Question

Solve the following Extensive Form game by Backward Induction, then covert them into Normal Form and find the pure-strategy Nash equilibria in Normal Form.

P1 V P2 (2, 2) P1 (1,3) B (3,4) (4,2)

Answer 1

Extensive form game. Playco I has 4 Strategices. OB, OA, IB, IA Playca - 2 has & Straties as. o ana cwing Back word induction : at final stage of the game Stat That is at decision nocle of Player I game can be described as (3,4) (4,2) Player-I will choose A. at this decision hode. at second staye of gome decision nocle of Prayer-2 game as be described as P-2 (1,3) ~(4,2)

So Rayco - 2 will choose o at his decision node Now at first stage of game can be described as. (22) (1,3) so Prager - I Wiu choose o at his fiast decision node will Overall game can be moued in this way as. (2, 2) 0,31 (3,4) (4,2) So outcome of the game Player. I A at his decision ho de will choose o and that leads to end of this game and both will get (2,2 Payo yy.

Normal form game Player-2 ο Ι OB (2,2) (2,2) Player-2 OA (212) (2, 2) IB (113) (3,4) IA (1,3) (4,2) . Vom Two fure Strategy wc of Normal form game are (OB, 0 ) COA, O)