Action Recommendations for Sequentially Rational Strategic Agents

2026-05-10

AI Summary

This study addresses the challenge of designing an optimal recommendation mechanism in a finite-horizon discrete-time dynamic system where a system designer cannot directly control the actions of two strategic agents. The designer aims to maximize their own objective by recommending actions based on shared historical information, while ensuring that the agents find it sequentially rational to follow these recommendations, thereby forming a sequential rationality equilibrium. To this end, the paper proposes a novel recommendation mechanism that explicitly satisfies sequential rationality constraints and develops a computationally tractable solution framework combining backward induction with linear programming. This approach achieves, for the first time, the optimization of the designer’s objective under strict sequential rationality conditions, demonstrating both the effectiveness and computational feasibility of the proposed mechanism.

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.

Problem

• sequential rationality
• strategic agents
• action recommendations
• dynamic system
• incentive design

Innovation

• sequential rationality
• action recommendations
• strategic agents
• incentive design
• linear programming