Question

Question 5.
You and a classmate are assigned a project on which you will receive one combined grade.
You each want to receive a good grade, but you also want to avoid hard work. In particular,
is as follows:
• If both of you work hard, you both get an A, which gives each of you 40 units of
happiness.
• If only one of you works hard, you both get a B, which gives each of you 30 units of
happiness.
• If neither of you work hard, you both get a D, which gives each of you 10 units of
happiness.
• Working hard costs 25 units of happiness.
a. Construct a payoff matrix based on the information above.
b. What is the likely outcome that you and your classmate have? Explain.
c. What is the dominant strategy for you in this situation?

Answer 1

A. LET THE PAYOFF BE SHOWN BY THE UNITS OF HAPPINESS A PLAYER RECEIVES.

IF BOTH PLAYERS WORK HARD, BOTH GET AN A. THEIR PAYOFF IS 40 EACH. BUT THEY WILL HAVE TO DEDUCT 25 UNITS OF HAPPINESS FOR DOING THE HARDWORK . THEIR PAYOFF= 40-25= 15 EACH

IF BOTH  PLAYERS DON'T WORK HARD, THEY WILL GET A D. THEIR PAYOFF= 10 EACH

IF ONE OF THEM WORK HARD, BOTH WILL GET 30 UNITS OF HAPPINESS. BUT THE PLAYER WHO DOES THE HARD WORK WILL HAVE TO DEDUCT 25 UNITS OF HAPPINESS FOR DOING THE HARD WORK ,HIS PAYOFF= 30-25= 5 . OTHER PLAYER WHO DIDN'T DO THE HARD WORK, HIS PAYOFF= 30

PLAYER 1	PLAYER 2
	WORK HARD	AVOID HARD WORK
WORK HARD	15, 15	5 ,30
AVOID HARD WORK	30,5	10,10

B. THE LIKELY OUTCOME SHALL BE THE NASH EQUILIBRIUM OF THIS GAME. WE WILL USE THE UNDERLINE METHOD TO FIND THE NASH EQUILIRIUM .

WE WILL UNDERLINE THE BEST RESPONSE OF A PLAYER, GIVEN THE OTHER PLAYER'S STRATEGY.

IF PLAYER 2 WORKS HARD, THE BEST RESPONSE OF PLAYER 1 IS TO AVOID HARD WORK.

PLAYER 1	PLAYER 2
	WORK HARD	AVOID HARD WORK
WORK HARD	15, 15	5 ,30
AVOID HARD WORK	30,5	10,10

IF PLAYER 2 AVOIDS HARD WORK, THE BEST RESPONSE OF PLAYER 1 IS TO AVOID HARD WORK

PLAYER 1	PLAYER 2
	WORK HARD	AVOID HARD WORK
WORK HARD	15, 15	5 ,30
AVOID HARD WORK	30,5	10,10

IF PLAYER 1 WORKS HARD, THE BEST RESPONSE OF PLAYER 2 IS TO AVOID HARD WORK

PLAYER 1	PLAYER 2
	WORK HARD	AVOID HARD WORK
WORK HARD	15, 15	5 ,30
AVOID HARD WORK	30,5	10,10

IF PLAYER 1 AVOIDS HARD WORK, THE BEST RESPONSE OF PLAYER 2 IS TO AVOID HARD WORK

PLAYER 1	PLAYER 2
	WORK HARD	AVOID HARD WORK
WORK HARD	15, 15	5 ,30
AVOID HARD WORK	30,5	10,10

THE NASH EQUILIBRIUM OF THIS GAME IS THAT BOTH AVOID THE HARD WORK. SO THE LIKELY OUTCOME FOR YOU AND YOUR CLASSMATE IS THAT YOU BOTH AVOID HARD WORK AND GET A D.

C. THE DOMINANT STRATEGY IN THIS SITUATION IS TO AVOID HARD WORK. NO MATTER WHAT THE OTHER PLAYER DOES, THE BEST RESPONSE THAT GIVES THE MOST PAYOFF IS TO AVOID HARD WORK. HENCE THE DOMINANT STARTERGY IS TO AVOID HARD WORK.