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A Linearly Convergent Distributed Nash Equilibrium Seeking Algorithm for Aggregative Games Over Time-Varying
IEEE Transactions on Cybernetics
|February 10, 2026
Summary
This study introduces a distributed algorithm to find Nash equilibrium in complex games with constraints. The method ensures convergence even with changing network conditions and constraints.
Area of Science:
- Control Theory
- Game Theory
- Networked Systems
Background:
- Distributed computation of Nash equilibrium (NE) is challenging.
- Time-varying unbalanced communication graphs introduce complexity.
- Local closed convex set constraints require specialized handling.
Purpose of the Study:
- To develop a distributed discrete-time algorithm for computing Nash equilibrium.
- To address challenges posed by time-varying unbalanced graphs and set constraints.
- To analyze the convergence properties and step-size bounds of the proposed algorithm.
Main Methods:
- A novel distributed discrete-time NE seeking algorithm is proposed.
- Combines average tracking and push-sum protocols for aggregate estimation.
- Employs the method of feasible direction to manage set constraints.
Main Results:
- The algorithm achieves linear convergence, proven using the small gain theorem.
- Explicit estimates for step-size upper bounds are derived.
- Numerical simulations confirm the algorithm's effectiveness in a Nash-Cournot game.
Conclusions:
- The proposed distributed algorithm effectively computes Nash equilibrium under dynamic and constrained conditions.
- The theoretical analysis provides guarantees on convergence and step-size selection.
- The findings are validated through practical simulations, demonstrating real-world applicability.
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