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Stable sets and max-convex decompositions of TU games

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Abstract

We study under which conditions the core of a game involved in a max-convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas’ five player game with a unique stable set different from the core, are reckoning and analyzed.

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References

  • Aumann R (1985) What is game theory trying to accomplish. In: Arrow K, Honkapohja S (eds) Frontiers of economics. Basil Blackwell, Oxford

    Google Scholar 

  • Einy E (1988) The Shapley value on some lattices of monotonic games. Math Soc Sci 15:1–10

    Article  Google Scholar 

  • Gillies D (1959) Solutions to general non-zero-sum games. In: Tucker A, Luce R (eds) Contributions to the theory of games. Princeton University Press, Princeton, pp 47–85

    Google Scholar 

  • Ichiishi T (1981) Supermodularity: Applications to convex games and to the Greedy Algorithm for L.P. J Econ Theory 25:283–286

    Article  Google Scholar 

  • Llerena F, Rafels C (2006) The vector lattice structure of the n-person TU games. Games Econ Behav 54:373–379

    Article  Google Scholar 

  • Lucas W (1968) A game with no solution. Bull Math Soc 74:237–239

    Article  Google Scholar 

  • Lucas W (1992) Von Neumann–Morgenstern stable sets. In: Aumann R, Hart S (eds) Handbook of game theory. Elsevier, Amsterdam, pp 543–590

    Google Scholar 

  • Martínez-de-Albéniz F, Rafels C (2004) An intersection theorem in TU cooperative game theory. Int J Game Theory 33:107–114

    Article  Google Scholar 

  • Peleg B, Sudhölter P (2007) Introduction to the theory of cooperative games. Springer, Berlin

    Google Scholar 

  • Rafels C, Tijs S (1997) On the cores of cooperative games and the stability of the Weber set. Int J Game Theory 26:491–499

    Article  Google Scholar 

  • Shapley L (1971) Cores of convex games. Int J Game Theory 1:11–26

    Article  Google Scholar 

  • von Neumann J, Morgenstern O (1944) Theory of games and economic behaviour. Princeton University Press, Princeton

    Google Scholar 

Download references

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Authors and Affiliations

  1. Departament de Gestió d’Empreses, Universitat Rovira i Virgili, Avda. Universitat 1, 43204, Reus, Spain

    Francesc Llerena

  2. Departament de Matemàtica Econòmica, Financera i Actuarial, Universitat de Barcelona, Avda. Diagonal 690, 08034, Barcelona, Spain

    Carles Rafels

Authors
  1. Francesc Llerena
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  2. Carles Rafels
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Correspondence to Francesc Llerena.

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Llerena, F., Rafels, C. Stable sets and max-convex decompositions of TU games. TOP 21, 313–322 (2013). https://doi.org/10.1007/s11750-011-0177-9

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  • DOI: https://doi.org/10.1007/s11750-011-0177-9

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