  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 KL 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.
