A Soft Inducement Framework for Incentive-Aided Steering of No-Regret Players

TL;DR

This paper introduces a framework for guiding no-regret players in repeated games using incentives and information design, establishing fundamental limits and proposing a two-phase approach that improves convergence to desired outcomes.

Contribution

It characterizes when successful steering is possible, derives payment bounds, and proposes a Stackelberg-based method to enhance convergence rates in incentive-aided steering.

Findings

Successful steering depends on game structure.

Constant payments are necessary for certain targets.

Two-phase approach improves convergence speed.

Abstract

In this work, we investigate a steering problem in a mediator-augmented two-player normal-form game, where the mediator aims to guide players toward a specific action profile through information and incentive design. We first characterize the games for which successful steering is possible. Moreover, we establish that steering players to any desired action profile is not always achievable with information design alone, nor when accompanied with sublinear payment schemes. Consequently, we derive a lower bound on the constant payments required per round to achieve this goal. To address these limitations incurred with information design, we introduce an augmented approach that involves a one-shot information design phase before the start of the repeated game, transforming the prior interaction into a Stackelberg game. Finally, we theoretically demonstrate that this approach improves the convergence rate of players' action profiles to the target point by a constant factor with high probability, and support it with empirical results.