To me, it is a numbers game. I would want to draw new customers to my operation who had not tried me before. I suspect that 90%+ will be price 'hoes looking for a the best they can get for the cheap pricing. Somewhere in that pack will possibly emerge a coupe or four customers who are quality customers who just had an excuse to try me with a coupon. If I attract four customers who become loyal/long term, then it will be a huge score. Remember that a loyal customer is worth something like $800+ per year (don’t remember the number or the source).
There are many other ways to attract customers . . . but, as a piec of a strategic marketing plan, this could be a keeper. Don’t do it as a gimmick or you’ll get burned. Part of a well conceived PLAN that ahs several facets and very clear GOALS for what you want to accomplish with the coupon promotion. Even set your POS to track which people bring in those coupons so you can see if you are getting skinned by one or two people.
Aggressive marketing is Dave Ostrander’s mantra. 100% guarantee on the OTHER guy’s pizza is one he used. Offer to your customers a chance to try the other guy, and if it isn’t up to YOUR quality they’ve come to love, then replace it with an equal pie . . . ONCE. No one should suffer poor pizza, but going back again is just dumb. Yopu gotta be top of the market with taste, quality and service before offering these kinds of deals, though.
Make that plan and see if the accepting of competitor coupons fits into the overall plan and identity of your shop.