2. Two producers of the same good repeatedly compete in prices for T periods. They have the same discount factor 8. In the stage game, each firm chooses between three price levels 2, 4, and 10. The Bertrand stage game profits are given by: (12 - pi)(pi - 2), Pi < p-i ui(pi, p-i) = - (12 Pi)(Pi-2), Pi = p-i Pip-i In each of the following parts you must explain your positive or negative answer. If your answer says that some path can be implemented in an SPNE, then you must list the strategies. (d) Suppose T = ∞0, and 8 € (0, 1). For which 8 can the path ((2, 2), (2, 2), ...) be implemented in a SPNE using any strategies? (e) Suppose T = ∞, and 8 = (0,1). For which 8 can the path ((10, 10), (10, 10), ...) be implemented in a SPNE using grim trigger strategies?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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2. Two producers of the same good repeatedly compete in prices for T periods. They have the same discount factor 8. In the
stage game, each firm chooses between three price levels 2, 4, and 10. The Bertrand stage game profits are given by:
(12 - pi)(pi - 2),
Pi < p-i
ui(pi, p-i) =
-
(12 Pi)(Pi-2), Pi = p-i
Pip-i
In each of the following parts you must explain your positive or negative answer. If your answer says that some path can be
implemented in an SPNE, then you must list the strategies.
Transcribed Image Text:2. Two producers of the same good repeatedly compete in prices for T periods. They have the same discount factor 8. In the stage game, each firm chooses between three price levels 2, 4, and 10. The Bertrand stage game profits are given by: (12 - pi)(pi - 2), Pi < p-i ui(pi, p-i) = - (12 Pi)(Pi-2), Pi = p-i Pip-i In each of the following parts you must explain your positive or negative answer. If your answer says that some path can be implemented in an SPNE, then you must list the strategies.
(d) Suppose T = ∞0, and 8 € (0, 1). For which 8 can the path ((2, 2), (2, 2), ...) be implemented in a SPNE using any strategies?
(e) Suppose T = ∞, and 8 = (0,1). For which 8 can the path ((10, 10), (10, 10), ...) be implemented in a SPNE using grim
trigger strategies?
Transcribed Image Text:(d) Suppose T = ∞0, and 8 € (0, 1). For which 8 can the path ((2, 2), (2, 2), ...) be implemented in a SPNE using any strategies? (e) Suppose T = ∞, and 8 = (0,1). For which 8 can the path ((10, 10), (10, 10), ...) be implemented in a SPNE using grim trigger strategies?
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