Action Recommendations for Sequentially Rational Strategic Agents

TL;DR

This paper develops an algorithm for a system designer to send optimal action recommendations to strategic agents in a dynamic setting, ensuring obedient strategies are sequentially rational and maximizing the designer's reward.

Contribution

It introduces a method to compute optimal recommendations using linear programs that incentivize obedient strategies in dynamic multi-agent systems.

Findings

The algorithm guarantees incentive compatibility for agents.

Optimal recommendations are derived via backward induction.

The approach maximizes the designer’s reward under strategic constraints.

Abstract

We consider a finite-horizon discrete-time dynamic system that is jointly controlled by two strategic agents. There is a system designer that has its own reward function but does not have direct control over the agents' actions. We consider an information structure where the current state and all past history are equally accessible by the designer and the agents. The designer sends action recommendations to the agents at each time step. Each agent can use the received recommendation and the available information to choose its action. We are interested in the setting where the designer would like to send recommendations in a way that incentivizes the agents to adopt obedient strategies, i.e., to take the action recommended by the designer. Our goal is to find an optimal action recommendation strategy for the designer that maximizes the designer's objective while ensuring that obedient strategies are \emph{sequentially rational} for the agents. We provide an algorithm for the designer's problem that involves solving a family of linear programs in a backward inductive manner.