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Two-Stage Bargaining with Reversible Coalitions: the Case of Apex Games

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  • Montero, Maria

    (University of Nottingham)

Abstract

This paper studies coalition formation and payoff division in a class of majority games (apex games) assuming that payoff division can only be agreed upon after forming the coalition (two-stage bargaining) and that negotiations in the coalition can break down and a new coalition be formed (reversible coalitions). In contrast with the results of other two-stage models, all minimal winning coalitions may form and expected payoffs coincide with the per capita nucleolus. These results are robust to small changes in the bargaining procedure. Surprisingly, having a two-stage process (rather than a one-stage process with simultaneous coalition formation and payoff division) benefits the apex player.

Suggested Citation

  • Montero, Maria, 2003. "Two-Stage Bargaining with Reversible Coalitions: the Case of Apex Games," Royal Economic Society Annual Conference 2003 157, Royal Economic Society.
  • Handle: RePEc:ecj:ac2003:157
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    References listed on IDEAS

    as
    1. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    2. repec:cup:apsrev:v:83:y:1989:i:04:p:1181-1206_08 is not listed on IDEAS
    3. Kalyan Chatterjee & Bhaskar Dutia & Debraj Ray & Kunal Sengupta, 2013. "A Noncooperative Theory of Coalitional Bargaining," World Scientific Book Chapters,in: Bargaining in the Shadow of the Market Selected Papers on Bilateral and Multilateral Bargaining, chapter 5, pages 97-111 World Scientific Publishing Co. Pte. Ltd..
    4. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    5. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475.
    6. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    7. Montero, M.P., 2001. "The Nucleolus as a Consistent Power Index in Noncooerative Majority Games," Discussion Paper 2001-39, Tilburg University, Center for Economic Research.
    8. Slikker, M., 2000. "Decision making and cooperation restrictions," Other publications TiSEM 61eead41-85c7-4ded-81c4-e, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    coalition formation; two-stage bargaining; reversible coalitions; apex games; per capita nucleolus;

    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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