# Incentive Design for Temporal Logic Objectives

## TL;DR

This paper presents a polynomial-time method for designing incentives to guide an agent's behavior in MDPs to satisfy temporal logic objectives, balancing cost and information sharing.

## Contribution

It introduces an optimal incentive synthesis algorithm for agents with finite horizons under temporal logic goals, including deterministic and stochastic MDP considerations.

## Key findings

- Deterministic MDPs allow hiding the principal's objective from the agent.
- Stochastic MDPs may require revealing the objective to achieve desired behavior.
- The method is demonstrated in motion planning scenarios with incentive-based trajectory control.

## Abstract

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.