We study a single-agent contracting environment where the agent has misspecified beliefs about the outcome distributions for each chosen action. First, we show that for a myopic Bayesian learning agent with only two possible actions, the empirical frequency of the chosen actions converges to a Berk-Nash equilibrium. However, through a constructed example, we illustrate that this convergence in action frequencies fails when the agent has three or more actions. Furthermore, with multiple actions, even computing an $\varepsilon$-Berk-Nash equilibrium requires at least quasi-polynomial time under the Exponential Time Hypothesis (ETH) for the PPAD-class. This finding poses a significant challenge to the existence of simple learning dynamics that converge in action frequencies. Motivated by this challenge, we focus on the contract design problems for an agent with misspecified beliefs and two possible actions. We show that the revenue-optimal contract, under a Berk-Nash equilibrium, can be computed in polynomial time. Perhaps surprisingly, we show that even a minor degree of misspecification can result in a significant reduction in optimal revenue.

翻译：我们研究一个单代理人契约环境，其中代理人对于每个所选行动的结果分布持有误设信念。首先，我们证明对于一个仅具有两种可能行动的短视贝叶斯学习代理人，所选行动的实证频率会收敛至一个Berk-Nash均衡。然而，通过一个构造性示例，我们阐明当代理人具有三种或更多行动时，这种行动频率的收敛性不再成立。此外，在具有多种行动的情况下，即便计算一个$\varepsilon$-Berk-Nash均衡，在PPAD类问题的指数时间假设（ETH）下，也至少需要拟多项式时间。这一发现对存在能够收敛于行动频率的简单学习动态构成了重大挑战。受此挑战启发，我们聚焦于信念误设且仅有两种可能行动的代理人的契约设计问题。我们证明，在Berk-Nash均衡下，收益最优的契约可以在多项式时间内计算得出。可能令人惊讶的是，我们表明即使轻微的信念误设也可能导致最优收益的显著降低。