One-dimensional Bargaining with Markov Recognition Probabilities
We study a process of bargaining over social outcomes represented by points in theunit interval. The identity of the proposer is determined by a general Markov process and the acceptance of a proposal requires the approval of it by all the players. We show that for every value of the discount factor below one the subgame perfect equilibrium in stationary strategies is essentially unique and equal to what we call the bargaining equilibrium. We provide a general characterization of the bargaining equilibrium. We consider next the asymptotic behavior of the equilibrium proposals when the discount factor approaches one. We give a complete characterization of the limit of the equilibrium proposals. We show that the limit equilibrium proposals of all the players are the same if the proposer selection process satisfies an irreducibility condition, or more generally, has a unique absorbing set. In general, the limit equilibrium proposals depend on the partition of the set of players in absorbing sets and transient states of the proposer selection process. We fully characterize the limit equilibrium proposals as the unique generalized fixed point of a particular function.This function depends in a simple way on the stationary distribution related to the proposer selection process. We compare the proposal selected according to our bargaining model to the one corresponding to the median voter theorem.
|Date of creation:||2007|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +31 (0)43 38 83 830
Web page: http://www.maastrichtuniversity.nl/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- P. Herings & Arkadi Predtetchinski, 2012.
"Sequential share bargaining,"
International Journal of Game Theory,
Springer, vol. 41(2), pages 301-323, May.
- Rubinstein, Ariel, 1982.
"Perfect Equilibrium in a Bargaining Model,"
Econometric Society, vol. 50(1), pages 97-109, January.
- Seok-ju Cho & John Duggan, 2001.
"Uniqueness of Stationary Equilibria in a one-Dimensional Model of Bargaining,"
Wallis Working Papers
WP23, University of Rochester - Wallis Institute of Political Economy.
- Cho, Seok-ju & Duggan, John, 2003. "Uniqueness of stationary equilibria in a one-dimensional model of bargaining," Journal of Economic Theory, Elsevier, vol. 113(1), pages 118-130, November.
- Cardona, Daniel & Ponsati, Clara, 2007. "Bargaining one-dimensional social choices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 627-651, November.
- Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-99, March.
- Tasos Kalandrakis, 2004. "Proposal Rights and Political Power," Wallis Working Papers WP38, University of Rochester - Wallis Institute of Political Economy.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- Cho, Seok-ju & Duggan, John, 2009.
"Bargaining foundations of the median voter theorem,"
Journal of Economic Theory,
Elsevier, vol. 144(2), pages 851-868, March.
- John Duggan & Seok-ju Cho, 2007. "Bargaining Foundations of the Median Voter Theorem," Wallis Working Papers WP49, University of Rochester - Wallis Institute of Political Economy.
- Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
- Tasos Kalandrakis, 2004.
"Regularity of Pure Strategy Equilibrium Points in a Class of Bargaining Games,"
Wallis Working Papers
WP37, University of Rochester - Wallis Institute of Political Economy.
- Tasos Kalandrakis, 2006. "Regularity of pure strategy equilibrium points in a class of bargaining games," Economic Theory, Springer, vol. 28(2), pages 309-329, 06.
- Brian Knight, 2005. "Estimating the Value of Proposal Power," American Economic Review, American Economic Association, vol. 95(5), pages 1639-1652, December.
- Eraslan, H. & Merlo, A., 2000.
"Majority Rule in a Stochastic Model of Bargaining,"
00-05, C.V. Starr Center for Applied Economics, New York University.
- Eraslan, Hulya, 2002. "Uniqueness of Stationary Equilibrium Payoffs in the Baron-Ferejohn Model," Journal of Economic Theory, Elsevier, vol. 103(1), pages 11-30, March.
- Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 61-80, January.
- Thomas Romer & Howard Rosenthal, 1978. "Political resource allocation, controlled agendas, and the status quo," Public Choice, Springer, vol. 33(4), pages 27-43, December.
- Kalandrakis, Tasos, 2004. "Equilibria in sequential bargaining games as solutions to systems of equations," Economics Letters, Elsevier, vol. 84(3), pages 407-411, September.
- 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.
- Imai, Haruo & Salonen, Hannu, 2000. "The representative Nash solution for two-sided bargaining problems," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 349-365, May.
When requesting a correction, please mention this item's handle: RePEc:unm:umamet:2007044. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Charles Bollen)
If references are entirely missing, you can add them using this form.