In business, do nice guys ?nish ?rst or last? In baseball, there is an old saying that ‘‘nice guys ?nish last.'' Is this true in the business world? Researchers at Harvard University attempted to answer this question and reported their results in Nature (March 20, 2008). In the study, Boston-area college students repeatedly played a version of the game ‘‘prisoner's dilemma,'' where competitors choose cooperation, defection, or costly punish- ment. (Cooperation meant paying 1 unit for the opponent to receive 2 units; defection meant gain- ing 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- grams (p. 102) plot average payoff (y) against level of cooperation use, defection use, and punishment use, respectively.
1200 1400 1600 1800 x
(a) Do you observe a trend, especially since the year 1400?
(b) The least squares line for the data since year 1400 is shown on the graph. Is the slope of the line positive or negative? What does this imply?
(a) Consider cooperation use (x) as a predictor of average payoff (y). Based on the scattergram, is there evidence of a linear trend?
(b) Consider defection use (x) as a predictor of average payoff (y). Based on the scattergram, is there evidence of a linear trend?
(c) Consider punishment use (x) as a predictor of average payoff (y). Based on the scattergram, is there evidence of a linear trend?
|
WEEK
1
|
NUMBER OF STRIKES
85
|
AGE OF FISH (days)
120
|
|
2
|
63
|
136
|
|
3
|
34
|
150
|
|
4
|
39
|
155
|
|
5
|
58
|
162
|
|
6
|
35
|
169
|
|
7
|
57
|
178
|
|
8
|
12
|
184
|
|
9
|
15
|
190
|
Refer to part c. Is the slope of the line relating punishment use (x) to average payoff (y) positive or negative?
(e) The researchers concluded that ‘‘winners don't punish.'' Do you agree? Explain.
