Predefined-Time Convergence Method for Resolving Player Conflict of Interest in Multi-Coalition Games

This paper investigates the inherent conflict between individual and collective interests within multi-coalition games. Unlike traditional noncooperative frameworks where players solely optimize a collective objective, our model incorporates individual player preferences, naturally formulating a constrained multi-objective game. To address this, we introduce an endogenous preference weight factor to scalarize the multi-objective problem into a tractable single-objective game. Furthermore, we propose distributed game strategies equipped with predefined-time convergence to compute the Nash equilibrium of the multi-coalition game, alongside the weight factors. Subsequently, consensus protocols and gradient descent methods are synthesized to locate the weighted Nash equilibrium of the scalarized game. The rigorous predefined-time convergence of the proposed algorithm is established via Lyapunov stability theory. Finally, numerical simulations validate the efficacy and superiority of the proposed framework.