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|
|Contact details of provider:|| Postal: P.O. Box 616, 6200 MD Maastricht|
Phone: +31 (0)43 38 83 830
Web page: http://www.maastrichtuniversity.nl/
More information through EDIRC
References listed on IDEAS
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.:
- 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.
- 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.
- 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.
- 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;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 309-329, 06.
- Kalandrakis, Tasos, 2004. "Equilibria in sequential bargaining games as solutions to systems of equations," Economics Letters, Elsevier, vol. 84(3), pages 407-411, September.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
- Eraslan, Hulya & Merlo, Antonio, 2002.
"Majority Rule in a Stochastic Model of Bargaining,"
Journal of Economic Theory,
Elsevier, vol. 103(1), pages 31-48, March.
- P. Herings & Arkadi Predtetchinski, 2012.
"Sequential share bargaining,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 41(2), pages 301-323, May.
- Ariel Rubinstein, 2010.
"Perfect Equilibrium in a Bargaining Model,"
Levine's Working Paper Archive
661465000000000387, David K. Levine.
- Brian Knight, 2005. "Estimating the Value of Proposal Power," American Economic Review, American Economic Association, vol. 95(5), pages 1639-1652, December.
- Cardona, Daniel & Ponsati, Clara, 2007. "Bargaining one-dimensional social choices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 627-651, November.
- 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.
- Tasos Kalandrakis, 2004. "Proposal Rights and Political Power," Wallis Working Papers WP38, University of Rochester - Wallis Institute of Political Economy.
- Haller, Hans, 1986. "Non-cooperative bargaining of N [ges] 3 players," Economics Letters, Elsevier, vol. 22(1), pages 11-13.
- 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.
- Thomas Romer & Howard Rosenthal, 1978. "Political resource allocation, controlled agendas, and the status quo," Public Choice, Springer, vol. 33(4), pages 27-43, December.
- Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 61-80.
- 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.
- 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.
- Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-399, March.
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: (Leonne Portz)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.