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Values for Markovian coalition processes

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  • Ulrich Faigle

    ()

  • Michel Grabisch

    ()

Abstract

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

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 51 (2012)
Issue (Month): 3 (November)
Pages: 505-538

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Handle: RePEc:spr:joecth:v:51:y:2012:i:3:p:505-538

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Related research

Keywords: Coalitional game; Coalition formation process; Exchange economy; Markov chain; Shapley value; C71;

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References

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  1. 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.
  2. Michel Breton & Shlomo Weber, 2005. "Stable partitions in a model with group-dependent feasible sets," Economic Theory, Springer, vol. 25(1), pages 187-201, 01.
  3. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  4. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  5. Shafer, Wayne J, 1980. "On the Existence and Interpretation of Value Allocation," Econometrica, Econometric Society, vol. 48(2), pages 466-76, March.
  6. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
  7. Roth, Alvin E, 1980. "Values for Games without Sidepayments: Some Difficulties with Current Concepts," Econometrica, Econometric Society, vol. 48(2), pages 457-65, March.
  8. Aumann, Robert J, 1987. "Value, Symmetry, and Equal Treatment: A Comment [Non-symmetric Cardinal Value Allocations]," Econometrica, Econometric Society, vol. 55(6), pages 1461-64, November.
  9. Thomas Liggett & Steven Lippman & Richard Rumelt, 2009. "The asymptotic shapley value for a simple market game," Economic Theory, Springer, vol. 40(2), pages 333-338, August.
  10. 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.
  11. Gustavo Bergantiños & Silvia Lorenzo-Freire, 2008. "A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems," Economic Theory, Springer, vol. 35(3), pages 523-538, June.
  12. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer, vol. 11(3), pages 603-627.
  13. Scafuri, Allen J & Yannelis, Nicholas C, 1984. "Non-symmetric Cardinal Value Allocations," Econometrica, Econometric Society, vol. 52(6), pages 1365-68, November.
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Cited by:
  1. Ulrich Faigle & Michel Grabisch, 2013. "A concise axiomatization of a Shapley-type value for stochastic coalition processes," Documents de travail du Centre d'Economie de la Sorbonne 13052, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. repec:hal:cesptp:halshs-00912889 is not listed on IDEAS
  3. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2013. "An allocation rule for dynamic random network formation processes," Documents de travail du Centre d'Economie de la Sorbonne 13063, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  4. repec:hal:cesptp:halshs-00976923 is not listed on IDEAS

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