Chatterje, Kalyan and Dutta, Bhaskar (2006) Markets with bilateral bargaining and incomplete information. Working Paper. University of Warwick, Department of Economics, Coventry.

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Abstract

We study the relationship between bargaining and competition with incomplete information. We consider a model with two uninformed and identical buyers and two sellers. One of the sellers has a privately-known reservation price, which can either be Low or High. The other seller’s reservation price is commonly known to be in between the Low and High values of the privately-informed seller. Buyers move in sequence, and make offers with the second buyer observing the offer made by the first buyer. The sellers respond simultaneously. We show that there are two types of (perfect Bayes) equilibrium. In one equilibrium, the buyer who moves second does better. In the second equilibrium, buyers’ expected payoffs are equalised, and the price received by the seller with the known reservation value is determined entirely by the equuilibrium of the two-player game between a single buyer and an informed seller. We also discuss extensions of the model to multiple buyers and sellers, and to the case where both sellers are privately informed.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Equilibrium (Economics), Bargaining, Competition, Game theory
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Date:	10 September 2006
Number:	No.762
Number of Pages:	32
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Economic and Social Research Council (Great Britain) (ESRC)
Grant number:	RES-000-22-0341 (ESRC)
References:	Ausubel, L.M., Cramton, P. and Deneckere, R. (2002). Bargaining with incomplete information, in Aumann, R.J. and Hart, S., eds., Handbook of Game Theory, Vol. 3, Amsterdam: Elsevier Science B.V., Chapter 50, pp.1897-1945. Binmore, K.G. and Herrero, M. (1988). Matching and bargaining in dynamic markets. Review of Economic Studies, 55, pp.17-32. Chatterjee, K. and Dutta, B. (1998). Rubinstein auctions: On competition for bargaining partners. Games and Economic Behavior, 23(2), pp.119-145. Chatterjee, K. and Samuelson, L. (1988). Bargaining under twosided incomplete information: the unrestricted offers case. Operations Research, 36(4), pp.605-618. Deneckere, R. and Liang, M.-Y. (2001). Bargaining with interdependent values. UWO Department of Economics Working Papers 20017. Fudenberg, D., Levine, D. and Tirole, J. (1985). Infinite horizon models of bargaining with incomplete information, in Roth, A.E. (Ed.) Game-Theoretic models of bargaining, Cambridge University Press, Cambridge and New York. Fudenberg, D., Levine, D. and Tirole, J. (1987). Incomplete information bargaining with outside opportunities. Quarterly Journal of Economics, 102(1), pp.37-50. Fudenberg, D. and Tirole, J. (1991). Game theory. MIT Press, Cambridge, Ma. Gale, D. (1986). Bargaining and competition: Part 1, Characterization. Econometrica, 54, pp.785-806. Hendon, E. & Torben, T. (1991). Sequential bargaining in a market with one seller and two different buyers. Games and Economic Behavior, Elsevier, vol. 3(4), pp.453-466, November. Rubinstein, A. and Wolinsky, A. (1985). Equilibrium in a market with sequential bargaining. Econometrica, 53, 1133-1150. Rubinstein, A. and Wolinsky, A. (1990). Decentralised trading, strategic behaviour and the Walrasian outcome. Review of Economic Studies, 57, pp.63-78. Samuelson, L. (1992). Disagreement in markets with matching and bargaining. Review of Economic Studies, 59, pp.177-186. Shubik, M. (1982). Game Theory in the social sciences, Vol.1, Concepts and solutions. MIT Press, Cambridge, Ma. Sobel, J. and Takahashi, I. (1983). A multistage model of bargaining. Review of Economic Studies, 50, pp.411-426.
URI:	http://wrap.warwick.ac.uk/id/eprint/37

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