Achieving cooperation under privacy concerns

Two players choose whether to cooperate on a project. Each of them is endowed with some evidence, and if both possess a sufficient amount, then cooperation is profitable. In order to facilitate cooperation, the players reveal evidence to one another. However, some players are concerned about privacy, and so revelation of evidence that does not result in cooperation is costly. We show that in equilibrium evidence can be exchanged both incrementally and all at once, and identify conditions under which the different rates of evidence exchange are optimal.