  We study the problem of designing an optimal sequence of incentives that a
principal should offer to an agent so that the agent's optimal behavior under
the incentives realizes the principal's objective expressed as a temporal logic
formula. We consider an agent with a finite decision horizon and model its
decision-making process as a Markov decision process (MDP). Under certain
assumptions, we present a polynomial-time algorithm to synthesize an incentive
sequence that minimizes the cost to the principal. We show that if the
underlying MDP has only deterministic transitions, the principal can hide its
objective from the agent and still realize the desired behavior through
incentives. On the other hand, an MDP with stochastic transitions may require
the principal to share its objective with the agent. Finally, we demonstrate
the proposed method in motion planning examples where a principal changes the
optimal trajectory of an agent by providing incentives.
