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Presumably, regular customers also react to these free offers. You always get your pizza from A, but because it's free you try B. Perhaps B think their pizzas are better. Perhaps B just offer you free pizzas long enough to break your habit with A, and your habit becomes B. Or you tend to stick with Italian, but because it's free you try Thai, and you find you like it. Businesses have many reasons for subsidising free promotions.

Mind you, I haven't done the math on this, and presumably neither have the participating restaurants. However, the logic is sound, and becomes even sounder if you treat a restaurant owner to a couple of glasses of wine.