midterm2 2008 solutions

you need to nd inequalities with p and n answer if

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Unformatted text preview: mode, W1 leads to W2 , W2 leads to W3 , . . . , Wn−1 leads to Wn , and Wn leads to the Collusion mode. If any firm deviates from what it is supposed to charge at any mode, then they go to W1 . (Every deviation takes us to the first day of a new war.) (You need to find inequalities with δ , p∗ , and n.) ANSWER: If nobody has ever deviated before: Payoff to not to deviate: 1/8 ,1/8, 1/8,...⇒ 1/8(1 − δ ) Payoff to deviate: 1/4, p*(1­p*)/2, p*(1­p*)/2,...,p*(1­p*)/2,1/8, 1/8,... n ∗ ∗ (1 n+1 ⇒ 1 + p (1−p )δδ) −δ ) + 8δ −δ) 4 2(1− (1 ∗ ∗ n n+1 (1 so one condition we have: 8(11 δ) > 1 + p (1−p )δδ) −δ ) + 8δ −δ) − 4 2(1− (1 If we are in a war mode: Notice that we don’t have to check for all the war modes. Because the lowest cost of deviattion happens in the first war mode (W1 ) and the benefit of deviation in a war mode is always the same. Payoff to not to deviate: p*(1­p*)/2, p*(1­p*)/2,...,p*(1­p*)/2,1/8, 1/8,... n ∗ ∗ )(1 δn ⇒ p (1−p −δ)−δ ) + 8(1−δ) 2(1 Payoff to deviate: The most profitable deviation is once again to undercut your opponent by...
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This document was uploaded on 03/21/2014 for the course ECON 14.12 at MIT.

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