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 \(\$ 100\) . If they decide to work together and both lower their 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 \(\$ 200\) . Table 10.6 represents the choices available to Mary and Raj. What is the bestchoice 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; \(\mathrm{B}=\) Cooperate and Lower Output. (Each results entry lists Raj's earnings first, and Mary's earnings second.)

Short answer

If Raj is sure that Mary will cooperate, his best choice is to work independently (A), as he will earn $200. If Mary thinks Raj will cheat, she should also work independently (A), as her earnings will be $100. The prisoner's dilemma result occurs when both choose to work independently (A) and earn $100 each, instead of cooperating and earning $150 each. If they could ensure cooperation, both should choose to cooperate (B) since they will earn a higher amount of money ($150 each) compared to the prisoner's dilemma outcome.

Step-by-step solution

Determine the best choice for Raj if he is sure that Mary will cooperate

If Raj is sure that Mary will cooperate, it means Mary will choose to lower her output (B). In this case, Raj has two options - to work independently (A) or to cooperate as well (B). We need to compare Raj's earnings in both situations: - If Raj chooses A (Independent) when Mary chooses B (Cooperate), his earnings will be $200. - If Raj chooses B (Cooperate) when Mary chooses B (Cooperate), his earnings will be $150. Comparing the earnings, Raj should choose to work independently (A) since his earnings will be higher ($200) if he is sure Mary will cooperate.

Determine what Mary should do if she thinks Raj will cheat

If Mary thinks that Raj will cheat (i.e., he will work independently (A)), she has two options - to work independently (A) or to cooperate (B). We need to compare Mary's earnings in both situations: - If Mary chooses A (Independent) when Raj chooses A (Independent), her earnings will be $100. - If Mary chooses B (Cooperate) when Raj chooses A (Independent), her earnings will be $0. Comparing the earnings, Mary should choose to work independently (A) if she thinks Raj will cheat since her earnings will be higher ($100).

Finding the prisoner's dilemma result

The Prisoner's Dilemma occurs when both individuals have a dominant strategy to choose an option that leads to a worse overall outcome than if they both chose to cooperate. In this case: - For Raj, working independently (A) is the dominant strategy since his earnings are higher when Mary chooses either A or B. - For Mary, working independently (A) is also her dominant strategy since her earnings are higher when Raj chooses either A or B. The prisoner's dilemma result is when both choose to work independently (A) and earn \(100 each, instead of cooperating and earning \)150 each.

Finding the preferred choice if they could ensure cooperation

If Mary and Raj could ensure cooperation, it means they trust each other and will choose option B (Cooperate) together. In this case, the preferred choice for both will be B (Cooperate) since they will earn a higher amount of money (\(150 each) compared to the prisoner's dilemma outcome of working independently and earning \)100 each.

Key concepts

Game Theory

Game Theory is a fascinating field that examines how individuals make decisions in strategic situations where the outcome depends not only on their own actions but also on the actions of others. In the context of the Prisoner's Dilemma, two players face a choice between cooperation and self-interested behavior.
The dilemma is whether to trust the other player and cooperate or act independently and potentially get a better immediate payoff.
For Mary and Raj, their choices directly influence their earnings depending on what the other decides to do.

• If both cooperate (lower their output), they can earn more together.
• If one cheats while the other cooperates, the cheating player benefits more.
• If both cheat and work independently, they end up with less than if they had cooperated.

This setup illustrates a classic example of game theory, emphasizing strategic interaction and decision-making under uncertainty.

Microeconomics

Microeconomics studies the behavior of individuals and firms in making decisions on the allocation of resources. It also examines how these decisions affect supply and demand, prices, and the overall market dynamics.
In the exercise involving Mary and Raj, microeconomic concepts are evident as we see how their choices influence the market for organically grown corn.

• By cooperating (producing less corn), they can potentially raise the price of corn due to reduced supply and increased scarcity.
• Each grower’s decision is a microeconomic decision impacting their profit and the market equilibrium.
• The results of their actions embody concepts like opportunity cost and competitive market behavior.

Through this microeconomic lens, we can explore how individual decisions impact broader market outcomes and why such dilemmas pose challenges to achieving optimal economic results.

Cooperative Strategy

A Cooperative Strategy involves players working together to achieve a better outcome than they would individually. In the Prisoner's Dilemma context, a cooperative strategy would mean Mary and Raj both lowering their production to maximize their collective earnings.
Trust and communication play vital roles in successfully adopting such strategies.
Unfortunately, without assurance that the other party will honor an agreement, the temptation to cheat for personal gain often prevails.

• When both fail to cooperate, they end up with a less optimal outcome, as seen in their independent earnings of $100 each.
• By cooperating, they could earn $150 each, demonstrating a significant benefit from joint action.
• Establishing mechanisms for trust and coordination can help surpass these dilemmas in real-world scenarios.

The case of Mary and Raj reflects the challenges of maintaining cooperation, balancing trust, and reaping the benefits of aligned interests.