Group-Based Joint Strategy Fictitious Play With Inertia for Potential Games

We propose a novel fictitious-play-based learning algorithm, called group-based joint strategy fictitious play (GJSFP) with inertia, to seek group-based Nash equilibria of group-based generalized ordinal potential games. The proposed GJSFP with inertia enables group-based Nash equilibria to possess an “ab sorption” property, and allows group-based generalized ordinal potential games to converge to group-based Nash equilibria under somecertain conditions. Notably, the convergence of group-based generalized ordinal potential games without additional conditions can be guaranteed under a fading memory GJSFP with inertia. For group-based networked potential games, fading memory GJSFP with inertia ensures that such games converge to a profile that is both a group-based Nash equilibrium and an individual-based Nash equilibrium.