midterm2 2008 solutions

181 payo to deviate notice that the only protable

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Unformatted text preview: ge pi = 1/2 until somebody deviates; they both charge 0 there­ after. (You need to find the range of δ .) ANSWER: If nobody has deviated before: Payoff to not deviate: 1/8, 1/8, ...⇒ 1/8(1 − δ ) Payoff to deviate: Notice that the only profitable deviation occurs by undercutting the price and the most profitable undercutting is just to charge infinitesmall less than your competition. You will get something very close to 1/4 by doing this so 1/4,0,0,0,...⇒ 1/4 3 So we need 1/8(1 − δ ) > 1/4 ⇒ 1 > 1 − δ ⇒ δ > 1 2 2 We don’t get any meaningful restrictions from the histories with previous deviations. b) (15 points) There are n + 1 modes: Collusion, the first day of war (W1 ), the second day of war (W2 ), ..., and the nth day of war (Wn ). The game starts in the Collusion mode. They both charge pi = 1/2 in the Collusion mode and pi = p∗ in the war modes (W1 ,. . . , Wn ), where p∗ < 1/2. If both players charge what they are supposed to charge, then the Collusion mode leads to the Collusion...
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This document was uploaded on 03/21/2014 for the course ECON 14.12 at MIT.

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