ROMJIST Volume 29, No. 3, 2026, pp. 249-260, DOI: 10.59277/ROMJIST.2026.3.04
Huawei HU, Yuxing XING, Jie WU, Jie CHEN, Radu-Emil PRECUP Toward a Nash Equilibrium for Multi-agent Dynamic Task Assignment via Multi-stage Distributed Potential Game
ABSTRACT: Dynamic task assignment in multi-agent systems aims to distribute limited agent resources among time-varying tasks to improve operational efficiency and reduce completion time. This paper develops a game-theoretic distributed learning framework for dynamic task assignment by modeling the problem as an exact potential game that aligns individual agent utilities with a global performance objective. The task dynamics capture time-varying task loads under fixed agent execution capacities, and an analysis of optimal static assignment characterizes completion-time minimization. Based on this potential game formulation, a synchronous distributed learning algorithm is proposed that utilizes the potential function as a Lyapunov measure, ensuring monotonic improvement and convergence to a pure-strategy Nash equilibrium without centralized coordination. The algorithm relies only on local information and supports parallel updates, enabling scalability and adaptability in dynamic environments. Numerical simulations demonstrate that the proposed method achieves improved convergence behavior and higher task completion efficiency compared with representative baseline algorithms.KEYWORDS: Distributed synchronous optimization; dynamic task assignment; Nash equilibrium; potential game.Read full text (pdf)