Values for Markovian coalition processes
Time series of coalitions (so-called scenarios) are studied that describe processes of coalition formation where several players may enter or leave the current coalition at any point in (discrete) time and convergence to the grand coalition is not necessarily prescribed. Transitions from one coalition to the next are assumed to be random and to yield a Markov chain. Three examples of such processes (the Shapley-Weber process, the Metropolis process, and an example of a voting situation) and their properties are presented. A main contribution includes notions of value for such series, i.e., schemes for the evaluation of the expected contribution of a player to the coalition process relative to a given cooperative game. Particular processes permit to recover the classical Shapley value. This methodology’s power is illustrated with well-known examples from exchange economies due to Shafer (Econometrica 48:467–476, 1980 ) and Scafuri and Yannelis (Econometrica 52:1365–1368, 1984 ), where the classical Shapley value leads to counterintuitive allocations. The Markovian process value avoids these drawbacks and provides plausible results. Copyright Springer-Verlag 2012
Volume (Year): 51 (2012)
Issue (Month): 3 (November)
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- Konishi, Hideo & Ray, Debraj, 2003.
"Coalition formation as a dynamic process,"
Journal of Economic Theory,
Elsevier, vol. 110(1), pages 1-41, May.
- Hideo Konishi & Debraj Ray, 2000. "Coalition Formation as a Dynamic Process," Boston College Working Papers in Economics 478, Boston College Department of Economics, revised 15 Apr 2002.
- Gustavo Bergantiños & Silvia Lorenzo-Freire, 2008. "A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 523-538, June.
- Aumann, Robert J, 1987. "Value, Symmetry, and Equal Treatment: A Comment [Non-symmetric Cardinal Value Allocations]," Econometrica, Econometric Society, vol. 55(6), pages 1461-1464, November.
- Grabisch, Michel & Funaki, Yukihiko, 2012. "A coalition formation value for games in partition function form," European Journal of Operational Research, Elsevier, vol. 221(1), pages 175-185.
- Michel Grabisch & Yukihiko Funaki, 2012. "A coalition formation value for games in partition function form," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00690696, HAL.
- Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
- Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
- René Brink & Ilya Katsev & Gerard Laan, 2011. "Axiomatizations of two types of Shapley values for games on union closed systems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 175-188, May.
- Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2009. "Axiomatizations of Two Types of Shapley Values for Games on Union Closed Systems," Tinbergen Institute Discussion Papers 09-064/1, Tinbergen Institute.
- Roth, Alvin E, 1980. "Values for Games without Sidepayments: Some Difficulties with Current Concepts," Econometrica, Econometric Society, vol. 48(2), pages 457-465, March.
- Shafer, Wayne J, 1980. "On the Existence and Interpretation of Value Allocation," Econometrica, Econometric Society, vol. 48(2), pages 466-476, March.
- Michel Breton & Shlomo Weber, 2005. "Stable partitions in a model with group-dependent feasible sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(1), pages 187-201, 01.
- Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
- Thomas Liggett & Steven Lippman & Richard Rumelt, 2009. "The asymptotic shapley value for a simple market game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(2), pages 333-338, August.
- Jana Hajduková, 2006. "Coalition Formation Games: A Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 613-641.
- Scafuri, Allen J & Yannelis, Nicholas C, 1984. "Non-symmetric Cardinal Value Allocations," Econometrica, Econometric Society, vol. 52(6), pages 1365-1368, November. Full references (including those not matched with items on IDEAS)