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Socially Structured Games

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  • P. Herings

    ()

  • Gerard Laan

    ()

  • Dolf Talman

    ()

Abstract

We generalize the concept of a cooperative non-transferable utility game by introducing a socially structured game. In a socially structured game every coalition of players can organize themselves according to one or more internal organizations to generate payoffs. Each admissible internal organization on a coalition yields a set of payoffs attainable by the members of this coalition. The strengths of the players within an internal organization depend on the structure of the internal organization and are represented by an exogenously given power vector. More powerful players have the power to take away payoffs of the less powerful players as long as those latter players are not able to guarantee their payoffs by forming a different internal organization within some coalition in which they have more power. We introduce the socially stable core as a solution concept that contains those payoffs that are both stable in an economic sense, i.e., belong to the core of the underlying cooperative game, and stable in a social sense, i.e., payoffs are sustained by a collection of internal organizations of coalitions for which power is distributed over all players in a balanced way. The socially stable core is a subset and therefore a refinement of the core. We show by means of examples that in many cases the socially stable core is a very small subset of the core. We will state conditions for which the socially stable core is non-empty. In order to derive this result, we formulate a new intersection theorem that generalizes the KKMS intersection theorem. We also discuss the relationship between social stability and the wellknown concept of balancedness for NTU-games, a sufficient condition for non-emptiness of the core. In particular we give an example of a socially structured game that satisfies social stability and therefore has a non-empty core, but whose induced NTU-game does not satisfy balancedness in the general sense of Billera. Copyright Springer 2007

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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 62 (2007)
Issue (Month): 1 (February)
Pages: 1-29

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Handle: RePEc:kap:theord:v:62:y:2007:i:1:p:1-29

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Web page: http://www.springerlink.com/link.asp?id=100341

Related research

Keywords: balancedness; core; non-transferable utility game; social stability; C71;

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References

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  1. HERINGS , P.Jean-Jacques, 1996. "An Extremely Simple Proof of the K-K-M-S Theorem," CORE Discussion Papers 1996003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Laan, G. van der & Talman, A.J.J. & Yang, Z., 1994. "Intersection theorems on polytopes," Discussion Paper 1994-20, Tilburg University, Center for Economic Research.
  3. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer, vol. 24(3), pages 439-454, 06.
  4. Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Game Theory and Information 0303010, EconWPA.
  5. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
  6. Nowak Andrzej S. & Radzik Tadeusz, 1994. "The Shapley Value for n-Person Games in Generalized Characteristic Function Form," Games and Economic Behavior, Elsevier, vol. 6(1), pages 150-161, January.
  7. Gerard van der Laan & Zaifu Yang & Dolf Talman, 1998. "Cooperative games in permutational structure," Economic Theory, Springer, vol. 11(2), pages 427-442.
  8. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
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Citations

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Cited by:
  1. Iehlé, Vincent, 2004. "Transfer Rate Rules and Core Selections in NTU Games," Economics Papers from University Paris Dauphine 123456789/86, Paris Dauphine University.
  2. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
  3. Erik Ansink & Hans-Peter Weikard, 2009. "Sequential Sharing Rules for River Sharing Problems," Working Papers 2009.114, Fondazione Eni Enrico Mattei.
  4. Lanzi, Diego, 2013. "Frames and social games," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 45(C), pages 227-233.
  5. Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores (revised version)," UFAE and IAE Working Papers 678.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  6. repec:ebl:ecbull:v:3:y:2004:i:42:p:1-10 is not listed on IDEAS

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