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Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index


  • Laruelle, Annick
  • Valenciano, Federico


In this paper we explore the noncooperative foundations of the bargaining power that a voting rule gives to each member of a committee that bargains in search of consensus over a set of feasible agreements under a voting rule. Assuming complete information, we model a variety of bargaining protocols and investigate their stationary subgame perfect equilibria. We show how the Shapley-Shubik index and other power indices can be interpreted as measures of 'bargaining power' that appear in this light as limit cases.

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  • Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
  • Handle: RePEc:eee:gamebe:v:63:y:2008:i:1:p:341-353

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    References listed on IDEAS

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    10. Laruelle, Annick & Valenciano, Federico, 2007. "Bargaining in committees as an extension of Nash's bargaining theory," Journal of Economic Theory, Elsevier, vol. 132(1), pages 291-305, January.
    11. Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992. "Noncooperative models of bargaining," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 7, pages 179-225 Elsevier.
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    Cited by:

    1. Okada, Akira, 2011. "Coalitional bargaining games with random proposers: Theory and application," Games and Economic Behavior, Elsevier, vol. 73(1), pages 227-235, September.
    2. Houba, Harold & van der Laan, Gerard & Zeng, Yuyu, 2014. "Asymmetric Nash Solutions in the River Sharing Problem," Strategic Behavior and the Environment, now publishers, vol. 4(4), pages 321-360, December.
    3. Di Giannatale, Paolo & Passarelli, Francesco, 2013. "Voting chances instead of voting weights," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 164-173.
    4. Herings P. Jean-Jacques & Britz Volker & Predtetchinski Arkadi, 2012. "On the Convergence to Nash Bargaining Solution for Endogenous Bargaining Protocols," Research Memorandum 030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. Masanori Mitsutsune & Takanori Adachi, 2014. "Estimating noncooperative and cooperative models of bargaining: an empirical comparison," Empirical Economics, Springer, vol. 47(2), pages 669-693, September.
    6. Eklund, Patrik & Rusinowska, Agnieszka & De Swart, Harrie, 2007. "Consensus reaching in committees," European Journal of Operational Research, Elsevier, vol. 178(1), pages 185-193, April.
    7. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2011. "On the asymptotic uniqueness of bargaining equilibria," Economics Letters, Elsevier, vol. 111(3), pages 243-246, June.
    8. Drouvelis, Michalis & Montero, Maria & Sefton, Martin, 2010. "Gaining power through enlargement: Strategic foundations and experimental evidence," Games and Economic Behavior, Elsevier, vol. 69(2), pages 274-292, July.
    9. Bram Driesen, 2016. "Bargaining, conditional consistency, and weighted lexicographic Kalai-Smorodinsky Solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 777-809, April.
    10. Akira Okada, 2015. "Cooperation and Institution in Games," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 1-32, March.
    11. Maria Montero, 2015. "A Model of Protocoalition Bargaining with Breakdown Probability," Games, MDPI, Open Access Journal, vol. 6(2), pages 1-18, April.
    12. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2014. "On the convergence to the Nash bargaining solution for action-dependent bargaining protocols," Games and Economic Behavior, Elsevier, vol. 86(C), pages 178-183.
    13. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 189-215, January.
    14. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "Non-cooperative support for the asymmetric Nash bargaining solution," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1951-1967, September.
    15. Moellers, Claudia & Normann, Hans-Theo & Snyder, Christopher M., 2017. "Communication in vertical markets: Experimental evidence," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 214-258.
    16. repec:eee:matsoc:v:89:y:2017:i:c:p:10-19 is not listed on IDEAS
    17. García-Valiñas, Maria A. & Zaporozhets, Vera, 2015. "Key-drivers of EU budget allocation: Does power matter?," TSE Working Papers 15-548, Toulouse School of Economics (TSE).
    18. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2015. "Delay, multiplicity, and non-existence of equilibrium in unanimity bargaining games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 192-202.
    19. Widgrén, Mika, 2008. "The Impact of Council Voting Rules on EU Decision-Making," Discussion Papers 1162, The Research Institute of the Finnish Economy.
    20. repec:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-017-0567-9 is not listed on IDEAS

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