Question

In studying for your economics final, you are concerned about only two things: your grade and the amount of time you spend studying. A good grade will give you a benefit of 20; an average grade, a benefit of 5; and a poor grade, a benefit of 0. By studying a lot, you will incur a cost of 10; by studying a little, a cost of 6. Moreover, if you study a lot and all other students study a little, you will get a good grade and they will get poor ones. But if they study a lot and you study a little, they will get good grades and you will get a poor one. Finally, if you and all other students study the same amount of time, everyone will get average grades. Other students share your preferences regarding grades and study time.

Model this situation as a two-person prisoner’s dilemma in which the strategies are to study a little and to study a lot, and the players are you and all other students. Construct a payoff matrix in which the payoffs account for both the cost and benefit of studying.

A) [20, 5; 0, 10]

B) [5, 20; 10, 0]

C) [10, 0; 6, 20]

D) [0, 10; 20, 6]

Answer 1

In the context of a prisoner's dilemma in economics, the payoff matrix representing the decision to study a lot or a little, accounting for both costs and benefits, is not reflected in any of the given options (A, B, C, D). The net benefits need to be calculated to find the payoff for each possible scenario combining the individuals' and the other students' strategies.

Step-by-step explanation:

When studying for an economics final, if a student is concerned only about their grade and the amount of time they spend studying, this situation can be modeled as a two-person prisoner’s dilemma. The strategies here are to study a lot or study a little, and the players are the individual student and all other students. Constructing a payoff matrix requires combining the cost of studying with the benefits of the possible grades.

To calculate the payoffs, subtract the cost of each strategy from the benefit of the outcome. If you study a lot (cost of 10), and others study little, you get a good grade (benefit of 20), so the net benefit is 20 - 10 = 10. If you both study a lot, you both get average grades (benefit of 5), and the net benefit is 5 - 10 = -5. If you study a little (cost of 6), and the others study a lot, you get a poor grade (benefit of 0), resulting in a net benefit of 0 - 6 = -6. If both parties study a little, both get an average grade, netting 5 - 6 = -1.

Therefore, the payoff matrix that represents the situation is:

You / Others | Study A Lot | Study A Little
Study A Lot | -5, -5 | 10, -6
Study A Little | -6, 10 | -1, -1

This matrix reflects the net benefits (benefits minus costs) for both strategies, for you and all other students.