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Bargaining with commitments

Author

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  • Juan J. Vidal-Puga

Abstract

We study a simple bargaining mechanism in which, given an order of players, the first n−1 players sequentially announce their reservation price. Once these prices are given, the last player may choose a coalition to cooperate with, and pay each member of this coalition his reservation price. The only expected final equilibrium payoff is a new solution concept, the “selective value”, which can be defined by means of marginal contributions vectors of a reduced game. The selective value coincides with the Shapley value for convex games. Moreover, for 3-player games the vectors of marginal contributions determine the core when it is nonempty. Copyright Springer-Verlag 2004

Suggested Citation

  • Juan J. Vidal-Puga, 2004. "Bargaining with commitments," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 129-144, January.
    • Handle: RePEc:spr:jogath:v:33:y:2004:i:1:p:129-144
    DOI: 10.1007/s001820400190
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    Cited by:

    1. Jiawei Li & Tianxiang Cui & Graham Kendall, 2022. "Equilibrium in a Bargaining Game of Two Sellers and Two Buyers," Mathematics, MDPI, vol. 10(15), pages 1-9, July.
    2. Montero, Maria & Vidal-Puga, Juan J., 2011. "Demand bargaining and proportional payoffs in majority games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 395-408, March.
    3. Breitmoser, Yves & Tan, Jonathan H.W., 2013. "Reference dependent altruism in demand bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 92(C), pages 127-140.
    4. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    5. Alfredo Valencia-Toledo & Juan Vidal-Puga, 2020. "A sequential bargaining protocol for land rental arrangements," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 65-99, June.
    6. Maria Montero & Juan Vidal-Puga, 2012. "A Violation of Monotonicity in a Noncooperative Setting," Discussion Papers 2012-04, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    7. Breitmoser, Yves, 2011. "Binomial menu auctions in government formation," MPRA Paper 28576, University Library of Munich, Germany.
    8. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    9. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2006. "Efficient bidding with externalities," Games and Economic Behavior, Elsevier, vol. 57(2), pages 304-320, November.
    10. , & ,, 2014. "Rhetoric in legislative bargaining with asymmetric information," Theoretical Economics, Econometric Society, vol. 9(2), May.
    11. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    12. Yves Breitmoser, 2009. "Demand commitments in majority bargaining or how formateurs get their way," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 183-191, June.
    13. Montero, Maria & Vidal-Puga, Juan J., 2007. "Demand Commitment in Legislative Bargaining," American Political Science Review, Cambridge University Press, vol. 101(4), pages 847-850, November.
    14. Bahel, Eric, 2021. "Hyperadditive games and applications to networks or matching problems," Journal of Economic Theory, Elsevier, vol. 191(C).
    15. Yuan Ju & David Wettstein, 2009. "Implementing cooperative solution concepts: a generalized bidding approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(2), pages 307-330, May.
    16. Gustavo Bergantiños & Juan Vidal-Puga, 2021. "A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 73-100, March.
    17. Chen, Ying & Eraslan, Hülya, 2013. "Rhetoric in legislative bargaining with asymmetric information," Discussion Paper Series In Economics And Econometrics 1309, Economics Division, School of Social Sciences, University of Southampton.
    18. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.
    19. Juan D. Moreno-Ternero & Min-Hung Tsay & Chun-Hsien Yeh, 2020. "A strategic justification of the Talmud rule based on lower and upper bounds," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1045-1057, December.
    20. Breitmoser, Yves & Tan, Jonathan H.W., 2011. "Ultimata bargaining: generosity without social motives," MPRA Paper 33613, University Library of Munich, Germany.

    More about this item

    Keywords

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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