Nash equilibrium seeking in non-convex multi-player game

Abstract: Seeking Nash equilibria (NE) in non-cooperative games has been widely investigated in social sciences and engineering. A strategy profile is called NE if no player can profit from unilaterally deviating from its own strategy. Attributed to the underlying non-convexity in many practical problems such as machine learning sensor localization and energy storage management, obtaining the existence condition of a global NE instead of a local or approximate NE is challenging, let alone designing theoretically guaranteed algorithms.

In this talk, I will present my research work on addressing these challenges. Firstly, I will discuss the existence condition of the global NE by employing the canonical duality theory to deal with the non-convexity in payoff functions. Then I will introduce a conjugate-based ordinary differential equation (ODE) with the assisted complementary dual information to compute the NE. Finally, I will focus on a class of non-convex sensor network localization problems and discuss a distributed implementation to seek NE therein.