Averaged sub-gradient method for finding ε -Nash equilibrium in non-cooperative multiplayer games

In non-cooperative multi-player games, an Average Sub-Gradient (ASG) strategy for finding an ε-Nash equilibrium. For convex (but not necessarily strictly convex) individual cost functions, the function convergence of the multi-player game is demonstrated. Applying Tanaka-Yokohama's formula that characterises the Nash equilibrium leads to finding the strategy for each player. A min-max formulation defines the corresponding solution for each player. The main result is proving the reachability of the desired regime, obtaining an explicit upper bound for Tanaka-Yokohama's function decrement. Detailed analyses for two-player and multi-player games are developed. For a class of two-player games with a convex performance function, a set of numerical studies shows the applicability of the proposed method.Highlights A new ASG strategy providing ε-Nash equilibrium in non-cooperative multi-participant games with imprecise mathematical models is suggested.The convergence of the participants' trajectories is proven for convex (not obligatory strictly convex) individual cost functions, and the rate of convergence is estimated.Numerical confirmation of all theoretical claims is evidenced