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Values for Markovian coalition processes

  • Ulrich Faigle

    ()

  • Michel Grabisch

    ()

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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File URL: http://hdl.handle.net/10.1007/s00199-011-0617-7
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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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  1. René Brink & Ilya Katsev & Gerard Laan, 2011. "Axiomatizations of two types of Shapley values for games on union closed systems," Economic Theory, Springer, vol. 47(1), pages 175-188, May.
  2. Shafer, Wayne J, 1980. "On the Existence and Interpretation of Value Allocation," Econometrica, Econometric Society, vol. 48(2), pages 466-76, March.
  3. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
  4. 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.
  5. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer, vol. 11(3), pages 603-627.
  6. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  7. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  8. 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.
  9. 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.
  10. Roth, Alvin E, 1980. "Values for Games without Sidepayments: Some Difficulties with Current Concepts," Econometrica, Econometric Society, vol. 48(2), pages 457-65, March.
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