Question

Consider the following extensive-form game with two players, 1 and 2.

Out 1. (2,1) In 1 A B N с D D (0,1) (5,2) (2,4) (-1,3)

a). Find the pure-strategy Nash equilibria of the game. [8 Marks]

b). Find the pure-strategy subgame-perfect equilibria of the game. [6 Marks]

c). Derive the mixed strategy Nash equilibrium of the subgame. If players play this mixed Nash equilibrium in the subgame, would 1 player In or Out at the initial mode? [6 Marks]

[Hint: Write down the normal-form of the subgame and derive the mixed Nash equilibrium of the subgame. Next, compare the payoff of player 1 from the mixed strategy equilibrium with 1's payoff from playing Out.]

Answer 1

(0) Mix trash of Sub game: D Oil 5,8 T 2,4 -13 For o to mix, TO U(A) = 0,(6) 09 + 5(1-2) = 22+ (4/(1-2) 5-52 = 2q-1+q 6=82 q=3 4 U2(C) = 2(D) 1(b) +4(1-P) = a (b)+31148 Ptu-up = 2p+3 - BP IP @ to mix, 1=QP p= Mix Mash Playes , plays a with Reob 2 C 1 4 Vic Mix Nath) = 0 (24) + 561-54) - $ S u lout) =2> Playes I will play out at initial nude.