Recall that college students repeatedly played a version of the game "prisoner's dilemma," where competitors choose cooperation, defection, or costly punishment. (Cooperation meant paying 1 unit for the opponent to receive 2 units, defection meant gaining 1 unit at a cost of 1 unit for the opponent, and punishment meant paying 1 unit for the opponent to lose 4 units.) At the conclusion of the games, the researchers recorded the average payoff and the number of times cooperation, defection, and punishment were used for each player. The scatter plots below plot average payoff (y) against level of cooperation use, defection use, and punishment use, respectively.
a. Consider cooperation use (x) as a predictor of average payoff (y). Based on the scatter plot, is there evidence of a linear trend?
b. Consider defection use (x) as a predictor of average payoff (y). Based on the scatter plot, is there evidence of a linear trend?
c. Consider punishment use (x) as a predictor of average payoff (y). Based on the scatter plot (reproduced from Exercise 2.123), is there evidence of a linear trend?
d. Refer to part c. Is the slope of the line relating punishment use (x) to average payoff (y) positive or negative?

For Information: Refer to the Nature (March 20, 2008) study of whether "nice guys finish last" in the business world. Exercise 2.123.

Transcribed Image Text:

0.8 0.4 -0.4 0 20 4060 80 0.8 0.4 0.4 0 20 40 60 80 Defection use 0.8 0.4 0.4 0 5 10 15 20