Inducing Social Optimality in Games via Adaptive Incentive Design

TL;DR

This paper introduces a two-timescale learning framework where a social planner adaptively adjusts incentives to guide strategic agents towards socially optimal outcomes in various game settings, ensuring convergence under certain conditions.

Contribution

It proposes a novel two-timescale learning dynamics that links incentive updates to agents' externalities, achieving social optimality in both atomic and non-atomic games.

Findings

The dynamics converge to socially optimal Nash equilibria under specified conditions.

The method applies to networked quadratic games, Cournot competition, and routing games.

Sufficient conditions for convergence are verified in multiple game models.

Abstract

How can a social planner adaptively incentivize selfish agents who are learning in a strategic environment to induce a socially optimal outcome in the long run? We propose a two-timescale learning dynamics to answer this question in both atomic and non-atomic games. In our learning dynamics, players adopt a class of learning rules to update their strategies at a faster timescale, while a social planner updates the incentive mechanism at a slower timescale. In particular, the update of the incentive mechanism is based on each player's externality, which is evaluated as the difference between the player's marginal cost and the society's marginal cost in each time step. We show that any fixed point of our learning dynamics corresponds to the optimal incentive mechanism such that the corresponding Nash equilibrium also achieves social optimality. We also provide sufficient conditions for the learning dynamics to converge to a fixed point so that the adaptive incentive mechanism eventually induces a socially optimal outcome. Finally, we demonstrate that the sufficient conditions for convergence are satisfied in a variety of games, including (i) atomic networked quadratic aggregative games, (ii) atomic Cournot competition, and (iii) non-atomic network routing games.