Pooling of Contracts for Outsourcing Problems with Two-Dimensional Asymmetric Information

In this paper, we model an outsourcing problem as a specific principal-agent relationship in which two-dimensional hidden characteristics describe the agent’s type. Assuming that the principal knows the joint probability distribution on the continuous type space, a standard solution technique for the resulting contracting problem is stochastic optimization on the set of incentive compatible menus of contracts from which the agent can choose a single contract according to the take-it-or-leave-it principle, respectively. In practice, however, the menu which maximizes the expected utility for the principal generally consists of infinitely many single contracts and cannot be determined analytically for all kinds of probability distributions. To address this issue, we present a novel two-step approach which, in a first step, partitions the rectangular type space into a predefined number of subsets and, in a second step, computes an optimal incentive compatible menu of contracts containing a mutual contract for each subset of pooled types by using quadratic programming. Within our computational study we finally show that our method not solely bypasses the above described solution difficulties but also guarantees small optimality gaps by using only few contracts.