ODE Gibbons.pdf X + X - File | C:/Users/Dylan%20Koehler/Documents/NYU/Strategic%20Decision%20Theory/Gibbons.pdf . . . 131 of 142 + 2 | A Read aloud | Draw V Highlight Erase 246 DYNAMIC GAMES OF INCOMPLETE INFORMATION Problems 247 mixed-strategy perfect Bayesian equilibrium? with equal probability. Specify a pooling perfect Bayesian equilib rium in which all three Sender types play L. R NNO M [p] [1- p] 2 L' R L' R' 1, 1 4 u 90,1 L t1 R - O Ow Ow (1/3) 1,0. d .0,0 Section 4.2 Receiver Receiver 4.3. a. Specify a pooling perfect Bayesian equilibrium in which both Sender types play R in the following signaling game. 2,10 u u 1, 1 L R 1,20 u (1/3) u 80,1 d d L R 0,0. . 1,0 Receiver Receiver 2,0. d d . 5 . 3,0 1,1 0 u .0,0 Receiver Nature Receiver t3 L R 0,0 u 5 . 1,0 (1/3) d d 0,0 2, 1 L to R 3,10 d 2,2 b. The following three-type signaling game begins with a move by nature, not shown in the tree, that yields one of the three types Type here to search O W 100% * ~ () 6 8 5:36 PM 12/7/2020ODE Gibbons.pdf X + X - File | C:/Users/Dylan%20Koehler/Documents/NYU/Strategic%20Decision%20Theory/Gibbons.pdf . . . 132 of 142 + 2 | A Read aloud | Draw V Highlight Erase| b. The following three-type signaling game begins with a move by nature, not shown in the tree, that yields one of the three types 248 DYNAMIC GAMES OF INCOMPLETE INFORMATION Problems 249 4.4. Describe all the pure-strategy pooling and separating perfect 4.5. Find all the pure-strategy perfect Bayesian equilibria in Prob- Bayesian equilibria in the following signaling games. lem 4.3 (a) and (b). 4.6. The following signaling game is analogous to the dynamic a. game of complete but imperfect information in Figure 4.1.1. (The types , and t2 are analogous to player I's moves of L and M 1,10 u 0 2,2 in Figure 4.1.1; if the Sender chooses R in the signaling game L t1 R then the game effectively ends, analogous to player 1 choosing R in Figure 4.1.1.) Solve for (i) the pure-strategy Bayesian Nash equilibria, and (ii) the pure-strategy perfect Bayesian equilibria of this signaling game. Relate (i) to the Nash equilibria and (ii) to 2,0. a 0,0 the perfect Bayesian equilibria in Figure 4.1.1. Receiver Nature Receiver 210 u t1 R a 0,0 u 5 . 1,0 .1,3 0,0 L R d d 0,10 1, 1 Receiver Nature Receiver 0,20 5 b. 01,3 3,0 u u *0,0 L R a L R 0,10 d 1,1 0 d 4.7. Draw indifference curves and production functions for a 5 04,1 two-type job-market signaling model. Specify a hybrid perfect Bayesian equilibrium in which the high-ability worker random- Receiver Nature Receiver izes. 3,30 u u 1,2 Section 4.3 L t2 R 4.8. Solve for the pure-strategy perfect Bayesian equilibria in the following cheap-talk game. Each type is equally likely to be drawn Type here to search O w 100% 4 ~ ) 68 5:36 PM 12/7/2020