solution12-spring11 - are p = 0, 2/3 and 1. e) Starting at...

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Eco 354K Solutions to HW 12 1. a) NE = {(L,L), (R,R), and (2/3, 2/3). b) Level-1 players would choose R, since R is the best-response to (½ , ½). Level-2 players could choose R, since R is the best-response to the Level-1 choice. c) Since after the first period, the history will have R more likely than L, all Level-n players will choose R. 2. a) EU(L) = 60p(t), and EU(R) = 40. b) Average AU(t) = p(t)EU(L) + [1-p(t)]EU(R) = 60 p(t) 2 + 40[1-p(t)]. c) dp/dt = kp(t){EU(L) – AU} = kp(t)[1-p(t)][60p(t) – 40], for some k > 0. d ) p(t) dp dt 2/3 d) The dynamic rest points
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Unformatted text preview: are p = 0, 2/3 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 (R,R) equilibrium. Indeed, the dynamics will converge to (R,R) for all p(0) < 2/3, and converge to (L,L) for all p(0) > 2/3. The basin of attraction for the bad (R,R) equilibrium is twice as large as the basin of attraction for the good (L,L) equilibrium. Note that the mixed-strategy NE at 2/3 is unstable since any perturbation will cause the population p(t) to diverge away from 2/3....
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This note was uploaded on 06/09/2011 for the course ECON 354 taught by Professor Econ during the Spring '11 term at University of Texas at Austin.

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