This is a sad sign of the times: The exhibition chain has decided it must give customers a special incentive to respect the movies, and each other. It unveiled today CineMode — a component within its iPhone and Android smartphone app — that can determine whether the owner uses the mobile device during a film, and send digital coupons to those who leave them alone. “It is important to develop tools that maximize and preserve the movie-going experience,” says Cinemark’s marketing and communications VP James Meredith. He adds that customers have asked the chain to “design an alternative and creative solution” to keep others from lighting up their phones in the dark theater. Before a film starts, Cinemark will flash a message on the movie screen urging customers to launch CineMode. The app will dim the smartphone’s screen and ask users to turn the volume off so incoming calls only cause the phone to vibrate. Customers must stay in CineMode throughout the film. If they do, then the company says it will automatically send a coupon to be stored in the app’s Rewards section. Exhibition execs are struggling to find a strategy to satisfy the growing number of patrons who won’t leave their phones alone in the theater, as well as those who want to preserve the traditional experience. Some have said they’d consider scheduling separate screenings of a film designating ones where texting would be allowed, and others where it wouldn’t.