Introduction

In analyzing a cooperative game with incomplete information, three kinds of solution concepts should be considered. First, we should characterize the set of coordination mechanisms or decision rules that are feasible for the players when they cooperate, taking account of the incentive constraints that arise because the players cannot always trust each other. Second, we should characterize the mechanisms that are efficient within this feasible set. Efficiency criteria for games with incomplete information have been discussed in detail by Holmström and Myerson (1983). Third, we should try to identify equitable mechanisms on the efficient frontier that are likely to actually be implemented by the players if they are sophisticated negotiators with equal bargaining ability. (We might also want to consider cases where one player has more bargaining ability than the others, as in principal – agent problems.) For this analysis, a concept of neutral bargaining solution has been axiomatically derived by Myerson (1983, 1984).

In this chapter, two bilateral trading problems with incomplete information are analyzed in terms of these three solution concepts. Sections 7.2 through 7.4 consider the symmetric uniform trading problem, a simple problem in which the buyer and seller each have private information about how much the object being traded is worth to him. This problem was first studied by Chatterjee and Samuelson (1983), and was also considered by Myerson and Satterthwaite (1983).