Online distributed NE seeking for multi-agent noncooperative games with time-varying delays

This paper investigates noncooperative online games in multi-agent systems with time-delay feedback constraints. In these games, all players individually minimize their own time-varying costs, yet these costs are coupled through the joint strategies of the entire group. The gradient feedback available to the player is subject to unknown, heterogeneous delays that vary across players and time instants. To address these challenges, a distributed online gradient-descent algorithm is developed to seek the time-varying Nash equilibrium in the game. The algorithm is proven to achieve a sublinear dynamic regret bound via an appropriate learning rate, provided that the path variations grow sublinearly. Finally, an online electricity market game with time-varying delays is provided to illustrate the effectiveness of the algorithm.