Suppose the market for widgets (a fictitious good) is characterized by an infinitely repeated oligopoly game (notice I have not given you any details on the game itself). A monopolist in this market would earn $12 million each period, but currently the market is supplied by FOUR (4) firms, each of whom earn $1 million per period in the Nash equilibrium of the one-shot game. Collusion is illegal, and these are honest, law-abiding firms. Nevertheless, they recognize their own interdependence. If the firms had somehow agreed to collectively produce the monopoly level of output, they all know that a firm who defects from that agreement would earn $4 million that period. Supposing that each of the players were to play a trigger strategy, compute the value of alpha above which such a strategy, when played by all firms, would represent a Nash equilibrium of the infinitely repeated game. Your answer should be a decimal between 0 and 1, rounded to the third decimal place (e.g. 0.768).

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Suppose the market for widgets (a fictitious good) is characterized by an infinitely repeated oligopoly game (notice I have not
given you any details on the game itself). A monopolist in this market would earn $12 million each period, but currently the
market is supplied by FOUR (4) firms, each of whom earn $1 million per period in the Nash equilibrium of the one-shot
game. Collusion is illegal, and these are honest, law-abiding firms. Nevertheless, they recognize their own interdependence.
If the firms had somehow agreed to collectively produce the monopoly level of output, they all know that a firm who defects
from that agreement would earn $4 million that period. Supposing that each of the players were to play a trigger strategy,
compute the value of alpha above which such a strategy, when played by all firms, would represent a Nash equilibrium of
the infinitely repeated game. Your answer should be a decimal between 0 and 1, rounded to the third decimal place (e.g.
0.768).
Transcribed Image Text:Suppose the market for widgets (a fictitious good) is characterized by an infinitely repeated oligopoly game (notice I have not given you any details on the game itself). A monopolist in this market would earn $12 million each period, but currently the market is supplied by FOUR (4) firms, each of whom earn $1 million per period in the Nash equilibrium of the one-shot game. Collusion is illegal, and these are honest, law-abiding firms. Nevertheless, they recognize their own interdependence. If the firms had somehow agreed to collectively produce the monopoly level of output, they all know that a firm who defects from that agreement would earn $4 million that period. Supposing that each of the players were to play a trigger strategy, compute the value of alpha above which such a strategy, when played by all firms, would represent a Nash equilibrium of the infinitely repeated game. Your answer should be a decimal between 0 and 1, rounded to the third decimal place (e.g. 0.768).
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