Question

In studying for his Economics final, Sam is concerned about only two things: his grade and the
amount of time he spends studying. A good grade will give him a benefit of 20; an average grade, a benefit of 5; and a poor grade, a benefit of 0. By studying a lot, Sam will incur a cost of
10; by studying a little, a cost of 6. Moreover, if Sam studies a lot and all other students study a little, he will get a good grade and they will get poor ones. But if they study a lot and he studies a little, they will get good grades and he will get a poor one. Finally, if he and all other students study for the same amount of time, everyone will get average grades. Other students share Sam’s preferences regarding grades and study time.


a. 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 Sam and all other students. Include the payoffs
in the matrix.

b. What is the equilibrium outcome in this game? From the students’ perspective, is it the best
outcome?

Answer 1

Answer:

Payoff = benefit -cost

•we look at the outcomes of the  combinations

–Sam studies a lot while all others also study a lot •

His payoff: 5-10 =-5;

others’ payoff: 5-10=-5–

Sam studies a lot but all others study a little•

Sam’s payoff: 20-10 =10;

others’ payoff: 0 –6 = -6

Sam studies a little but all others study a lot

Sam’s payoff: 0-6 = -6;  others’ payoff: 20-10= 10

Sam studies a little while all others also study a little

•Sam’s payoff: 5-6= -1; others’ payoff: 5-6= -1•

Lets construct a Matrix for the above

                                                                         All others

                                                    Study a lot                    Study little

Sam                Study a lot         -5 for Sam;                     10 for Sam

                                                  -5 for others                  -6 for others

                      Study a little        -6 for Sam;                      -1 for Sam;

                                                   10 for others                  -1 for others

What is the equilibrium outcome in this game? From the students’ perspective, is it the best

outcome?

Sam and other students have dominant strategy for studying a lot. Sam and others will have an average grade of 5 or a payoff of -5

The outcome is not the best

Explanation:

Payoff = benefit -cost

•we look at the outcomes of the  combinations

–Sam studies a lot while all others also study a lot •

His payoff: 5-10 =-5;

others’ payoff: 5-10=-5–

Sam studies a lot but all others study a little•

Sam’s payoff: 20-10 =10;

others’ payoff: 0 –6 = -6

Sam studies a little but all others study a lot

Sam’s payoff: 0-6 = -6;  others’ payoff: 20-10= 10

Sam studies a little while all others also study a little

•Sam’s payoff: 5-6= -1; others’ payoff: 5-6= -1•

Lets construct a Matrix for the above

                                                                         All others

                                                    Study a lot                    Study little

Sam                Study a lot         -5 for Sam;                     10 for Sam

                                                  -5 for others                  -6 for others

                      Study a little        -6 for Sam;                      -1 for Sam;

                                                   10 for others                  -1 for others

What is the equilibrium outcome in this game? From the students’ perspective, is it the best

outcome?

Sam and other students have dominant strategy for studying a lot. Sam and others will have an average grade of 5 or a payoff of -5

The outcome is not the best

A dominant strategy is the the best strategy that a players perform irrespective of others