Contracting Between Two Parties with Private Information

A risk averse buyer and seller contract over the trade of an item. At the time of trading they each privately know their value s and cost r respectively, but these are not known when the contract is drawn up. The contract specifies a Bayesian revelation mechanism for implementing a trading rule and prices, as functions of their types s and r. An optimal (second-best) contract balances the goal of efficient trading and risk sharing against the need to provide the agents with incentives to reveal their type truthfully. An optimal contract is characterized. First, it is efficient to have some insurance from a third party: even though neither the buyer nor the seller will be fully insured, there is no need for the buyer to be exposed to the seller's risk or vice versa. Second, there will be less than first-best trade (underproduction). Third, once they have privately learnt their type—but before they have played the mechanism—both the buyer and the seller prefer that the final outcome will be trade rather than no trade. Fourth, although the trade prices increase with s and r, the rest of the contract need not be monotonic. This lack of monotonicity means that the standard methodology fails: it is not enough simply to appeal to local incentive compatibility, since global incentive constraints may bind. A nonstandard technique has to be used to find the nature of the second-best distortions.