Consider the location game between two bakeries, Pie Belly and the Lazy Croissant. Pie Belly moves first, chooses to locate either in the Mall or on the Side Alley. Observing this, the Lazy Croissant then chooses its location, which can similarly be in the Mall or on the Side Alley. The payoffs are as follows: if both firms choose Mall the payoffs are (50, 30) to Pie Belly and the Lazy Croissant; if Pie Belly chooses Mall and the Lazy Croissant the Side Alley the payoffs are (40, 40); if Pie Belly chooses the Side Alley and the Lazy Croissant opts for the Mall, the payoffs are (60, 35); and if both firms opt for the Side Alley the payoffs are (30, 20) respectively. Which statement is true?Group of answer choicesIn the credible equilibria, we observe Pie Belly choosing Mall and then the Lazy Croissant the Side Alley; there is a second-mover advantageIn the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Side Alley; there is a second-mover advantageIn the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Side Alley; there is a first-mover advantageIn the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Mall; there is a first-mover advantageNone of the above statements are true
Question
Consider the location game between two bakeries, Pie Belly and the Lazy Croissant. Pie Belly moves first, chooses to locate either in the Mall or on the Side Alley. Observing this, the Lazy Croissant then chooses its location, which can similarly be in the Mall or on the Side Alley. The payoffs are as follows: if both firms choose Mall the payoffs are (50, 30) to Pie Belly and the Lazy Croissant; if Pie Belly chooses Mall and the Lazy Croissant the Side Alley the payoffs are (40, 40); if Pie Belly chooses the Side Alley and the Lazy Croissant opts for the Mall, the payoffs are (60, 35); and if both firms opt for the Side Alley the payoffs are (30, 20) respectively. Which statement is true?Group of answer choicesIn the credible equilibria, we observe Pie Belly choosing Mall and then the Lazy Croissant the Side Alley; there is a second-mover advantageIn the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Side Alley; there is a second-mover advantageIn the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Side Alley; there is a first-mover advantageIn the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Mall; there is a first-mover advantageNone of the above statements are true
Solution
The correct answer is: In the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Mall; there is a first-mover advantage.
Here's the step-by-step reasoning:
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Pie Belly moves first and will choose the location that gives it the highest possible payoff, considering the potential responses of the Lazy Croissant.
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If Pie Belly chooses the Mall, it risks the Lazy Croissant also choosing the Mall, which would give Pie Belly a payoff of 50. If the Lazy Croissant chooses the Side Alley, Pie Belly gets a payoff of 40.
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If Pie Belly chooses the Side Alley, the Lazy Croissant could also choose the Side Alley, giving Pie Belly a payoff of 30. But if the Lazy Croissant chooses the Mall, Pie Belly gets a higher payoff of 60.
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Given these options, Pie Belly will choose the Side Alley, hoping that the Lazy Croissant will choose the Mall.
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Observing Pie Belly's choice, the Lazy Croissant will choose the Mall, because it gives a higher payoff (35) than choosing the Side Alley (20).
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Therefore, in the credible equilibria, we observe Pie Belly choosing Side Alley and then the Lazy Croissant the Mall. Since Pie Belly's initial choice influences the Lazy Croissant's decision, there is a first-mover advantage.
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