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Socially structured games

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Author Info

  • Herings, P.J.J.

    (Tilburg University)

  • Laan, G. van der
  • Talman, A.J.J.

    (Tilburg University)

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

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-195975.

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Date of creation: 2007
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Publication status: Published in Theory and Decision (2007) v.62, p.1-29
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-195975

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Web page: http://www.tilburguniversity.edu/

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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. Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Working Papers 1160, California Institute of Technology, Division of the Humanities and Social Sciences.
  4. 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.
  5. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Herings,P. Jean-Jacques & Predtetchinski,Arkadi, 2002. "A Necessary and Sufficient Condition for Non--emptiness of the Core of a Non--transferable Utility Game," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  7. Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 1998. "Cooperative games in permutational structure," Open Access publications from Tilburg University urn:nbn:nl:ui:12-76584, Tilburg University.
  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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Cited by:
  1. 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.
  2. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer, vol. 38(2), pages 187-210, February.
  3. repec:ebl:ecbull:v:3:y:2004:i:42:p:1-10 is not listed on IDEAS
  4. Jean-Marc Bonnisseau & Vincent Iehle, 2004. "Payoffs-dependent Balancedness and Cores," Game Theory and Information 0403004, EconWPA.
  5. Iehlé, Vincent, 2004. "Transfer Rate Rules and Core Selections in NTU Games," Economics Papers from University Paris Dauphine 123456789/86, Paris Dauphine University.
  6. 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).

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