Do nice guys finish first or last? Refer to the Nature (March 20, 2008) study of the use o...

Do nice guys finish first or last? Refer to the Nature (March 20, 2008) study of the use of punishment in cooperation games, Exercise.

Do nice guys really finish last? In baseball, there is an old saying that “nice guys finish last.” Is this true in the competitive corporate 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 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 punishment was used for each player. A graph of the data is shown in the accompanying scatterplot.

a. Consider punishment use ( x ) as a predictor of average payoff ( y ). Based on the scatterplot, is there evidence of a linear trend?

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b. Refer to part a. Is the slope of the line relating punishment use ( x ) to average payoff ( y ) positive or negative?

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c. The researchers concluded that “winners don’t punish”? Do you agree? Explain.

Recall that college students repeatedly played a version of the game “prisoner’s dilemma” and the researchers recorded the average payoff ( y ) and the number of times punishment was used ( x ) for each player. A negative correlation was discovered between x and y.

a. Give the null and alternative hypothesis for testing whether average payoff and punishment use are negatively correlated.

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b. The test, part a , yielded a p -value of .001. Interpret this result.

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c. Does the result, part b , imply that increasing punishment causes your payoff to decrease? Explain.