How do movie studios align the incentives of theaters?

In the 1930's a series of antitrust settlements resulted in separation of studio/theatre ownership.  This inevitably led to incentive conflict between studios and theaters over price, promotion, placement, among other things.

Disney aligns incentives of theaters on price by taking a bigger revenue split on popular movies (60% instead of 50%), but also by computing its revenue based on nationwide average tickets prices (even if the theatre charges less).

Mr. Fithian’s biggest concern in the letter was Disney’s proposal to use a national-average ticket price, published by NATO, as the minimum price on which Disney will split box-office revenue, even if a given theater charges less.

Such minimums are a standard tool used by studios, which cannot dictate the prices theaters charge [due to antitrust laws], to ensure they are not subject to steep discounts. Deep discounting could otherwise be attractive to theater operators looking to get more people in the door and sell them popcorn and soda.