  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.
