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Problem_Set_10_Solutions

# Problem_Set_10_Solutions - Kaushik Basu Spring 2008 Econ...

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Kaushik Basu Spring 2008 Econ 367: Game-Theoretic Methods Problem Set 10 [This is a take-home examination.—Total 10 points. Your answer must be turned in (hard copies, please) by 10 April, 5 pm. You may hand it over to Sarah or Vidya after class any time before that. Do not discuss the questions with anybody till the answers are posted on the course website.] 1. Consider the single-shot game, G, described below. L R T 2, 2 0, 1 B 1, 0 1, 1 Now suppose this game will be played twice (with the outcome revealed to both players after each period). Each player has a discount factor of δ , where 0 < δ < 1. (a) Is there a subgame perfect equilibrium such that in the first period the outcome is (B,L)? Explain your answer. Answer: No. Suppose (B,L) is played in the first period and. Then P2 gets 2 δ if (T,L) is played in the second period or δ if (B,R) is played in the second period. However, if P2 deviates in the first period, then he can get at least (1+ δ ) which is always more than 2 δ or δ . Therefore there is a unilateral deviation by P2 and thus in a SPE, (B,L) is never played in the first period. (b) Now suppose that G will be played twice, δ = 1, and the outcome of period 1’s play is revealed to the players only at the end of the two periods. Draw the full extensive form of this two-period game.

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Answer: In game theory we usually assume “perfect recall or memory” unless otherwise stated. So each player remembers what he/she has played in the first period while
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Problem_Set_10_Solutions - Kaushik Basu Spring 2008 Econ...

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