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Socially Structured Games

  • P. Herings

    ()

  • Gerard Laan

    ()

  • Dolf Talman

    ()

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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File URL: http://hdl.handle.net/10.1007/s11238-006-9007-1
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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
Contact details of provider: Web page: http://www.springerlink.com/link.asp?id=100341

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  1. 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.
  2. 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.
  3. Gerard van der Laan & Zaifu Yang & Dolf Talman, 1998. "Cooperative games in permutational structure," Economic Theory, Springer, vol. 11(2), pages 427-442.
  4. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 1999. "Intersection theorems on polytypes," Other publications TiSEM 7cc2ec6a-3a45-4ad1-a99b-7, Tilburg University, School of Economics and Management.
  5. 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.
  6. P. Jean-Jacques Herings, 1997. "An extremely simple proof of the K-K-M-S Theorem," Economic Theory, Springer, vol. 10(2), pages 361-367.
  7. Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Working Papers 1160, California Institute of Technology, Division of the Humanities and Social Sciences.
  8. 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.
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