Robust contracting under common value uncertainty

A buyer makes an offer to a privately informed seller for a good of uncertain quality. Quality determines both the seller's valuation and the buyer's valuation, and the buyer evaluates each contract according to its worst-case performance over a set of probability distributions. This paper demonstrates that the contract that maximizes the minimum payoff over all possible probability distributions of quality is a screening menu that separates all types, whereas the optimal contract for any given probability distribution is a posted price, which induces bunching. Using the e-contamination model, according to which the buyer's utility is a weighted average of his single prior expected utility and the worst-case scenario, the analysis further shows that for intermediate degrees of confidence, the optimal mechanism combines features of both of these contracts.