A payoff-based learning approach for Nash equilibrium seeking in continuous potential games

Abstract

This work addresses the Nash equilibrium seeking problem in continuous potential games in a situation that the payoff functions and actions of players are blind to each other due to privacy security or communication limitation. To this end, a payoff-based learning dynamics is proposed with the limitation that only available information for each agent is its own past actions and several observed payoffs. In detail, we formulate a trial-and-error learning protocol to search for proper moving direction and length for action adjustment of each agent, and prove that following the proposed learning dynamics, the action profile of agents will be guaranteed to converge to a Nash equilibrium of the continuous potential game. For illustration of the theoretical development, the proposed payoff-based learning dynamics is further utilized to design an absolute distance-based consensus protocol for multi-agent systems. It is shown that agents can eventually reach a consensus point even when they do not know the relative positions with other agents.