Question

Use the following payoff matrix for a one-shot game to answer the accompanying questions. Player 2 Strategy X Y Player 1 A 32, 32 4, -25 B -25, 4 40, 40 a. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication. Instructions: In order to receive full credit, you must make a selection for each option. For correct answer(s), click the box once to place a check mark. For incorrect answer(s), click twice to empty the box. (32,32) unchecked (40,40) unchecked (-25,4) unchecked (4,-25) unchecked Which of these outcomes would you consider most likely? (32,32) (-25,4) (40,40) (4,-25) b. Suppose player 1 is permitted to "communicate" by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter? B A What outcome do you think would occur as a result? (-25,4) (32,32) (4,-25) (40,40) c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move structure is known by both players. What outcome would you expect? (32,32) (40,40) (-25,4) (4,-25)

Answer 1

A) we have two Nash equilibrium in this case ( A,X) and ( B,Y) that is (32,32) and (40,40)

b) Therefore, player 1 will always utter B hence possible outcome is (40, 40)

c) 40, 40

Step-by-step explanation:

A) we have two Nash equilibrium in this case ( A,X) and ( B,Y) that is (32,32) and (40,40)

b) we need to determine mixed strategy Nash equilibrium

32q + 4(1-q)

= -25q + 40( 1-q)

= 57q = 36(1-q)

q = 36/93 = 12/31

also

p = 12/31 , hence 1-q = 19/31 and 1- p = 19/31 then we can say that possible outcome is (BB,Y) = (40 ,40)

Therefore, player 1 will always utter B hence possible outcome is (40, 40)

c) 40, 40