We analyze competitive information design games between two designers who want to influence the final action of a decision-maker. Each designer  controls the public information on a private  persistent state:  in each period, the designers can disclose information to the decision-maker about their own state. Using tools from  repeated games with incomplete information on both sides, we study and characterize equilibrium  payoffs and strategies depending on the timing of the game  and the possible deadline. Our analysis covers standard environments with no constraint on the information disclosure policies as well as environments in which designers have restrictions on the statistical experiments they can use. In the latter framework, there may be no  bound on the number of disclosure stages required at equilibrium. We apply our results to competition in product demonstration and show that less information is revealed when firms have no deadline to disclose information.