Robust pooling for contracting models with asymmetric information

We consider a principal-agent contracting model between a seller and a buyer with single-dimensional private information. The buyer's type follows a continuous distribution on a bounded interval. We present a new modelling approach where the seller offers a menu of finitely many contracts to the buyer. The approach distinguishes itself from existing methods by pooling the buyer types using a partition. That is, the seller first chooses the number of contracts offered and then partitions the set of buyer types into subintervals. All types in a subinterval are pooled and offered the same contract by the design of our menu. We call this approach robust pooling and apply it to a utility maximisation problem adapted from the literature. For this problem we are able to express structural results as a function of a single new parameter, which remarkably does not depend on all instance parameters. We determine the optimal partition and the corresponding optimal menu of contracts. This results in new insights into the (sub)optimality of the equidistant partition. For example, the equidistant partition is optimal for a family of instances. Finally, we derive performance guarantees for the equidistant and optimal partitions for a given number of contracts. For the considered problem the robust pooling approach has good performances when using only a few contracts.

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