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John Fithian, president of the National Association of Theatre Owners, said cinema operators already are under pressure to spend billions of dollars to upgrade their venues with digital projectors and 3-D capable screens to support a format that kept North American box office revenues from declining last year.

“Absolutely the wrong time to experiment with risky models is when that massive investment is being made,” Mr. Fithian said.

Small art-house theaters may especially be at risk, said Stephen Gyllenhaal, an independent film director and the father of Hollywood stars Jake and Maggie Gyllenhaal.

If smaller ticket sales result in theater closures, independent filmmakers will lose an important venue to promote their films, he said.

“I’m interested in protecting those theaters,” he said. “They are our direct line to an audience.”