Repeated Game and Collusion Consider two firms that are playing a Bertrand game at each stage of an infinitely repeated game. They have the same discount factor d < 1 and the same constant marginal cost c. If they co-operate in the stage game then they each produce half the monopoly quantity qm and sell at the monopoly price pm. (a) What strategies, based on a threat of charging c in the stage game, the collusive outcome? will produce (b) For what values of 6 do these strategies constitute a sub-game perfect Nash equi- librium?

Microeconomic Theory
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Chapter15: Imperfect Competition
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Repeated Game and Collusion
Consider two firms that are playing a Bertrand game at each stage of an infinitely
repeated game. They have the same discount factor 8 < 1 and the same constant
marginal cost c. If they co-operate in the stage game then they each produce half the
monopoly quantity q" and sell at the monopoly price p".
(a) What strategies, based on a threat of charging c in the stage game, will produce
the collusive outcome?
(b) For what values of o do these strategies constitute a sub-game perfect Nash equi-
librium?
Transcribed Image Text:Repeated Game and Collusion Consider two firms that are playing a Bertrand game at each stage of an infinitely repeated game. They have the same discount factor 8 < 1 and the same constant marginal cost c. If they co-operate in the stage game then they each produce half the monopoly quantity q" and sell at the monopoly price p". (a) What strategies, based on a threat of charging c in the stage game, will produce the collusive outcome? (b) For what values of o do these strategies constitute a sub-game perfect Nash equi- librium?
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