1) Consider the following extensive form game of coordination. Firms 1 and 2 must choose between technologies A and B. Firm 1 prefers technology A while firm 2 prefers technology B, but the firms obtain value from coordination. The following extensive form represents the game: Firm 1 A B Firm 2 Firm 2 A1 B1 0,0 A2 -0,0 2,1 B2 Note that this game is not simultaneous. 1,3 a) Find all the pure strategy Nash equilibria of this game b) Which outcomes satisfy the criterion of backward induction? c) Before Firm 2 makes its move, it sees a press release from firm 1 saying that it believes that the industry will converge to technology A. Would such a statement change the outcome of the game?
1) Consider the following extensive form game of coordination. Firms 1 and 2 must choose between technologies A and B. Firm 1 prefers technology A while firm 2 prefers technology B, but the firms obtain value from coordination. The following extensive form represents the game: Firm 1 A B Firm 2 Firm 2 A1 B1 0,0 A2 -0,0 2,1 B2 Note that this game is not simultaneous. 1,3 a) Find all the pure strategy Nash equilibria of this game b) Which outcomes satisfy the criterion of backward induction? c) Before Firm 2 makes its move, it sees a press release from firm 1 saying that it believes that the industry will converge to technology A. Would such a statement change the outcome of the game?
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:1) Consider the following extensive form game of coordination. Firms 1 and 2 must choose between technologies A and B. Firm 1 prefers technology A while firm 2 prefers technology B, but the firms obtain value from coordination. The following extensive form represents the game:
Diagram:
- Firm 1 chooses between A and B.
- If Firm 1 chooses A, Firm 2 can then choose between A1 and A2.
- A1 results in a payoff of (2,1) to Firm 1 and Firm 2, respectively.
- A2 results in a payoff of (0,0) to both firms.
- If Firm 1 chooses B, Firm 2 can then choose between B1 and B2.
- B1 results in a payoff of (0,0) to both firms.
- B2 results in a payoff of (1,3) to Firm 1 and Firm 2, respectively.
Note that this game is not simultaneous.
a) Find all the pure strategy Nash equilibria of this game.
b) Which outcomes satisfy the criterion of backward induction?
c) Before Firm 2 makes its move, it sees a press release from firm 1 saying that it believes that the industry will converge to technology A. Would such a statement change the outcome of the game?
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