(a) Consider the influence function f(p) in Figure 7.13, which has four equi- libria p* =...

    

Transcribed Image Text:

(a) Consider the influence function f(p) in Figure 7.13, which has four equi- libria p* = 0, and 1. Suppose we start with p(0) = 0.01 (or some number slightly greater than 0). Find the equilibrium fraction, denoted as Poo- f(p) 1 f(p) = p Figure 7.13 An original curve to model flipping. f(p) 1 f(p) d = (d)f 1 P d = (d)f Figure 7.14 The curve is modified. It does not cross the origin now. P 1 Figure 7.15 The curve is modified again. It does not touch the 45-degree line now. (b) Suppose f(p) is slightly modified as in Figure 7.14, such that the point p=0 is no longer an equilibrium. Again use a graphical argument to find p(oo), starting at p(0) = 0. (c) Suppose f(p) is further slightly modified as in Figure 7.15, such that f(p)>p for 0 p < 1. Find p(oo) starting at p(0) = 0. (a) Consider the influence function f(p) in Figure 7.13, which has four equi- libria p* = 0, and 1. Suppose we start with p(0) = 0.01 (or some number slightly greater than 0). Find the equilibrium fraction, denoted as Poo- f(p) 1 f(p) = p Figure 7.13 An original curve to model flipping. f(p) 1 f(p) d = (d)f 1 P d = (d)f Figure 7.14 The curve is modified. It does not cross the origin now. P 1 Figure 7.15 The curve is modified again. It does not touch the 45-degree line now. (b) Suppose f(p) is slightly modified as in Figure 7.14, such that the point p=0 is no longer an equilibrium. Again use a graphical argument to find p(oo), starting at p(0) = 0. (c) Suppose f(p) is further slightly modified as in Figure 7.15, such that f(p)>p for 0 p < 1. Find p(oo) starting at p(0) = 0.