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

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

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

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

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

 

C (0,1) A D (5,2) 1+ In 2 Out B ~ (2,4) (2,1) D (-1,3)