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Analysis of the core under inequality-averse utility functions


  • Seiji Takanashi

    (Graduate School of Information Science and Electrical Engineering, Kyushu University)


In this paper, we study cooperative games with the players whose pref- erences depend on all players’ allocations, which we refer to as the social preferences. The social preferences we study in this paper are represented by the utility functions proposed by Fehr and Schmidt (1999) or the util- ity functions proposed by Charness and Rabin (2002). First, we define and characterize the cores, which are the same as the standard core except that the utility functions are the Fehr-Schmidt or the Charness-Rabin type. We show that the Fehr-Schmidt type core becomes smaller if the players become more envious and that it may become larger or smaller if the players become more compassionate. We also show that the Charness-Rabin type core be- comes smaller if the players pay more attention to care about the minimal allocation and that it may become larger or smaller if the players pay more attention to care about the social welfare. Moreover, we analyze the alpha- core and the beta-core of the cooperative games consisting of players with these types of social preferences, as well as a new core concept that takes ac- count of networks among the players. We show that the Fehr-Schmidt type core is the smallest among these cores and that the alpha-core coincides with the beta-core under the Fehr-Schmidt utility functions.

Suggested Citation

  • Seiji Takanashi, 2018. "Analysis of the core under inequality-averse utility functions," KIER Working Papers 1006, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:1006

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    References listed on IDEAS

    1. Gary Charness & Matthew Rabin, 2002. "Understanding Social Preferences with Simple Tests," The Quarterly Journal of Economics, Oxford University Press, vol. 117(3), pages 817-869.
    2. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 817-868.
    3. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    4. Javier Arin & Jeroen Kuipers & Dries Vermeulen, 2008. "An axiomatic approach to egalitarianism in TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 565-580, December.
    5. Anindya Bhattacharya, 2004. "On the equal division core," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 391-399, April.
    6. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 187-193.
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    More about this item


    Social preference; Inequality-aversion; Cooperative game; Core; Network;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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