A dynamic principal‐agent problem as a feedback Stackelberg differential game

We consider situations in which a principal tries to induce an agent to spend effort on accumulating a state variable that affects the well‐being of both parties. The only incentive mechanism that the principal can use is a state‐dependent transfer of her own utility to the agent. Formally, the model is a Stackelberg differential game in which the players use feedback strategies. Whereas in general Stackelberg differential games with feedback strategy spaces the leader's optimization problem has non‐standard features that make it extremely hard to solve, in the present case this problem can be rewritten as a standard optimal control problem. A linear‐quadratic example is used to illustrate our approach.