7. Consider the following extensive-form game with two players, 1 and 2. E U F (1,0) (5,2) 1 1 A B D E (4,1) F (2,2) (1,1) (a) Find the pure-strategy Nash equilibria of the game. (b) Find the pure-strategy subgame-perfect equilibria of the game. (c) Find the mixed-strategy subgame-perfect equilibrium of the game. (Hint: Find the mixed-strategy Nash equilibrium of the subgame. Given this is played in the subgame, which action is chosen initially? Hence construct the mixed-strategy subgame-perfect equilibrium.)

A9

NE 2). Consider the following extensive form game between two players. (1,10) u D 1 B X (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)

rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.