2. Two producers of the same good repeatedly compete in prices for .. periods. They have the same discount factor ... In the

stage game, each firm chooses between three price levels given below in each part of the problem. The profits are as in the

Bertrand game:

....(...., .....) =

...........

(12 . ....)(.... . 2), ....

12

(12 . ....)(.... . 2), .... = .....

0, .... > .....

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.

Part I: Suppose .... {2, 4, 10}.

(a) [0.5pt] Suppose .. = 2, and .. = 1. Can the path ((4, 4), (4, 4)) be implemented in a SPNE?

Hint: Start by drawing a 3 x 3 table representing the normal form of the stage game and find all stage NE.

(b) [0.5pt] Suppose .. = 2, and .. = 1. Can the path ((10, 10), (10, 10)) be implemented in a SPNE?

(c) [0.5pt] Suppose .. = 2, and .. = 1. Can the path ((10, 10), (4, 4)) be implemented in a SPNE?

(d) [0.5pt] Suppose .. = ?, and .. ? (0, 1). For which .. can the path ((2, 2), (2, 2),?) be implemented in a SPNE?

(e) [0.5pt] Suppose .. = ?, and .. ? (0, 1). For which .. can the path ((10, 10), (10, 10),?) be implemented in a SPNE?

Part II: Suppose .... {3, 4, 10}.

(a) [0.5pt] Suppose .. = 2, and .. = 1. Can the path ((4, 4), (4, 4)) be implemented in a SPNE?

(b) [0.5pt] Suppose .. = 2, and .. = 1. Can the path ((10, 10), (10, 10)) be implemented in a SPNE?

(c) [0.5pt] Suppose .. = 2, and .. = 1. Can the path ((10, 10), (4, 4)) be implemented in a SPNE?

(d) [0.5pt] Suppose .. = ?, and .. ? (0, 1). For which .. can the path ((10, 10), (10, 10),) be implemented in a SPNE?

(e) [0.5pt] Suppose .. = ?, and .. ? (0, 1). For which .. can the path ((4, 4), (4, 4),?) be implemented in a SPNE?

2. Two producers of the same good repeatedly compete in prices for T periods. They have the same discount factor 6. In the stage game, each firm chooses between three price levels given below in each part of the problem. The profits are as in the Bertrand game: (12 - pi)(pi - 2), pi = pi (12 - pi)(pi - 2), pi = P-i pi > p-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. Part I: Suppose pi E {2, 4, 10}. (a) [0.5pt] Suppose T = 2, and 6 = 1. Can the path ((4, 4), (4,4)) be implemented in a SPNE? Hint: Start by drawing a 3 x 3 table representing the normal form of the stage game and find all stage NE. (b) [0.5pt] Suppose T = 2, and 8 = 1. Can the path ((10, 10), (10, 10)) be implemented in a SPNE? (c) [0.5pt] Suppose T = 2, and 6 = 1. Can the path ((10, 10), (4, 4)) be implemented in a SPNE? (d) [0.5pt] Suppose T = co, and 6 E (0, 1). For which & can the path ((2, 2), (2, 2), ..) be implemented in a SPNE? (e) [0.5pt] Suppose T = co, and & E (0, 1). For which & can the path ((10, 10), (10, 10), ..) be implemented in a SPNE? Part II: Suppose p; E {3, 4, 10}. (a) [0.5pt] Suppose T = 2, and 6 = 1. Can the path ((4, 4), (4, 4)) be implemented in a SPNE? (b) [0.5pt] Suppose T = 2, and 8 = 1. Can the path ((10, 10), (10, 10)) be implemented in a SPNE? e by 11:59 pm May 24, 2021 Econ 109 - Game Theory - Spring 2021 Problem Set 4 (c) [0.5pt] Suppose T = 2, and $ = 1. Can the path ((10, 10), (4, 4)) be implemented in a SPNE? (d) [0.5pt] Suppose T = co, and & E (0, 1). For which & can the path ((10, 10), (10, 10), ..) be implemented in a SPNE? (e) [0.5pt] Suppose T = co, and 6 E (0, 1). For which & can the path ((4, 4), (4, 4), ..) be implemented in a SPNE