Learning to Play Best Response in duopoly Games

We consider a quantity-setting duopoly market where firms lack perfect knowledge of the market demand function. They use estimated and therefore misspecified demand functions instead and determine their optimal strategies from the corresponding subjective payoff functions. The central issue of this paper is the question under which conditions a firm can learn the true demand function as well as the response function of its competitor from repeated estimations of historical market data. As soon as estimation errors are negligible, the correct response function is known and a firm is able to play best response in the usual game theoretic sense.