Question

Problem 1: (20 points) For the normal form game shown below find: (a) (10 points) the set of Nash equilibria. (b) (5 points) the set of perfect equilibria. (c) (5 points) the set of proper equilibria. LR U (3,0) (3,0) M (2, 1) (4,2) D (2,1) (1,0)

Answer 1

Player - 2 Problem-1 U (3,0) (3,0) - Player 1 M (2.1) (4,2) D 1(2.1) (1,0) finding leve strategy flash Equilibrium When player 1 chooses. Ug Player -2 chooses is indifferent between L & R (Sinu both gini When player. I chooses m, player-2 chooses R When player I chooses D, plays - 2 choosed L When player 2 chooses L, players choosest When player-2 chooses R, player. I chooses m Pure strategy dach . L R Equilibria (U, L) and (M, R) / 2,1 412 Pure strategy Mash 3,0 3,0 D 211 1,0

finding Mixed strategy Hash Equilibrium Now players will randomim among their strategies available, Sinu player 1, Never chooses strategy D so he will randomise only beturen strategy U&m. and player-2 will randomiss between strategy a pol 3,0 3,0 I-PM/ 2,1 4,2 july man Player 1 39 + 3 (19) = 2q +4(1-9) 74 +3 - 34 = 2g 44-4 3=4-29 24-1 q=Y2 1912

Mayer-2 0.8+(1-P) 1 = 0.8+ 2.4-p) IP = 2-21 1. P = 42 I-p="/ So, both the players will randomia with probability hall Player 1 = {}, " , 0} Playn - 2 = {12 , /2} - (a) Set of Hash Equilibriu (U,L) and (M,r) E (6) Set of perfut equilibula 1, 2) and (MR) - (c) Set of proper equilibria T1 = {1, 112, 103 mixed strategy of Jo a {1212} Player 1 & 2.