a2 - Econ 485 Answer key 2 Fahad Khalil 1. Unique NE is...

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Econ 485 Fahad Khalil Answer key 2 1. Unique NE is (T,L), but it is Pareto Dominated by (B,R) L C R 1 , 1 0, 0 0, 0 0, 0 0, 1 3, 0 T M B 0, 0 1, 0 2, 2 2. To obtain an understanding of what F does, let us look at the problem of firm 1 given q 2 . Firm 2’s problem will be similar. π 1 (q 1 , q 2 ) = (1-q 1 -q 2 )q 1 – F ∂π 1 /∂ q 1 = 1 – 2q 1 – q 2 = 0, which implies that BR 1 (q 2 ) is given by (1-q 2 )/2 if π 1 (q 1 (q 2 ), q 2 ) 0, q 1 (q 2 ) = 0 if π 1 (q 1 (q 2 ), q 2 ) < 0. Note that π 1 (q 1 (q 2 ), q 2 ) = (1-q 1 (q 2 )-q 2 )q 1 (q 2 ) – F, therefore, we can replace (1-q 2 )/2 for q 1 (q 2 ) to show that π 1 (q 1 (q 2 ), q 2 ) 0 [1 - (1-q 2 )/2 – q 2 ] (1-q 2 )/2 F 1- 2 F q 2 . This means the BR 1 (q 2 ) will look as follows depending on the value of F. q 2 q 2 1- 2 F q 1 q 1 F = 0 F > 0 If F = 0, we get the usual BR with no discontinuity. But if F > 0, the optimal q 1 is zero for q 2
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a2 - Econ 485 Answer key 2 Fahad Khalil 1. Unique NE is...

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