Action Recommendations for Sequentially Rational Strategic Agents
This work provides a novel algorithmic framework for a system designer to influence strategic agents in dynamic settings, addressing a known bottleneck in incentive-compatible recommendation systems.
The paper addresses the problem of a system designer sending action recommendations to two strategic agents in a finite-horizon dynamic system, ensuring the agents' obedient strategies are sequentially rational. The authors provide an algorithm that solves a family of linear programs in a backward inductive manner to maximize the designer's objective.
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.