Question

Suppose Agnieszka and Stephanie are playing rock, paper, scissors game. They choose their actions simultaneously. The consequences are as follows: the one who loses has to grade all BUS1040 essays, the one who wins does not have to grade any exams. In case of a tie, they split the pile of BUS1040 essays equally for grading. Assuming that Agnieszka and Stephanie do not like grading exams, which answer is correct?

a. There is no Nash Equilibrium in this game.

b. There are three Nash Equilibria in this game.

c. In the unique Nash Equilibrium, Agnieszka and Stephanie split the midterms equally for grading.

d. Both Agnieszka and Stephanie have weakly dominant strategy.

e. c and d are true

Answer 1

Answer is option a)

No pure strategy Nash equilibrium exists in rock paper scissors game .

Only one mixed strategy Nash equilibrium exists

Rock beats scissors, scissors beat paper & paper beats rock.

If tie, both gets zero

If one wins , then he gets 1, the loser gets -1

Strategy	rock	paper	scissors
Rock	(0,0)	(-1,1•)	(1*,-1)
Paper	(1*,-1)	(0,0)	(-1,1•)
Scissors	(-1,1•)	(1*,-1)	(0,0)

So put * on best response on player 1)

& Put • on BR of P2)

No pure strategy NE