2. Consider the following "centipede game." The game starts with player 1 choosing be- tween terminate (T) and continue (C'). If player 1 chooses C, the game proceeds with player 2 choosing between terminate (t) and continue (c). The two players choose be- tween terminate and continue in turn if the other player chooses continue until the terminal nodes with (player l's payoff, player 2's payoff) are reached as shown below. Player 1 Player 2 Player 1 Player 2 (3, 3)| (1, 1) (0, 3) (2, 2) (1, 4)

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter13: best-practice Tactics: Game Theory
Section: Chapter Questions
Problem 2E
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2. Consider the following "centipede game." The game starts with player 1 choosing be-
tween terminate (T) and continue (C). If player 1 chooses C, the game proceeds with
player 2 choosing between terminate (t) and continue (c). The two players choose be-
tween terminate and continue in turn if the other player chooses continue until the
terminal nodes with (player l's payoff, player 2's payoff) are reached as shown below.
TTTT
Player 1
Player 2
Player 1
Player 2
(3, 3)
t
(1, 1)
(0, 3)
(2, 2)
(1, 4)
(a) List all possible strategies of each player.
(b) Transform the game tree into a normal-form matrix representation.
(c) Find all pure-strategy Nash equilibria.
(d) Find the unique pure-strategy subgame-perfect equilibrium.
Transcribed Image Text:2. Consider the following "centipede game." The game starts with player 1 choosing be- tween terminate (T) and continue (C). If player 1 chooses C, the game proceeds with player 2 choosing between terminate (t) and continue (c). The two players choose be- tween terminate and continue in turn if the other player chooses continue until the terminal nodes with (player l's payoff, player 2's payoff) are reached as shown below. TTTT Player 1 Player 2 Player 1 Player 2 (3, 3) t (1, 1) (0, 3) (2, 2) (1, 4) (a) List all possible strategies of each player. (b) Transform the game tree into a normal-form matrix representation. (c) Find all pure-strategy Nash equilibria. (d) Find the unique pure-strategy subgame-perfect equilibrium.
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