Hi, I'm stuck on how to do some steps for finding the set of sequential equilibria for this question:

Exercise 5.14 (OR 225.1). Find the set of sequential equilibria of the Selten's Horse C to C 1,1,1 D d 3 ........:6: L L R 3,3,2 0,0,0 4,4,0 0.0,11. [Exercise 5.14 in Lecture Notes] Let of be Player 1's probability of playing C, 62 Player 2's probability of playing c (conditional on reaching her information set), and 63 Player 3's probability of playing L (conditional on reaching her information set). Also, denote by a Player 3's belief that the history is D conditional on reaching her information set. The player's expected utilities are w (D) = 363, " (C) = 62 + 463 - 46262 un(c) = 1, un(d) = 463 23 ( L) = 2p1, us( R) = 1 - / hence Player 1 plays D if 363 2 62 + 463 - 46263, Player 2 plays c if 63 5 1/4, and Player 3 plays [ if p 2 1/2. By Bayes' Rule, whenever possible we have 1 - 61 1 -61+ 6 (1 -62) We proceed by backwards induction and analyze sequential rationality for every possible case of (a) If / > 1/3 => P3 chooses I (6, = 1) = P2 chooses d (62 = 0) => P1 chooses C (6 =1) = =0, a contradiction. (b) If / P3 chooses R (63 = 0) = P2 chooses c (62 = 1) => P1 chooses C (6 = 1) => # cannot be computed using Bayes' Rule. (c) If u = 1/3, there are two possibilities: i. 2(1 - 61) = 61(1 - 62) > 0. This implies 62 62 5 1/3. Hence, this situation is possible with dy $ 1/4.Now we need to check consistency in each case. Let & denote the profile of behavioral strategies, and take * + 0. 2. p