Adaptive Incentive Design

We apply control theoretic and optimization techniques to adaptively design incentives for principal-agent problems in which the principal faces adverse selection in its interaction with multiple agents. In particular, the principal's objective depends on data from strategic decision makers (agents) whose decision-making process is unknown a priori. We consider both the cases where agents play best response to one another (Nash) and where they employ myopic update rules. By parametrizing the agents' utility functions and the incentives offered, we develop an algorithm that the principal can employ to learn the agents' decision-making processes while simultaneously designing incentives to change their response to one that is more desirable. We provide convergence results for this algorithm both in the noise-free and noisy cases and present illustrative examples.