  Consider the relationship between a regulator (the principal) and an
experimenter (the agent) such as a pharmaceutical company. The pharmaceutical
company wishes to sell a drug for profit, whereas the regulator wishes to allow
only efficacious drugs to be marketed. The efficacy of the drug is not known to
the regulator, so the pharmaceutical company must run a costly trial to prove
efficacy to the regulator. Critically, the statistical protocol used to
establish efficacy affects the behavior of a strategic, self-interested agent;
a lower standard of statistical evidence incentivizes the agent to run more
trials that are less likely to be effective. The interaction between the
statistical protocol and the incentives of the pharmaceutical company is
crucial for understanding this system and designing protocols with high social
utility. In this work, we discuss how the regulator can set up a protocol with
payoffs based on statistical evidence. We show how to design protocols that are
robust to an agent's strategic actions, and derive the optimal protocol in the
presence of strategic entrants.
