The Power of Menus in Contract Design

TL;DR

This paper demonstrates that menus of contracts significantly outperform single contracts in principal-agent problems with adverse selection and moral hazard, offering substantial utility gains through randomized and deterministic menu designs.

Contribution

It establishes the first quantitative bounds showing the advantage of menus over individual contracts in complex principal-agent settings, partially resolving an open research question.

Findings

Menus can provide a factor Omega(max(n, log T)) utility gain over single contracts.

Randomized linear menus can outperform the best linear contract by a factor of Omega(T).

Deterministic menus can be substantially better than randomized menus of contracts.

Abstract

We study the power of menus of contracts in principal-agent problems with adverse selection (agents can be one of several types) and moral hazard (we cannot observe agent actions directly). For principal-agent problems with $T$ types and $n$ actions, we show that the best menu of contracts can obtain a factor $\Omega(\max(n, \log T))$ more utility for the principal than the best individual contract, partially resolving an open question of Guruganesh et al. (2021). We then turn our attention to randomized menus of linear contracts, where we likewise show that randomized linear menus can be $\Omega(T)$ better than the best single linear contract. As a corollary, we show this implies an analogous gap between deterministic menus of (general) contracts and randomized menus of contracts (as introduced by Castiglioni et al. (2022)).