| Abstract: |
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. |