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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. 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.
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  9. 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.
  10. 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.
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