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Chainstore paradox
The chain store paradox is a game theory problem that challenges conventional rational choice assumptions about strategic behavior in sequential games. It describes a scenario where an incumbent chain store faces sequential entry threats from multiple potential competitors in different markets. The paradox emerges from the conflict between two compelling strategies: the logically sound approach of backward induction prescribed by classical game theory, and the intuitively appealing "deterrence strategy" that involves building a reputation for aggressive behavior to discourage future market entry. While standard equilibrium analysis suggests the chain store should accommodate all entrants, real-world business behavior often follows the deterrence approach, creating an apparent contradiction between game-theoretic predictions and observed strategic decisions. This paradox has implications for behavioral economics, industrial organization, and the study of credible threats in strategic interactions.
The paradox was first formulated by German economist and Nobel laureate Reinhard Selten in 1978.
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 the competitor chooses in, player A must respond with one of two pricing strategies, cooperative or aggressive. If A chooses cooperative, both players 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 optimal 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 to 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 not be able to deter player 20 from entering. Player 19 knows this and chooses in. Player A chooses to 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.
This theory states that Player A will be able to get payoff of higher than 40. Suppose Player A finds the induction argument convincing. He will decide how many periods at the end to play such a strategy, say 3. In periods 1–17, he will decide to always be aggressive against the choice of IN. If all of the potential competitors know this, it is unlikely potential competitors 1–17 will bother the chain store, thus risking the safe payout of 1 ("A" will not retaliate if they choose "out"). If a few do test the chain store early in the game, and see that they are greeted with the aggressive strategy, the rest of the competitors are likely not to test any further. Assuming all 17 are deterred, Player A receives 91 (17×5 + 2×3). Even if as many as 10 competitors enter and test Player A's will, Player A will still receive a payoff of 41 (10×0+ 7×5 + 3×2), which is better than the induction (game theoretically correct) payoff.
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Chainstore paradox AI simulator
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Chainstore paradox
The chain store paradox is a game theory problem that challenges conventional rational choice assumptions about strategic behavior in sequential games. It describes a scenario where an incumbent chain store faces sequential entry threats from multiple potential competitors in different markets. The paradox emerges from the conflict between two compelling strategies: the logically sound approach of backward induction prescribed by classical game theory, and the intuitively appealing "deterrence strategy" that involves building a reputation for aggressive behavior to discourage future market entry. While standard equilibrium analysis suggests the chain store should accommodate all entrants, real-world business behavior often follows the deterrence approach, creating an apparent contradiction between game-theoretic predictions and observed strategic decisions. This paradox has implications for behavioral economics, industrial organization, and the study of credible threats in strategic interactions.
The paradox was first formulated by German economist and Nobel laureate Reinhard Selten in 1978.
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 the competitor chooses in, player A must respond with one of two pricing strategies, cooperative or aggressive. If A chooses cooperative, both players 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 optimal 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 to 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 not be able to deter player 20 from entering. Player 19 knows this and chooses in. Player A chooses to 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.
This theory states that Player A will be able to get payoff of higher than 40. Suppose Player A finds the induction argument convincing. He will decide how many periods at the end to play such a strategy, say 3. In periods 1–17, he will decide to always be aggressive against the choice of IN. If all of the potential competitors know this, it is unlikely potential competitors 1–17 will bother the chain store, thus risking the safe payout of 1 ("A" will not retaliate if they choose "out"). If a few do test the chain store early in the game, and see that they are greeted with the aggressive strategy, the rest of the competitors are likely not to test any further. Assuming all 17 are deterred, Player A receives 91 (17×5 + 2×3). Even if as many as 10 competitors enter and test Player A's will, Player A will still receive a payoff of 41 (10×0+ 7×5 + 3×2), which is better than the induction (game theoretically correct) payoff.