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)).

翻译：我们研究了逆向选择（代理人可以是若干类型之一）和道德风险（无法直接观察代理人行动）情境下委托-代理问题中合同菜单的力量。针对具有$T$种类型和$n$种行动的委托-代理问题，我们证明：最优合同菜单为委托人带来的效用比最优单一合同高出因子$\Omega(\max(n, \log T))$，部分解决了Guruganesh等人（2021）提出的开放性问题。随后，我们关注随机线性合同菜单，同样证明随机线性菜单可比最优单一线性合同提升$\Omega(T)$的效用。作为推论，我们表明这揭示了确定性（一般）合同菜单与随机合同菜单（由Castiglioni等人（2022）引入）之间的类似差距。