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On the gamma-core of asymmetric aggregative games

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  • Stamatopoulos, Giorgos

Abstract

This paper analyzes the core of cooperative games generated by asymmetric aggregative normal-form games, i.e., games where the payoff of each player depends on his strategy and the sum of the strategies of all players. We assume that each coalition calculates its worth presuming that the outside players stand alone and select individually optimal strategies (Chander & Tulkens 1997). We show that under some mild monotonicity assumptions on payoffs, the resulting cooperative game is balanced, i.e. it has a non-empty gamma-core. Our paper thus offers an existence result for a core notion that is considered quite often in the theory and applications of cooperative games with externalities.

Suggested Citation

  • Stamatopoulos, Giorgos, 2018. "On the gamma-core of asymmetric aggregative games," MPRA Paper 88722, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:88722
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    References listed on IDEAS

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    1. Parkash Chander, 2007. "The gamma-core and coalition formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 539-556, April.
    2. Marini, Marco A. & Currarini, Sergio, 2003. "A sequential approach to the characteristic function and the core in games with externalities," MPRA Paper 1689, University Library of Munich, Germany, revised 2003.
    3. Parkash Chander & Henry Tulkens, 2006. "The Core of an Economy with Multilateral Environmental Externalities," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 153-175, Springer.
    4. Uyanık, Metin, 2015. "On the nonemptiness of the α-core of discontinuous games: Transferable and nontransferable utilities," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 213-231.
    5. Aymeric Lardon, 2018. "Convexity of Bertrand oligopoly TU-games with differentiated products," Post-Print halshs-00544056, HAL.
    6. László Kóczy, 2007. "A recursive core for partition function form games," Theory and Decision, Springer, vol. 63(1), pages 41-51, August.
    7. Aymeric Lardon, 2009. "The gamma-core in Cournot oligopoly TU-games with capacity constraints," Post-Print halshs-00544042, HAL.
    8. Aymeric Lardon, 2017. "Endogenous interval games in oligopolies and the cores," Annals of Operations Research, Springer, vol. 248(1), pages 345-363, January.
    9. Stamatopoulos Giorgos, 2016. "The Core of Aggregative Cooperative Games with Externalities," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(1), pages 389-410, January.
    10. Carsten Helm, 2001. "On the existence of a cooperative solution for a coalitional game with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 141-146.
    11. Heinrich H. Nax, 2014. "A Note on the Core of TU-cooperative Games with Multiple Membership Externalities," Games, MDPI, vol. 5(4), pages 1-13, October.
    12. Aymeric Lardon, 2020. "Convexity of Bertrand oligopoly TU-games with differentiated products," Annals of Operations Research, Springer, vol. 287(1), pages 285-302, April.
    13. Huang, Chen-Ying & Sjostrom, Tomas, 2003. "Consistent solutions for cooperative games with externalities," Games and Economic Behavior, Elsevier, vol. 43(2), pages 196-213, May.
    14. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
    15. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
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    Cited by:

    1. Sokolov, Denis, 2022. "Shapley value for TU-games with multiple memberships and externalities," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 76-90.

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    More about this item

    Keywords

    cooperative game; aggregative game; balancedness; core;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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