Nash equilibrium seeking with infinitely-many players

We introduce a non-model based approach for the stable attainment of a Nash equilibrium in noncooperative static games with infinitely-many (non-atomic) players. In classical game theory algorithms, each player employs the knowledge of the functional form of his payoff and of the other players´ actions, whereas in the proposed algorithm, the players need to measure only their own payoff values. This strategy is based on the extremum seeking approach, which has previously been developed for standard optimization problems and employs sinusoidal perturbations to estimate the gradient of an unknown function. We consider games with quadratic payoff functions, proving convergence to a neighborhood of the Nash equilibrium, and provide simulation results for an example price game.