In a study, college students repeatedly played a version of the game "prisoner's dilemma," where competitors chose 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 accompanying scatterplots plot average payoff (y) against level of cooperation use, defection use, and punishment use, respectively. Complete parts a through d below. Click the icon to view the scatterplots. X Prisoner's Dilemma Scatterplots a. Q 1.2 T .. Q a. Consider cooperation use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable increases. b. Consider defection use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable decreases c. Consider punishment use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, there is no pattern to the value of the y-variable. 0.8 0.44 ✔ + H . 0- 20 40 60 80 Cooperation use d. Refer to part c. Is the slope of the line relating punishment use (x) to average payoff (y) positive or negative? The slope is negative. 2 -0.4 0 0.8 0.4- 0- -0.4- 0.8 0.4 0 . 20 40 60 80 Defection use 0- -0.4+ 0 10 15 20 Punishment use Q Q C Q a C
In a study, college students repeatedly played a version of the game "prisoner's dilemma," where competitors chose 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 accompanying scatterplots plot average payoff (y) against level of cooperation use, defection use, and punishment use, respectively. Complete parts a through d below. Click the icon to view the scatterplots. X Prisoner's Dilemma Scatterplots a. Q 1.2 T .. Q a. Consider cooperation use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable increases. b. Consider defection use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable decreases c. Consider punishment use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend? There is no evidence of a linear trend, because as the value of the x-variable increases, there is no pattern to the value of the y-variable. 0.8 0.44 ✔ + H . 0- 20 40 60 80 Cooperation use d. Refer to part c. Is the slope of the line relating punishment use (x) to average payoff (y) positive or negative? The slope is negative. 2 -0.4 0 0.8 0.4- 0- -0.4- 0.8 0.4 0 . 20 40 60 80 Defection use 0- -0.4+ 0 10 15 20 Punishment use Q Q C Q a C
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:In a study, college students repeatedly played a version of the game "prisoner's dilemma," where competitors chose 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 accompanying scatterplots plot average payoff (y) against level of cooperation use, defection use, and
punishment use, respectively. Complete parts a through d below.
Click the icon to view the scatterplots.
X
Prisoner's Dilemma Scatterplots
a.
Q
1.27
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●
Q
0.8-
P
a. Consider cooperation use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend?
There is no evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable increases.
b. Consider defection use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend?
There is evidence of a linear trend, because as the value of the x-variable increases, the value of the y-variable decreases.
c. Consider punishment use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend?
There is no evidence of a linear trend, because as the value of the x-variable increases, there is no pattern to the value of the y-variable.
0.4-
d. Refer to part c. Is the slope of the line relating punishment use (x) to average payoff (y) positive or negative?
The slope is negative.
b.
C.
Average payoff
Average payoff
Average payoff
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20 40
Cooperation use
+8
60 80
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20 40 60 80
Defection use
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5 10 15 20
Punishment use
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