Incomplete Information, Incentive Compatibility and the Core

We consider an exchange economy in which agents possess private information at the time of engaging in state contingent contracts. While com-munication of private information is permitted, the true information state is not verifiable. The enforcement of contracts is, therefore, limited by incentive com-patibility constraints. We formalize a notion of the core for such an economy. Our analysis can be viewed as an attempt to incorporate incentive compatibility in Wilson's [1978] coarse core, or as an attempt to introduce coalitional contracts in the Holmstrom-Myerson [1983] notion of incentive efficiency. While there are some special cases in which the incentive compatible core is non-empty, our main result shows that this is not generally true.