The authors provide game theoretic foundations for the classic kinke d demand curve and Edgeworth cycle. In their alternating-move model, there are multiple Markov perfect equilibria of both the kinked deman d curve and Edgeworth cycle variety. In any Markov perfect equilibria , profit is bounded away from the Bertrand equilibria level. A kinked demand curve at the monopoly price is the unique symmetric "renegot iation proof" equilibrium when there is little discounting. The auth ors then endogenize the timing by allowing firms to move at any time. They find that firms end up alternating, thus vindicating the fixed timing assumption of the simpler model.