A note on linked bargaining

• Published in: Journal of mathematical economics 2010-03, Vol.46 (2), p.238-247
• Main Author: Cohn, Zachary
• Format: Article
• Language: English
• Subjects: Bargaining; Bayesian analysis; Bayesian equilibrium; Bayesian method; Decision making; Distribution; Efficiency; Equilibrium; Game theory; Linked bargaining; Linked bargaining Mechanism design Bayesian equilibrium Efficiency; Mechanism design; Studies; Utility functions
• ISSN: 0304-4068; 1873-1538
• DOI: 10.1016/j.jmateco.2009.11.010

A recent result by Jackson and Sonnenschein (2007) describes a general framework for overcoming incentive constraints by linking together independent copies of a Bayesian decision problem. A special case of that work shows that if copies of a standard two-player Bayesian bargaining problem are independently linked (players receive valuations and trade simultaneously on a number of identical copies), then the utility cost associated with incentive constraints tends to 0 as the number of linked problems tends to infinity. We improve upon that result, increasing the rate of convergence from polynomial to exponential and eliminating unwanted trades in the limit, by introducing a mechanism that uses a slightly richer and more refined strategy space. Although very much in the same spirit, our declarations are constrained by a distribution which is skewed away from the expected distribution of player types. When a sufficiently large number of bargaining problems are linked, “truth” is an equilibrium. Moreover, this equilibrium is incentive compatible with the utility cost of incentive constraints almost surely equal to 0.