Optimal timing of tv commercials: symmetrical model

In this paper I study the behavior of two TV broadcasters on a market where viewers perpetually make a decision whether to watch TV and which TV channel to watch. Both broadcasters optimally allocate time periods where their TV program is replaced by advertising. While TV programs represent broadcaster's costs, commercials bring in revenue that is proportional to the audience reach. I assume that viewers choose among products and the outside option following a Markov process where probabilities of transition reflect various attractiveness of the products. Given symmetrical positions of the broadcasters, I prove that their optimal strategy is to put their commercial breaks into the same or very close times. In the case when commercials overlap perfectly, both broadcasters are better off if they fragment their breaks into shorter breaks keeping the total amount of commercial time the same.