Mary and Sam are the only two growers who provide organically grown corn to a local...

Mary and Sam 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 $100. If they decide to work together and both lower their output, they can each earn $150. If one person lowers output and the other does not, the person who lowers output will earn $0 and the other person will capture the entire market and will earn $200. The table below represents the choices available to Mary and Sam. Answer the following questions: -What is the best choice for Sam if he is sure that Mary will cooperate? -If Mary thinks Sam 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 Sam's earnings first, and Mary's earnings second.)

		Mary
Sam		A	B
	A	($100, $100)	($200, $0)
	B	($0, $200)	($150, $150)

Solutions

Expert Solution

A: Do not Cooperate/ Work independently
B: Cooperate

-What is the best choice for Sam if he is sure that Mary will cooperate?
Sam gets higher payoff by not cooperating as (200 > 150). So, best choice for Sam is to not cooperate.

-If Mary thinks Sam will cheat, what should Mary do and why?
Mary should also not cooperate. Because if Sam will cheat that is he choose strategy A, then Mary's best response is A as $100 > $0 so she will also choose to cheat.

-What is the prisoner’s dilemma result?
Given that Sam choose A, Mary's best response is A($100)
Given that Sam choose B, Mary's best response is A($200)
Given that Mary choose A, Sam's best response is A($100)
Given that Mary choose B, Sam's best response is A($100)
So, the result is (A, A) as best response of both players occur simultaneously when they choose A.

-What is the preferred choice if they could ensure cooperation?
If they could ensure cooperation then they both would choose to lower output as their profit could be increased to $150 from $100

Rahul Sunny answered 1 year ago

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