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Values for Markovian coalition processes

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  • Ulrich Faigle

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  • Michel Grabisch

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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

Suggested Citation

  • Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 505-538, November.
  • Handle: RePEc:spr:joecth:v:51:y:2012:i:3:p:505-538
    DOI: 10.1007/s00199-011-0617-7
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    References listed on IDEAS

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    1. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
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    Cited by:

    1. repec:hal:journl:halshs-00881125 is not listed on IDEAS
    2. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 283-313, October.
    3. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.
    4. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-01207823, HAL.
    5. repec:hal:journl:halshs-01207823 is not listed on IDEAS
    6. repec:hal:cesptp:halshs-00912889 is not listed on IDEAS
    7. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Discounted Tree Solutions," Working Papers hal-01377923, HAL.
    8. Ulrich Faigle & Michel Grabisch, 2013. "A concise axiomatization of a Shapley-type value for stochastic coalition processes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00841259, HAL.
    9. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Games, MDPI, Open Access Journal, vol. 8(4), pages 1-25, November.
    10. René Brink & Chris Dietz & Gerard Laan & Genjiu Xu, 2017. "Comparable characterizations of four solutions for permission tree games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 903-923, April.
    11. repec:spr:etbull:v:1:y:2013:i:2:d:10.1007_s40505-013-0020-6 is not listed on IDEAS
    12. repec:spr:etbull:v:1:y:2013:i:2:d:10.1007_s40505-013-0003-7 is not listed on IDEAS
    13. repec:hal:cesptp:halshs-00976923 is not listed on IDEAS
    14. Ulrich Faigle & Michel Grabisch, 2013. "A note on values for Markovian coalition processes," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 111-122, November.
    15. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01207823, HAL.

    More about this item

    Keywords

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

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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