Approximate Equilibrium and Incentivizing Social Coordination

TL;DR

This paper develops algorithms to incentivize self-interested agents to coordinate socially desirable strategies in complex games, ensuring near-stable solutions with minimal incentives, applicable to various real-world scenarios.

Contribution

It introduces methods to compute approximate equilibria and near-optimal solutions with small incentives in coordination games with diverse preferences and complementarities.

Findings

Efficient algorithms for approximate equilibrium computation

Near-optimal solutions stabilized by small payments

Stability factor linear in complementarity degree

Abstract

We study techniques to incentivize self-interested agents to form socially desirable solutions in scenarios where they benefit from mutual coordination. Towards this end, we consider coordination games where agents have different intrinsic preferences but they stand to gain if others choose the same strategy as them. For non-trivial versions of our game, stable solutions like Nash Equilibrium may not exist, or may be socially inefficient even when they do exist. This motivates us to focus on designing efficient algorithms to compute (almost) stable solutions like Approximate Equilibrium that can be realized if agents are provided some additional incentives. Our results apply in many settings like adoption of new products, project selection, and group formation, where a central authority can direct agents towards a strategy but agents may defect if they have better alternatives. We show that for any given instance, we can either compute a high quality approximate equilibrium or a near-optimal solution that can be stabilized by providing small payments to some players. We then generalize our model to encompass situations where player relationships may exhibit complementarities and present an algorithm to compute an Approximate Equilibrium whose stability factor is linear in the degree of complementarity. Our results imply that a little influence is necessary in order to ensure that selfish players coordinate and form socially efficient solutions.