Seems awfully dumb to attempt the whole "collusion on prices" thing when both you and your partner in crime are locked in your own cutthroat duopoly battles. What's to stop Coca-cola+Target from turning around and crushing Walmart+Pepsi on pricing the instant they try to "price-gouge"?
The whole point of Duopoly is to have a “competitor” so that you can continue to act as a monopoly behind the scenes while avoiding the appearance of a monopoly. You get to point finger at the other guy when there’s scrutiny and argue there’s no monopoly, but also increase your own prices when your competitor does it.
It’s not cutthroat, it’s comfortable partnership with a cutthroat veneer. If either of them wins, they have a monopoly and are at higher risk of regulation or breakup. So they fight openly over small fries, and keep writing dividend checks.
It's kind of like what's to stop you from stealing your neighbor's lawn gnome? You get a free gnome once and now neither of you can ever have anything on your property not bolted down ever again. Better to not hurt both of you by rocking the boat and instead slowly raise prices together. Cooperation is only hard when there's a lot of people involved.
