Abstract
This paper presents a new extension of the Rubinstein-Ståhl bargaining model to the case with n players, called sequential share bargaining. The bargaining protocol is natural and has as its main feature that the players’ shares in the surplus are determined sequentially rather than simultaneously. The protocol also assumes orderly voting, a restriction on the order in which players respond to a proposal. The bargaining protocol requires unanimous agreement for proposals to be implemented. Unlike all existing bargaining protocols with unanimous agreement, the resulting game has unique subgame perfect equilibrium utilities for any value of the discount factor. The result builds on the analysis of so-called one-dimensional bargaining problems. We show that also one-dimensional bargaining problems have unique subgame perfect equilibrium utilities for any value of the discount factor.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Banks J, Duggan J (2000) A bargaining model of collective choice. Am Polit Sci Rev 94: 73–88
Binmore K (1987) Perfect equilibria in bargaining models. In: Binmore K, Dasgupta P (eds) The economics of bargaining. Basil Blackwell, Oxford, pp 77–105
Binmore K, Osborne MJ, Rubinstein A (1992) Non-cooperative models of bargaining. In: Aumann RJ, Hart S (eds) Handbook of game theory, vol 1. North Holland, Amsterdam, pp 179–225
Cardona D, Ponsataí C (2007) Bargaining one-dimensional social choices. J Econ Theory 137: 627–651
Chae S, Yang J-A (1988) The unique perfect equilibrium of an N-Person bargaining game. Econ Lett 28: 221–223
Chae S, Yang J-A (1994) An N-Person pure bargaining game. J Econ Theory 62: 86–102
Cho SJ, Duggan J (2003) Uniqueness of stationary equilibria in a one-dimensional model of bargaining. J Econ Theory 113: 118–130
Haller H (1986) Non-cooperative bargaining of N ≥ 3 players. Econ Lett 22: 11–13
Hart S, Kurz M (1983) Endogenous formation of coalitions. Econometrica 51: 1047–1064
Herings PJJ, Predtetchinski A (2010) One-dimensional bargaining with Markov recognition probabilities. J Econ Theory 145: 189–215
Herrero M (1985) A strategic bargaining approach to market Institutions. PhD Thesis, London School of Economics, London
Huang C-Y (2002) Multilateral bargaining: conditional and unconditional offers. Econ Theory 20: 401–412
Imai H, Salonen H (2000) The representative nash solution for two-sided bargaining problems. Math Social Sci 39: 349–365
Jun BH (1987) A strategic model of 3-person bargaining. Unpublished paper. State University of New York at Stony Brook
Kalandrakis T (2004) Equilibria in sequential bargaining games as solutions to systems of equations. Econ Lett 84: 407–411
Krishna V, Serrano R (1996) Multilateral bargaining. Rev Econ Stud 63: 61–80
Osborne MJ, Rubinstein A (1990) Bargaining and markets. Academic Press, San Diego
Rubinstein A (1982) Perfect equilibrium in a bargaining model. Econometrica 50: 97–109
Ståhl I (1972) Bargaining theory. Economics Research Institute, Stockholm School of Economics, Stockholm
Suh S-C, Wen Q (2006) Multi-agent bilateral bargaining and the Nash bargaining solution. J Math Econ 42: 61–73
Yang J-A (1992) Another n-Person bargaining game with a unique perfect equilibrium. Econ Lett 38: 275–277
Acknowledgments
The authors would like to thank the Netherlands Organisation for Scientific Research (NWO) for financial support.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Herings, P.JJ., Predtetchinski, A. Sequential share bargaining. Int J Game Theory 41, 301–323 (2012). https://doi.org/10.1007/s00182-011-0286-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-011-0286-6