solution12

# solution12 - are p = 0 ¾ and 1 e Starting at p(0 = 0.5...

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Eco 354K - Honors Solutions to HW 12 1. a) NE = {(X,X), (Y,Y), and (3/4, 1/4), (3/4, 1/4). b) Level-1 players would choose Y, since Y is the best-response to (½ , ½). Level-2 players could choose Y, since Y is the best-response to the Level-1 choice. c) Since after the first period, the history will have Y more likely than X, all Level-n players will choose Y. 2. a) EU(X) = 20p(t), and EU(Y) = 15. b) Average AU(t) = p(t)EU(X) + [1-p(t)]EU(Y) = 20 p(t) 2 + 15[1-p(t)]. c) dp/dt = kp(t){EU(X) – AU} = kp(t)[1-p(t)][20p(t) – 15], for some k > 0. d ) d) The dynamic rest points
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Unformatted text preview: are p = 0, ¾ and 1. e) Starting at p(0) = 0.5, dp/dt < 0, and remains so for all p < 0.5. Therefore, p(t) will converge to 0; the (Y,Y) equilibrium. Indeed, the dynamics will converge to (Y,Y) for all p(0) < ¾, and converge to (X,X) for all p(0) > ¾. The basin of attraction for the bad (Y,Y) equilibrium is three times larger than the basin of attraction for the good (X,X) equilibrium. Note that the mixed-strategy NE at ¾ is unstable since any perturbation will cause the population p(t) to diverge away from ¾. ¾ p(t) dp dt...
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