businesses regularly offer discounts to attract customers, especially in zero-sum markets (such as supermarkets) where attracting a new customer essentially means stealing one away from some other retailer. The discount is a fixed amount, usually done with a coupon or electronic savings card (such as the Safeway card).

In applying a solution in search of a problem, I realized that in psychology classes we are taught that variable rates of reinforcment are much more powerful motivators of behavior than fixed schedules. So if you want to train gamblers to put money into your machines and pull the lever, it is much more effective to randomly give payouts than to give them on a fixed schedule such as every 5th pull. Rats trained to press a lever will persist much longer if the rewards come on average every nth press rather than if they are on a fixed schedule of every nth press. If you want to train your dog to do something it is better to occasionally give a reward than to give a reward every time because dogs trained this latter way quickly lose interest when no reward comes.

So with this principle in mind, why do stores give rewards on a fixed 1:1 schedule? It would be more powerful if they gave the same dollar amount in discounts but instead had them average that amount over several shopping trips instead of giving the fixed amount each trip. An ideal business for this is one where many small items of (to a first order) similar price are purchased, and one example that pops to mind is the neighborhood supermarket.

Given this idea, there are lots of ways to run with it. On the one hand you could award each customer free their 100th item on average purchased. This is roughly the same as a 1% discount but you never know what item it will be since it isn't the 100th item exactly, its just that if you purchase 500 items you will have gotten 5 of them free; maybe it will be the carrots, or maybe its that bag of steaks. To do this a customer would have to have a card and use it every time (something the stores want to track purchases), and you have an incentive to do ALL your shopping at a store since each purchase helps bring you closer to that next free item.

Or maybe you could allow a little unfairness between customers and make every 100th item sold in the store free. You could have lights flashing and buzzers going off and make the place exciting, as they would be going off every few minutes! A big LED sign at the front of the store could flash the item (eg. "just won -- 1 dozen eggs") which is known since everything is scanned by UPC codes.

The overall point is you can add entertainment value to shopping, as well as use well-known psychological principles, in order to attract customers to your store and away from your competitors. Furthermore there is an "early mover" advantage to some of the possible schemes; for example you might make the odds better the more cumulative items that have been purchased so it would be harder for a new entrant to get them to switch their loyalty.

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