Abstract
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.
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Long, N.V., Sorger, G. A dynamic principal-agent problem as a feedback Stackelberg differential game. Cent Eur J Oper Res 18, 491–509 (2010). https://doi.org/10.1007/s10100-010-0172-5
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DOI: https://doi.org/10.1007/s10100-010-0172-5