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Investing in institutions for cooperation

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Abstract

We examine the effects of endogenizing contribution productivity in a repeated public good game. In our experimental treatment, subjects collectively decide (by voting) how much to invest in augmenting the technology for producing the public good, and subsequently make individual voluntary contributions to provision. In the control, contribution productivity is exogenous. Contributions in the two treatments are similar.

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Notes

  1. With four person groups, there is not a unique vote that is the median vote. However, four person groups are the most common in the literature (Ledyard 1995; Chaudhuri 2011), and we want for our only departure from the literature to be the addition of the investment stage.

  2. There exist voting rules that make it weakly dominant to truthfully reveal and elicit a continuum of investment outcomes. For example, investment could be the lower (or higher) of the two middle votes. However, this potentially creates downward (or upward) pressure on investment.

  3. The endogenous determination of M means that M could be less than 0.25, in which case the contribution stage is no longer a social dilemma. However, the concavity of M means that very low investment is required for this to happen. The lowest investment that occurred was \(I=0.75\rightarrow M=0.27\).

  4. The investment stage adds complexity to the conventional game. To prevent confusion, the instructions (see Appendix) include multiple examples of determining M from different sets of votes. In addition, we are an engineering school, with students who are generally very comfortable with equations. All students are required to do a year of calculus to fulfill general degree requirements.

  5. There are other Nash equilibria. They involve sets of votes such that a unilateral deviation in voting does not change the investment outcome. Such equilibria result in positive investment. However, it is never optimal to contribute anything.

  6. We omit the trend of average votes in the experimental treatment because it is very similar to the trend of average investment.

  7. The analysis of the difference in average payoffs between treatments is very similar (results available upon request).

  8. The differences in average cumulative earnings, of course, are also highly significant (Wilcoxon \(p<0.01\) in both cases).

  9. Smith (2013) discusses using fixed effects to help correct the bias associated with estimating autoregressive models using least squares. See Smith (2012) for a paper on the importance of correctly modeling the autoregressive nature of behavior in public good games.

  10. At least in absolute terms. We do find that subjects contribute higher proportions of their remaining money when they have higher Ms, consistent with Isaac and Walker (1988) finding that subjects choose higher contribution percentages when they have higher MPCRs. These regressions are available upon request.

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Acknowledgements

Financial support from Worcester Polytechnic Institute (WPI) is gratefully acknowledged. We thank seminar participants from Temple University, the College of the Holy Cross, and the University of Massachusetts at Lowell. We thank conference participants from the 2013 North American ESAs in Santa Cruz, the 2014 International ESAs in Honolulu, and the 2014 North American ESAs in Fort Lauderdale. We are also grateful to the anonymous referees and Co-Editor Nikos Nikiforakis for excellent, and very helpful, comments and suggestions.

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Correspondence to Alexander Smith.

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Smith, A., Wen, X. Investing in institutions for cooperation. J Econ Sci Assoc 3, 75–87 (2017). https://doi.org/10.1007/s40881-017-0033-2

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