an:05676176
Zbl 1200.91121
Cohn, Zachary
A note on linked bargaining
EN
J. Math. Econ. 46, No. 2, 238-247 (2010).
00259050
2010
j
91B26 91A35
linked bargaining; mechanism design; Bayesian equilibrium; efficiency
Summary: A recent result by \textit{M. O. Jackson} and \textit{H. F. Sonnenschein} [Econometrica 75, No.~1, 241--257 (2007; Zbl 1201.91036)] 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.
Zbl 1201.91036