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Gunning for efficiency with third party enforcement in threshold public goods


When public goods can only be provided when donations cross a minimum threshold, this creates an advantage in that Pareto Efficient outcomes can be Nash Equilibria. Despite this, experiments have shown that groups struggle to coordinate on one of the many efficient equilibria. We apply a mechanism used successfully in continuous public goods games, the Hired Gun Mechanism (Andreoni and Gee in J. Public Econ. 96(11–12):1036–1046, 2012), to see if it can successfully get subjects across the threshold. When we use the mechanism to eliminate only inefficient equilibria, without addressing coordination, there is a modest but statistically insignificant improvement with the mechanism. However, when we hone the mechanism to eliminate all but one of the provision-point equilibria, thereby addressing the coordination issue, the mechanism moves all subjects to the desired efficient outcome almost immediately. In fact, after only one round using the hired gun mechanism, all subject are coordinating on the chosen equilibrium. The mechanism can be applied in settings where a group (1) has a plan for public good provision, (2) can measure contributions, (3) can fine members and (4) has an agreed upon standard for expected contributions. In these settings simple punishments, when focused on solving coordination as well as free riding, can greatly improve efficiency.

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  1. 1.

    In some of these examples contributions cannot be fully refunded after they have been contributed (e.g. time given to a group project), while others can be refunded (e.g. donations pledged toward fundraising). We test the hired gun mechanism in a setting with a money back guarantee, which is more closely related to the pledges which can be refunded. We chose the money back guarantee because it has been shown to increase provision of threshold public goods, and we wanted to show if we could improve on this best-case baseline (Isaac et al. 1989).

  2. 2.

    In fact, online fundraising websites like already give prizes like stickers and t-shirts to more generous contributors, so in essence they withhold prizes from lower contributors.

  3. 3.

    Thank you to Aaron Schroeder for suggesting this example (

  4. 4.

    Additionally we chose homogenous endowments and valuations because Croson and Marks (2001) found that in the heterogenous case the mere suggestion of contributions had an effect on actions. Thus we are biased away from suggestion driving our results by choosing the homogenous setting.

  5. 5.

    Given our parameter choices any set of contributions that exactly meet the threshold are a Nash equilibria of the game, so we avoid the “cheap riding” problem described by Isaac et al. (1989) where some sets of contributions meeting the threshold are not equilibria.

  6. 6.

    See Savikhin Samek and Sheremeta (2014) for a mechanism where the sanctioning takes the form of listing the largest free riders rather than a monetary fine. See Bornstein et al. (2002) for a mechanism where the largest free riding team is punished rather than the largest free riding individual.

  7. 7.

    Note, the use of strangers matching also is known to add variance to the data (Andreoni and Croson 2008), which handicaps the analysis against finding significant effects.

  8. 8.

    To choose the random period after the end of the 20th period, a subject was given a 20 sided die. The subject was asked to verify if the die had 20 sides, roll the die, and announce the outcome on the die out loud.

  9. 9.

    There are 12 subjects in each session in each period, so there are 12 choose 4, or 495 unique combinations. To see how actual versus possible groups may change the outcomes consider an example where three of the 12 subjects chose g=0 while the remaining 9 subjects each chose g=5. If the three selfish subjects were each assigned to different groups, then no group would reach the threshold [(0,5,5,5);(0,5,5,5);(0,5,5,5)], while if they ended up together in one group then two of three groups would succeed [(0,0,0,5);(5,5,5,5);(5,5,5,5)]. In both cases, however, the choices of subjects were the same but the impression of the outcome is different.

  10. 10.

    For actual level of public good provision p=0.60 using a Kolomogrov-Smirnov test at the session level. We use a Kolomogrov-Smirnov test because we only have 3 observations at the session level for the TPG (11–20) and GunEff games. The same result can be shown with a random effects regression P>|z|=0.112.

  11. 11.

    For the possible level of public good provision using all the possible group permutations p=0.10 using a Kolomogrov Smirnov test at the session level. The same result can be shown with a random effects regression P>|z|=0.001.

  12. 12.

    For actual or possible level of public good provision p=0.10 using a Kolomogrov Smirnov test at the session level. The same result can be shown with a random effects regression P>|z|=0.000.

  13. 13.

    For actual (possible) level of efficient public good provision p=0.60 (p=0.40) using a Kolomogrov Smirnov test at the session level. The same results can be shown with a random effects regression.

  14. 14.

    For actual and possible level of efficient public good provision p=0.10 using a Kolomogrov Smirnov test at the session level. The same results can be shown with a random effects regression.

  15. 15.

    The difference is statistically significant. For the actual and possible level of equitable and efficient public good provision p=0.10 using a Kolomogrov Smirnov test at the session level. The same results can be shown with a random effects regression.

  16. 16.

    The difference is statistically significant. For the actual proportion of groups punished p=0.10 and level of punishment p=0.10 using a Kolomogrov Smirnov test at the session level.

  17. 17.

    This would happen if the largest free rider gave 0 tokens and all the other players gave 8 tokens: P=2(8−0)+2.25=18.25. In fact, in the GunSelect treatment only 2 subjects are ever punished at the low level of $2.25.

  18. 18.

    Additionally in all treatments we stated that “if each person in your group invests 5 tokens in the BLUE investment, this will be the most equal way to reach 20 tokens.” Recall the BLUE investment is the public good.

  19. 19.

    We thank an anonymous reviewer for suggesting this alternative explanation for why the GunSelect mechanism works so well. Punishment is only realized in the GunEff treatment if the threshold is not met, so it only punishes actualized free riding instead of the intention to free ride. In the GunEff treatment when the threshold is met, the best response is to be the lowest contributor. In contrast the GunSelect treatment punishes both actual and intended free riding, so the best response is always the fair contribution of 5. If a subject was in a group which met the threshold in period T, then that subject might want to lower her contribution in period T+1 in the GunEff treatment, but not in the GunSelect treatment. We found that subjects lower their contribution in the period after the public good is provided by −0.08 tokens in GunEff and by −0.02 in GunSelect, however this difference is not statistically significantly different (Kolomogrov Smirnoff p=0.04).

  20. 20.

    We ran three sessions of the GunEff treatment. Two of those sessions had a single unimproving player, and the remaining session had two unimproving players.


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Corresponding author

Correspondence to Laura K. Gee.

Additional information

Andreoni would like to thank the National Science Foundation (SES-1024683), and the Science of Generousity Initiative for financial support. This research was approved by the UCSD IRB. We would also like to thank Mark Isaac, James Walker, two anonymous referees, Christopher Cotton, Jennifer Coats, Joseph Falkinger, Rosemarie Nagel, David Scmidtz, Jeff Zabel, and participants at the ESA and BABEEW conferences for their helpful comments.

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Andreoni, J., Gee, L.K. Gunning for efficiency with third party enforcement in threshold public goods. Exp Econ 18, 154–171 (2015).

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  • Public goods
  • Experiment
  • Laboratory
  • Equilibrium selection
  • Punishment
  • Free riding

JEL Classification

  • C72
  • C91
  • C92
  • D7
  • H41
  • H42