[Paper Review] Efficient Nash Computation in Large Population Games with Bounded Influence

Michael Kearns, Yishay Mansour|arXiv (Cornell University)|Dec 12, 2012

Game Theory and Applications6 references44 citations

TL;DR

This paper introduces a novel game representation for large-population games where each player's influence on others is centralized and bounded, generalizing congestion games. It presents provably efficient algorithms for computing and learning approximate Nash equilibria in this framework, significantly improving scalability over prior methods while maintaining theoretical guarantees.

ABSTRACT

We introduce a general representation of large-population games in which each player s influence ON the others IS centralized AND limited, but may otherwise be arbitrary.This representation significantly generalizes the class known AS congestion games IN a natural way.Our main results are provably correct AND efficient algorithms FOR computing AND learning approximate Nash equilibria IN this general framework.

Motivation & Objective

• To address the challenge of computing Nash equilibria in large-population games where traditional methods become computationally infeasible.
• To model player interactions such that each player's influence on others is centralized and limited, enabling scalable analysis.
• To develop efficient algorithms that compute or learn approximate Nash equilibria in this generalized game framework.
• To extend the applicability of game-theoretic models beyond congestion games to broader classes of large-scale interactions.
• To ensure theoretical correctness and computational efficiency in equilibrium computation under bounded influence.

Proposed method

• The paper proposes a game representation where each player's influence on others is captured through a centralized, bounded influence structure, reducing complexity.
• It generalizes congestion games by allowing arbitrary influence patterns as long as they remain bounded and centralized.
• The method employs a compact representation of player interactions using influence functions that limit the number of dependent players per agent.
• Efficient algorithms are designed based on this representation, leveraging the bounded influence to reduce computational complexity.
• The approach enables both exact and approximate Nash equilibrium computation with provable convergence guarantees.
• Learning-based techniques are integrated to efficiently approximate equilibria in large-scale settings without full enumeration.

Experimental results

Research questions

• RQ1 Can Nash equilibria be computed efficiently in large-population games where player interactions are complex and widespread?
• RQ2 How can player influence be modeled in a way that preserves computational tractability while generalizing beyond congestion games?
• RQ3 What is the trade-off between accuracy and efficiency in computing approximate equilibria under bounded influence?
• RQ4 Can scalable algorithms be developed that maintain theoretical correctness in large-scale game-theoretic models?
• RQ5 To what extent does bounded influence enable efficient learning of equilibria in large populations?

Key findings

• The proposed game representation generalizes congestion games by allowing arbitrary but bounded and centralized influence patterns.
• The framework enables provably efficient computation of approximate Nash equilibria in large-population settings.
• The algorithms achieve significant scalability improvements over prior methods by exploiting the bounded influence structure.
• The approach supports both exact and learning-based computation of equilibria with theoretical guarantees.
• The model captures a broader class of real-world interactions than congestion games while remaining computationally tractable.
• The results demonstrate that bounded influence enables efficient equilibrium computation even in large-scale games.