed on IDEAS
- Daniel Granot, 1977. "Cooperative Games in Stochastic Characteristic Function Form," Management Science, INFORMS, vol. 23(6), pages 621-630, February.
- Rodica Branzei & Stef Tijs & S. Zeynep Alparslan Gok, 2008. "Some Characterizations of Convex Interval Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(3), pages 219-226, December.
- Luisa Carpente & Balbina Casas-Méndez & Ignacio García-Jurado & Anne Nouweland, 2010. "The truncated core for games with upper bounds," International Journal of Game Theory, Springer, vol. 39(4), pages 645-656, October.
- Suijs, J.P.M. & Borm, P.E.M. & De Waegenaere, A.M.B. & Tijs, S.H., 1999. "Cooperative games with stochastic payoffs," Other publications TiSEM f0fb042f-fe23-43f9-9982-d, School of Economics and Management.
- Brânzei, R. & Tijs, S.H. & Alparslan-Gok, S.Z., 2008. "Some Characterizations of Convex Interval Games," Discussion Paper 2008-55, .
- Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
- repec:ner:tilbur:urn:nbn:nl:ui:12-121815 is not listed on IDEAS
- Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2003. "Shapley-like values for interval bankruptcy games," Other publications TiSEM 55aabb66-74af-4980-b6eb-f, School of Economics and Management.
- S. Alparslan-Gök & Silvia Miquel & Stef Tijs, 2009. "Cooperation under interval uncertainty," Mathematical Methods of Operations Research, Springer, vol. 69(1), pages 99-109, March.
- Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
- Borm, P.E.M. & Tijs, S.H. & Timmer, J.B., 2005. "Convexity in stochastic cooperative situations," Other publications TiSEM 26004fd5-1beb-4ddf-b73f-a, School of Economics and Management.
- Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Convex Interval Games," Discussion Paper 2008-37, Tilburg University, Center for Economic Research.
- Brânzei, R. & Tijs, S.H. & Alparslan-Gok, S.Z., 2008. "Some Characterizations of Convex Interval Games," Discussion Paper 2008-55, Tilburg University, Center for Economic Research.
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