Chainstore Paradox Seems Ridiculous

• John Vandivier

The Chainstore Paradox is a game theory paradox which it seems to me has an obvious real-world answer that is disallowed by the rules. From <a href="http://en.wikipedia.org/wiki/Chainstore_paradox">Wikipedia:

A monopolist (Player A) has branches in 20 towns. He faces 20 potential competitors, one in each town, who will be able to choose IN or OUT. They do so in sequential order and one at a time. If a potential competitor chooses OUT, he receives a payoff of 1, while A receives a payoff of 5. If he chooses IN, he will receive a payoff of either 2 or 0, depending on the response of Player A to his action. Player A, in response to a choice of IN, must choose one of two pricing strategies, COOPERATIVE or AGGRESSIVE. If he chooses COOPERATIVE, both player A and the competitor receive a payoff of 2, and if A chooses AGGRESSIVE, each player receives a payoff of 0.

These outcomes lead to two theories for the game, the induction (game theoretically correct version) and the deterrence theory (weakly dominated theory)

---

The obvious real world solution it seems to me would be for the chain store to pay off the local stores. The chain store would earn 5 in each area and pay out 2, earning a total of 60 which is higher than the other answers which earn about 40.

The reason this matters is because <a href="http://en.wikipedia.org/w/index.php?title=Coase_theorem&oldid=660587941#Criticism">the Chainstore Paradox is raised as an objection to the Coase Theorem. As far as I can tell, the payoff solution, which seems consistent with a Coasian approach, only fails because it is specifically disallowed by the strange rules of the game.

Update/Note 3/14/16: The game-theoretic result of the Chain-Store Game is that the chain-store accommodates the small firm. It is the weakly-dominated deterrence theory which can function as an objection to the Coase Theorem. However, not only is the deterrence theory rejected by standard game theory, it further fails on it's own logic by the ignorance of the payoff solution given above.

It's also cool to note that the failure of deterrence theory has widespread implications for military policy and other situations.