Mechanisms for a No-Regret Agent: Beyond the Common Prior

TL;DR

This paper reformulates mechanism design as a reinforcement learning problem, removing the need for common priors by allowing both principal and agent to learn over time through repeated interactions, using behavioral assumptions based on counterfactual internal regret.

Contribution

It introduces a new approach to mechanism design that does not rely on common priors, using reinforcement learning and behavioral assumptions to achieve natural benchmarks.

Findings

Mechanisms attain natural benchmarks without assumptions on the state process.

Reformulation as a reinforcement learning problem enables adaptive mechanism design.

Novel behavioral assumptions based on counterfactual internal regret are central to the approach.

Abstract

A rich class of mechanism design problems can be understood as incomplete-information games between a principal who commits to a policy and an agent who responds, with payoffs determined by an unknown state of the world. Traditionally, these models require strong and often-impractical assumptions about beliefs (a common prior over the state). In this paper, we dispense with the common prior. Instead, we consider a repeated interaction where both the principal and the agent may learn over time from the state history. We reformulate mechanism design as a reinforcement learning problem and develop mechanisms that attain natural benchmarks without any assumptions on the state-generating process. Our results make use of novel behavioral assumptions for the agent -- centered around counterfactual internal regret -- that capture the spirit of rationality without relying on beliefs.