Question

1-4 Player 2 2 Question 4: (15pt total] Consider the following game: X Y Player 1 p A1, 32, 4 1-p B 0,28,0 Suppose Player 1 plays A with probability p, and Player 2 plays X with probability q. Let E1 (-) and E2(-) be the expected payoff functions. 4)a) [8pt total] Calculate the following: 4)a)i) (2pt] E1(A) 4)a) ii) (2pt] E1(B) 4)a) iii) [2pt] E2(X) = 4)a)iv) (2pt] E(Y) = 4)b) (3pt) Indifference strategy for Player 1: Answer: 4)c) (3pt) Indifference strategy for Player 2: Answer: 4)d) (1pt) Mixed Nash Equilibrium:

Answer 1

2 1-q 1 4 P A (2,4) B 0,2) (8,0) I-P 1 1 player plays a with probability p, and player 2 plays x with probability a i) E, CA) 1.9 +2:(1-2) q+Q-29 a-q iv) E,CB) og+861-9) of 8 - 89 8- 89

mi) Ex) 3. P+ 2 C1-p) = 3p+2-2p Prz iv) E₂(4) = 4P+ 0.1 - 4p. 9 ) b ) Indifterence strategy for player is E,CA) = ECB) 2-9 = 8-89 2- 8 = - 89ta t6 =114 q +6/7 9 = 6/3

4) Inditterence strategy for player 2 Ez(x) = 624) pt2 = 40 3p=2 P=2² di Mixed Hash equilibrium is, 649,243) (2/3,64) ) Thus the mixed strategies are (617,43) (43,611) nash equilibrium-