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A strategic approach for the discounted Shapley values

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  • Emilio Calvo

  • Esther Gutiérrez-López

Abstract

The family of discounted Shapley values is analyzed for cooperative games in coalitional form. We consider the bargaining protocol of the alternating random proposer introduced in Hart and Mas-Colell (Econometrica 64:357–380, 1996) . We demonstrate that the discounted Shapley values arise as the expected payoffs associated with the bargaining equilibria when a time discount factor is considered. In a second model, we replace the time cost with the probability that the game ends without agreements. This model also implements these values in transferable utility games, moreover, the model implements the $$\alpha $$ α -consistent values in the nontransferable utility setting. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Emilio Calvo & Esther Gutiérrez-López, 2016. "A strategic approach for the discounted Shapley values," Theory and Decision, Springer, vol. 80(2), pages 271-293, February.
    • Handle: RePEc:kap:theord:v:80:y:2016:i:2:p:271-293
    DOI: 10.1007/s11238-015-9500-5
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    Cited by:

    1. Surajit Borkotokey & Loyimee Gogoi & Dhrubajit Choudhury & Rajnish Kumar, 2022. "Solidarity induced by group contributions: the MI $$^k$$ k -value for transferable utility games," Operational Research, Springer, vol. 22(2), pages 1267-1290, April.
    2. Marco Rogna, 2022. "The Burning Coalition Bargaining Model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 735-768, October.
    3. Emilio Calvo & Esther Gutiérrez-López, 2018. "Discounted Solidarity Values," Discussion Papers in Economic Behaviour 0418, University of Valencia, ERI-CES.
    4. Calvo, Emilio & Gutiérrez-López, Esther, 2021. "Recursive and bargaining values," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 97-106.
    5. Tomohiko Kawamori, 2016. "Hart–Mas-Colell implementation of the discounted Shapley value," Theory and Decision, Springer, vol. 81(3), pages 357-369, September.
    6. Surajit Borkotokey & Dhrubajit Choudhury & Rajnish Kumar & Sudipta Sarangi, 2023. "A new value for cooperative games based on coalition size," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(4), pages 830-854, December.

    More about this item

    Keywords

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    JEL classification:

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

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