Dynamic Exploitation of Myopic Best Response

How can a rational player manipulate a myopic best response player in a repeated two-player game? We show that in games with strategic substitutes or strategic complements the optimal control strategy is monotone in the initial action of the opponent, in time periods, and in the discount rate. As an interesting example outside this class of games we present a repeated textbook-like Cournot duopoly with nonnegative prices and show that the optimal control strategy involves a cycle.