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# a1 - ∂π 2/∂ P 2 =(P 1 3(P 2-4-3P 2-4 P 2-3 = 0(2(1...

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ECON 485 Fahad Khalil Answer key 1 1. L R or L C is strictly dominated by M R or M C . Since players will not play strictly dominated strategies no matter what their opponent does, we can eliminate either. Let us eliminate L R first. Then eliminate L C . H R can be eliminated sine it is now strictly dominated by M C . Similarly, H R , and then H C , so that we end up with M C and M R . 2. (1, 0) (-1, 1) (0, -1) (-1, -1) (1, 0) (0, 1) (-1, 1) (0, -1) (1, 0) 3. π 1 (P 1 , P 2 ) = (P 1 -4)(P 2 /P 1 ) 2 = (P 1 -4) (P 2 ) 2 (P 1 ) -2 . π 2 (P 1 , P 2 ) = (P 2 -4)(P 1 /P 2 ) 3 = (P 2 -4)(P 1 ) 3 (P 2 ) -3 . ∂π 1 /∂ P 1 = (P 2 ) 2 [(P 1 -4) (-2P 1 -3 ) + P 1 -2 ] = 0 (1) ∂π
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Unformatted text preview: ∂π 2 /∂ P 2 = (P 1 ) 3 [(P 2-4) (-3P 2-4 ) + P 2-3 ] = 0 (2) (1) ⇒ [-2(P 1-4)] / (P 1 3 ) + 1/P 1 2 = 0 or -2(P 1-4) + P 1 = 0 ⇒ P 1 = 8. (2) ⇒ [-3(P 2-4)] / (P 2 4 ) + 1/P 2 3 = 0 or -3(P 2-4) + P 2 = 0 ⇒ P 2 = 6. Since, the first order conditions (1) and (2) imply that the prices are chosen independently of the other player's price, each must be a dominant strategy. We can also safely predict that these choices will be carried out by the players, and therefore, the outcome is (P 1 = 8, P 2 = 6)....
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