3 Consider the following scenario. There are two players, S and R. S may be of one of two types, 1 or 2, with probabilities 0.5 and 0.5, respectively. S's type is her private information. R is of a single type. The game proceeds as follows. First, S takes an action it or r". R observes this action and plays one of the actions at or d. Then the game ends and the payoffs are realised. Confine your attention to pure strategies only. Suppose the payoff to player 3' E {1, 2} when S is of type t E {1,2} and when S has played action m e {5, r} and R has played action it e {2.5, d} is represented by u,(t, m, n). NOW let: 33(313533') = 7! UR(t1::u) = 5! \"30135360 = 4! \"Ralagad) = 9! \"3(t2353u) = 3! 1512052: 3\") = 8! \"3&2: 3 d) = 5! UR(t2:~ad) = 5! E"SUM Ta\") = 4,2LR(t1,T,EL) = 2! \"SUD\" d) = 11, uR(t1,r', d) = 4, u3(t2, r, u) = 5, uR(t2, r, u) = 6, u3(t2, r,d) = 7, uR(t2, r,d) = 6. 51) Draw the extensive-form game of the above scenario. Then write down the possible pure strategies and pure strategy equilibria of this game. [30%] b) Analyse which of the pure strategy equilibria you identified exist(s). Show your work and explain the intuition behind your work. [70%] Please define every concept carefully before you use it