The monoclus of a coalitional game
The analysis of single-valued solution concepts, providing payoffs to players for the grand coalition only, has a long tradition. Opposed to most of this literature we analyze allocation scheme rules, which assign payoffs to all players in all coalitions. We introduce several closely related allocation scheme rules, each resulting in a population monotonic allocation scheme (PMAS) whenever the underlying coalitional game with transferable utilities has a PMAS. Monotonicities, which measure the payoff difference for a player between two nested coalitions, are the driving force. These monotonicities can best be compared with the excesses in the definition of the (pre-)nucleolus. Variants are obtained by considering different domains and/or different collections of monotonicities. We deal with nonemptiness, uniqueness, and continuity, followed by an analysis of conditions for (some of) the rules to coincide. We then focus on characterizing the rules in terms of subbalanced weights. Finally, we deal with computational issues.
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- Marco Slikker & Henk Norde & Stef Tijs, 2003.
"Information Sharing Games,"
International Game Theory Review (IGTR),
World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-12.
- Slikker, M. & Norde, H.W. & Tijs, S.H., 2000. "Information Sharing Games," Discussion Paper 2000-100, Tilburg University, Center for Economic Research.
- Slikker, M. & Norde, H.W. & Tijs, S.H., 2003. "Information sharing games," Other publications TiSEM fa5460d9-0abc-47e1-a794-7, Tilburg University, School of Economics and Management.
- Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
- Norde, Henk & Reijnierse, Hans, 2002. "A dual description of the class of games with a population monotonic allocation scheme," Games and Economic Behavior, Elsevier, vol. 41(2), pages 322-343, November.
- Norde, H.W. & Reijnierse, J.H., 2000. "A Dual Description of the Class of Games with a Population Monotonic Allocation Scheme," Discussion Paper 2000-99, Tilburg University, Center for Economic Research.
- Maschler, M & Potters, J A M & Tijs, S H, 1992. "The General Nucleolus and the Reduced Game Property," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 85-106.
- Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
- Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667 Elsevier.
- Maschler, M. & Potters, J.A.M. & Tijs, S.H., 1992. "The general nucleolus and the reduced game property," Other publications TiSEM ab187dab-1b5b-40c3-a673-8, Tilburg University, School of Economics and Management.
- Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December. Full references (including those not matched with items on IDEAS)
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