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Chainstore paradox


The chainstore paradox (or "chain-Store paradox") is a concept that purports to refute standard game theory reasoning.

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):

Consider the decision to be made by the 20th and final competitor, of whether to choose in or out. He knows that if he chooses in, Player A receives a higher payoff from choosing cooperate than aggressive, and being the last period of the game, there are no longer any future competitors whom Player A needs to intimidate from the market. Knowing this, the 20th competitor enters the market, and Player A will cooperate (receiving a payoff of 2 instead of 0).

The outcome in the final period is set in stone, so to speak. Now consider period 19, and the potential competitor's decision. He knows that A will cooperate in the next period, regardless of what happens in period 19. Thus, if player 19 enters, an aggressive strategy will be unable to deter player 20 from entering. Player 19 knows this and chooses in. Player A chooses cooperate.

Of course, this process of backward induction holds all the way back to the first competitor. Each potential competitor chooses in, and Player A always cooperates. A receives a payoff of 40 (2×20) and each competitor receives 2.


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