Balancing Expected and Worst-Case Utility in Contracting Models with Asymmetric Information and Pooling

We consider a principal-agent contracting problem between a seller and a buyer, where the buyer has single-dimensional private information. The buyer's type is assumed to be continuously distributed on a closed interval. The seller designs a menu of finitely many contracts by pooling the buyer types a priori using a partition scheme. He maximises either his minimum utility, his expected utility, or a combination of both (a multi-objective approach). For each variation, we determine tractable reformulations and the optimal menu of contracts under certain conditions. These results are applied to a contracting problem with quadratic utilities. We show that the optimal objective value is completely determined by the partition scheme, a single aggregate instance parameter, and a parameter encoding the seller's guaranteed obtained utility. This enables us to derive the optimal partition and exact performance guarantees. Our analysis shows that the seller should always offer at least two contracts in order to have reasonable performance guarantees, resulting in at least 88% of the expected utility compared to offering infinitely many contracts. By also optimising obtained worst-case utility, he can potentially achieve only 64% of the maximum expected utility.