Question

Mary and Raj are the only two growers who provide organically grown corn to a local grocery store. They know that if they cooperated and produced less corn, they could raise the price of the corn. If they work independently, they will each earn $\backslash (100$. If they decide to work together and both lower their output, they can each earn $\backslash )150$. If one person lowers output and the other does not, the person who lowers output will earn $\backslash (0$and the other person will capture the entire market and will earn $\backslash )200$. Table $10.6$represents the choices available to Mary and Raj. What is the best choice for Raj if he is sure that Mary will cooperate? If Mary thinks Raj will cheat, what should Mary do and why? What is the prisoner’s dilemma result? What is the preferred choice if they could ensure cooperation? A = Work independently; B = Cooperate and Lower Output. (Each results entry lists Raj’s earnings first, and Mary's earnings second.)

RAJ	MARY
(A)	(B)
$(\backslash (100,\backslash )100)$	$(\backslash (200,\backslash )0)$
$(\backslash (0,\backslash )200)$	$(\backslash (150,\backslash )150)$

Short answer

• If Raj is sure that Mary will cooperate, the best choice for Raj is that he will cheat and earn$\$100$
• If Mary thinks Raj will cheat, Mary should cheat and earn
• The result of the prisoner's dilemma is that both will cheat and left with an earing of $\$100$each.
• If they could ensure cooperation, the preferred choice will be$(\$150,\$150).$

Step-by-step solution

Step 1. Definition

A scenario in game theory where individuals can get beter payoff through cooperating rather than following self-interest is known as prisoner's dilemma.

Step 2. Answer of the 1st question

If Raj is sure that Mary will not cheat, Raj will have two choices - 1. Raj will not cheat and earn$\$150$(in this case both will earn $\$150$), 2. Raj will cheat and earn (in this case Raj will earn $\$200$and Mary will earn $0).

Raj will prefer to cheat and earn $\$200$and this is the best choice for him if he is sure that Mary will not cheat.

Step 3. Answer of the 2nd question

If Mary is sure Raj will cheat, Marry will have two choices - 1. Mary will not cooperate and earn $\$0$(in this case Raj will earn $\$200$), 2. Raj will cheat and earn $\$100$(in this case both will earn$\$100$).

Mary should choose to cheat and earn $\$100$otherwise he will be left with $\$0$earning as Raj will get the share of the whole market.

Step 4. Result of the prisoner's dilemma

The result of the prisoner's dilemma is that both will cheat and left with an earing of $\$100$each.

Step 5. Answer of the 4th question

If they could ensure cooperation, the preferred choice will be ($\$150,\$150$) which means both will earn$\$150$each.