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Unformatted text preview: 2 1. Find a. Nash equilibrium of the bimatrix game with payoff matrix _ (1,6)(41)
3 “’5; ~11 a “I Q”
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W21“ < “S! "I;
W 0141+] ” é”7lE/#I 5 3 2. Modify the Cournot model of duopoly in which the price is related to the quantity
produced by P(quq2l:a*q1—Q2 by assuming that the cost per unit for ﬁrm 1 is c1 and the cost per unit for ﬁrm 2
is Cg. Find the Nash equilibrium for this model. { l‘ ‘
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gov/Cth _/ a?
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amac+Ci 4 3. Set up the matrix for the strategic form of the game with Kuhn tree below, but £111 in the entries of the matrix only for the row corresponding to the pure strategy
b for player I, showing your work. I 5 4. Let é be a strategy for Colin (player II) and let e“ be Rose’s (player 1) best
response to (3 among all her pure strategies, that is, 63,1146! 2 eEAQ for all 2'. Let p
be any mixed strategy for Rose. Prove that pTAé S egkAtj. 6 5. Solve the matrix game ,1 O O ,,
I] C) I
(g 0 MI VOW 3
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 Spring '10
 FUCKHEAD

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