Fixed-Time Nash Equilibrium Seeking in Non-Cooperative Games

We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a \mathcal{K}\mathcal{L} function with a settling time that can be upper bounded by a positive constant that is independent of the initial conditions of the players, and which can be prescribed a priori by the system designer. The dynamics are model-free, in the sense that the mathematical forms of the cost functions of the players are unknown. Instead, in order to update its own action, each player needs to have access only to real-time evaluations of its own cost, as well as to auxiliary states of neighboring players characterized by a communication graph. Stability and convergence properties are established for both potential games and strongly monotone games. Numerical examples are presented to illustrate our theoretical results.