Ugo Bolletta : ugo.bolletta2[at]unibo.it
Mathieu Faure : mathieu.faure[at]univ-amu.fr
We introduce a stochastic learning process designed for games with continuous action sets, called the dampened gradient approximation process, which requires from players no sophistication and no knowledge of the game (i.e. a payoff -based learning process). We show that despite such limited information, players will converge to Nash in large classes of games, as soon as payoff functions are single-peaked. In particular, convergence to a Nash equilibrium which is stable is guaranteed in all games with strategic complements as well as in generalized zero-sum games; convergence to Nash often happens in all locally ordinal potential games; and convergence to Nash occurs with positive probability in all games with isolated equilibria. Our paper shows that it is possible to construct simple payoff-based learning procedures for continuous games with good convergence properties.