Question

1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of player 2's strategies. (2 points) (ii) Construct a payoff matrix and identify all Nash equilibria to the game. (2 points) (iii) Use backwards induction to find all subgame perfect equilibria of the game. (2 points)

Answer 1

a) player I has two strategies c. and D. player 2 Actions Actions moves available available after c and D. to player 2 after c to player 2 after D are are E and F G and H. a and function either that assigns or H 6 A strategy of player 2 is elther E or F to Wistory c after history D. So, playersa's strategies EG, EH, FG, FH are For example, in. EH, E is assigned and it is assigned to history c to history D.

Camlin Page Date player 2 EN 2, 213 FG. FH EG 20 1012 player i 012 23 There are hire Nash equilibras. They are (c, EG); (C, Et); (c, FG); (6 Ft); (DEHY At Wash equilibrium, no single player has an incentive to deviate se, no single player com deviate from a Nash equilibrium strategy and can be better off. (147. : Eng (211) (3, 1) (012) (213) BACKWARD INDUCTION : player I ankcipates about player als more. It chooses it because player I chooses D, plauer 2 them what he gets if he chooses & It player I chooses c player 2 is indifferent between choosing t and F since both of them give him equal payoff that is 1.

a t So, If player 2 is player I will choose choosing c and D about to choose EH be indiffesent between b since both give hom payoff It player 2 is about to choose FH, plauer. I will choose c over o because by choosing C he gets payoff 3 whereas by choosing D he will get prey off 2. 0 Therefore, subgame perfect equilibria are on (C, EH ); (D) EH);(C,FH) ? Note that sub game perfect 1 Nash equilibrium in every equilibrium is a subgame.