The concept of independent stamp companies sounds absolutely insane nowadays, but here's how it worked.
I start a stamp company, let's say, BlueStamp. I call some major retailers and sell them rolls of my BlueStamp, that's where I make money.
See, people will want BlueStamps, because I've got amazing products they can get for free (the retailer paid for them by buying stamps). The retailers want to buy my stamps, because people will want them, which will make them shop at their store.
I just have to smart about it. I'll only sell my BlueStamps to BobMart and not AndyShop, because I don't want then they don't get to benefit as much. After all, If you can get BlueStamps everywhere, why would Bob or Andy even get them? I offer to supermarkt chain A, and not B, I offer it to Appliance store C, but not D. A BlueStamo saver will prefer a BlueStamp store over a Green stamp store, after all.
I might even give some big comapanies a discount on my stamps, because a bigger network offers more value, and I'll sell more stamps to these companies. Getting, say, Walmart in my system will make me very popular, and then I can charge every corner store at full price.
And that system worked really well, untill it got popular. There were literally hundreds of these systems, which make it all fall apart pretty quickly, and everyone just started offering their own savings programs.