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Socially Structured Games and their Applications

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

    (Tilburg University, Center for Economic Research)

Abstract

In this paper we generalize the concept of a non-transferable utility game by introducing the concept of a socially structured game.A socially structured game is given by a set of players, a possibly empty collection of internal organizations on any subset of players, for any internal organization a set of attainable payo.s and a function on the collection of all internal organizations measuring the power of every player within the internal organization.Any socially structured game induces a non-transferable utility game.In the derived nontransferable utility game, all information concerning the dependence of attainable payo.s on the internal organization gets lost.We show this information to be useful for studying non-emptiness and re.nements of the core. For a socially structured game we generalize the concept of p-balancedness to social stability and show that a socially stable game has a non-empty socially stable core.In order to derive this result, we formulate a new intersection theorem that generalizes the KKM-Shapley intersection theorem.The socially stable core is a subset of the core of the game.We give an example of a socially structured game that satis.es social stability, whose induced non-transferable utility game therefore has a non-empty core, but does not satisfy p-balanced for any choice of p.The usefulness of the new concept is illustrated by some applications and examples.In particular we de.ne a socially structured game, whose unique element of the socially stable core corresponds to the Cournot-Nash equilibrium of a Cournot duopoly.This places the paper in the Nash research program, looking for a unifying approach to cooperative and non-cooperative behavior in which each theory helps to justify and clarify the other.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2003-40.

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Date of creation: 2003
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Handle: RePEc:dgr:kubcen:200340

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Keywords: game theory;

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References

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  1. Gerard van der Laan & Zaifu Yang & Dolf Talman, 1998. "Cooperative games in permutational structure," Economic Theory, Springer, vol. 11(2), pages 427-442.
  2. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  4. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2001. "Measuring the Power of Nodes in Digraphs," Discussion Paper 2001-72, Tilburg University, Center for Economic Research.
  5. 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).
  6. 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.
  7. 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).
  8. 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.
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Cited by:
  1. Herings, P. Jean-Jacques & van der Laan, Gerard & Talman, Dolf, 2007. "The socially stable core in structured transferable utility games," Games and Economic Behavior, Elsevier, vol. 59(1), pages 85-104, April.
  2. Jean-Marc Bonnisseau & Vincent Iehle, 2004. "Payoffs-dependent Balancedness and Cores," Game Theory and Information 0403004, EconWPA.
  3. Iehlé, Vincent, 2004. "Transfer Rate Rules and Core Selections in NTU Games," Economics Papers from University Paris Dauphine 123456789/86, Paris Dauphine University.
  4. Predtetchinski,Arkadi, 2004. "The Fuzzy Core and the (Π, β)- Balanced Core," Research Memorandum 025, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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