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

Now we need to check consistency in each case. Let & denote the profile of behavioral strategies, and take * + 0. 2. u p, and * is computed from 8* using Bayes' Rule, then (8, p) is a sequential equilibrium. 1. [Exercise 5.14 in Lecture Notes] Let o be Player 1's probability of playing C, 62 Player - # =0: Take the following sequences 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 Ble = ((1 - (#) 2, (8#) 2 ). ( 1 - 8#, 8# ), (4, 1 - 8#)) ; and 3's belief that the history is D conditional on reaching her information set. The player's expected utilities are H" = TEXT2 + (1 - (@ ) = ) -+ 1 - (ek]]. 21 (D) = 363, w (C) = 62 + 463 - 46263 As 8* is completely mixed, 8* + 8, ,* + 0, and a* is computed from 3* using Bayes' u2(c) = 1, u2(d) = 463 Rule, then (8, p) is a sequential equilibrium. Intuitively, to create a belief p* + 0, we u3 (L) = 241, u3(R) = 1 - 4 need for Player 1's tremble to be less likely (by an order of magnitude) than Player 2's tremble. That is why the e is squared in Player I's strategy. hence Player 1 plays D if 363 2 62 + 463 - 46263, Player 2 plays c if 63 5 1/4, and Player 3 plays L if u 2 1/3. By Bayes' Rule, whenever possible we have 3.(b) # = 1/3, 8 = ((1,0), (1, 0), (63, 1 - 63)) with 63 5 1/4. Take the following sequences 1 -61 "= 1-di+ 61(1 -62) BE = (1 -2#,8#) . (1 - (1- EX)' (1 - EAT). (63 + ek, 1 - 63 - et) ) ; and We proceed by backwards induction and analyze sequential rationality for every possible case of As B* is completely mixed, B* + 8, p + 4, and a is computed from B* using Bayes' (a) If u > 1/3 = P3 chooses L (63 = 1) = P2 chooses d (62 = 0) => Pl chooses C Rule, then (8, () is a sequential equilibrium. (61 = 1) = =0, a contradiction. (b) If p P3 chooses R (63 = 0) = P2 chooses c (62 = 1) => P1 chooses C (61 = 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 = 163 - 1 For 62 ( [0, 1] we need 63 2 1/3, But in this case Player 2 prefers to play d, hence 62 = 0, and 63/463-1 > 0. Therefore this situation is impossible. ii. (1 -61) = 61(1 - 62) =0. This implies 61 = 1 and 62 = 1. For 62 = 1 we need 63 $ 1/4, and as 62 = 1 for 61 = 1 we need 363 5 1 + 463 - 463 63 5 1/3. Hence, this situation is possible with 63 5 1/4.Exercise 5.14 (OR 225.1). Find the set of sequential equilibria of the Selten's Horse C 2 C 1,1,1 D 3 R L 3,3,2 0,0,0 4,4,0 0,0,1