We provide game theoretic foundations for the classic kinked demand curve equilibrium and Edgeworth cycle. We analyze a model in which firms take turns choosing prices; the model is intended to capture the idea of reactions based on short-run commitment. In a Markov perfect equilibrium (MPE), a firm's move in any period depends only on the other firm's current price. There are multiple MPE's, consisting of both kinked demand curve equilibria and Edgeworth cycles. In any MPE, profit is bounded away from the Bertrand equilibrium level. We show that a kinked demand curve at the monopoly price is the unique symmetric "renegotiation proof" equilibrium when there is little discounting. We then endogenize the timing by allowing firms to move at any time subject to we short-run commitments. We find that firms end up alternating, thus vindicating the ad hoc timing assumption of our simpler model. We also discuss how the model can be enriched to provide explanations for excess capacity and market sharing.