Learning Against a Strategic Agent in Principal-Agent Games

Principal-Agent interactions, studied within the framework of incentive design problems, deal with the Principal (P) designing strategies such that the Agent's (A's) actions would favor P's cost. It is well known that when A has more information, then P faces a loss in optimality, known as information rent. While a plethora of solutions seek to devise mechanisms to tackle information asymmetry in single-stage games, we consider here the scenario of a principal who learns. Via a prototype incentive design game with continuous types and action sets, we show that P can indeed overcome the information rent through repeated interaction via an explore-then-commit (ETC) incentive policy design, when A responds myopically. We illustrate that the story is more nuanced when the agent responds in a non-myopic fashion.