Abstract
This paper investigates theoretically and experimentally the social benefits and cost to have an endogenous punishment-enforcing authority in public goods game. An authority is chosen among members of a society via an imperfectly discriminating contest prior to a public goods game. Once chosen the authority has a large degree of discretion to inflict punishment. Our theoretical result shows that an efficiency gain from having the endogenous authority always comes with a social cost from competing for being the authority. The larger the society is, however, the bigger the efficiency gain and the smaller the rent dissipation. The completely efficient outcome can be approximated as the size of society tends to infinity. The experimental results confirm that the presence of endogenous authority for a given group size increases the public goods contributions and the efficiency gain is significantly bigger in a larger group.
Funding statement: This study is supported by an SUG Grant from the Nanyang Technological University and by the Hong Kong University of Science and Technology, and Fundamental Research Fund for the Central Universities (Grant Number: JBK1902038).
Acknowledgements
We thank Kyung Hwan Baik, John Hamman, Yohanes Eko Riyanto, Fangfang Tan, Walter Edgar Theseira, Joseph Tao-Yi Wang, and Maoliang Ye for their helpful comments and suggestions. We have also benefited from discussions with the seminar participants at the Nanyang Technological University, the 2013 International Workshop on Experimental Economics at the Xiamen University, and the 2014 Annual Meeting of the Canadian Economic Association. We would like to thank the two anonymous reviewers for their suggestions and comments which greatly improve the paper. This research is supported by the Fundamental Funds for the Central Universities (JBK1902038, JBK1805007, and JBK190601).
Appendix
A Appendix – Dynamic Analysis
In this appendix, we document the dynamics of contest spending, punishment, and contributions. Precisely, we provide aggregate level overviews on (1) who wins the contest and becomes authority, (2) how individual winners vary in their behavior as the authority, (3) whether past winners or lowers increase or decrease their contest spending, and (4) whether individuals who were punished in the past increase or decrease their contest spending.
Fraction of being authority in different treatments.
Who Wins the Contest and Becomes Authority?Figure 10 presents the distributions of number of winning in the pre-LPG contests. As shown in the figure, more people in the treatments with a larger group size (around 37 %) have never been the authority than in the treatments with a smaller group size (around 10 %). One remarkable observation is that there are a few individuals who repeatedly became the authority in both treatments. Thus, we would like to see if this observation is driven by their aggressiveness in the pre-LPG contests.
Spending in contest for authority in different treatments.
How Individual Winners Vary in Their Behavior as the Authority?Figure 11 reports the distributions of authorities’ contest spending. It is immediately clear that these subjects behaved very aggressively in the pre-LPG contests relative to the equilibrium contest spending (2.727 for Treatment A4 and 1.691 for Treatment A8).
Spending in contest for past winners and losers authority.
Do Past Winners or Lowers Increase or Decrease their Contest Spending? Past winners and losers behaved differently in terms of their contest spending. As shown in Figure 12, past contest winners spent significantly more in the later contests than those who lost the contest. Forty-eight percent of losers spent zero in next round of contest and only 12 % of winners spent zero. This result implies that learning across different rounds took place in the experiments.
Contribution rate and punishment.
Do Individuals who were Punished in the Past Increase or Decrease their Contest Spending? Given that learning is an important determinant of the contest spending, we also expect to observe a positive correlation between individual’s experience of being punished and their contest spending when they are not the authority. Confirming this conjecture, Figure 13 shows that the contribution rate increased significantly right after individuals were punished relative to their contribution rate before they got punished.
Appendix - Instruction for Treatment 4
Instruction
Welcome to the experiment. This experiment studies decision making between eight individuals. In the following two hours or less, you will participate in 30 rounds (first 15 rounds and second 15 rounds) of decision making. Please read the instructions below carefully; the cash payment you will receive at the end of the experiment depends on how well you make your decisions according to these instructions. If you have a question at any point, please raise your hand and wait for one of us to come over. We will then privately answer your question. We ask that you turn off your mobile phone and any other electronic devices. Communication of any kind with other participants is not allowed.
Your Group
In each and every round, you will be randomly matched with seven other participants to form a group of eight. You will not be told the identity of the participants you are matched with, nor will those participants be told your identity—even after the end of the experiment. The eight members in a group make decisions that will affect their rewards in the round. Participants will be randomly rematched after each round to form new groups.
First 15 Rounds: BLUE and RED Investment Decision
Blue and red investment.
In each round, you will be endowed with 50 tokens and asked to decide how to divide 50 tokens into two investment opportunities; BLUE investment and RED investment. You input your investment decision by clicking on a line with a green ball on it (see Figure 14). The left end of the line represents 0 tokens in BLUE investment and 50 tokens in RED investment; the right end of the line represents 50 tokens in BLUE investment and 0 tokens in RED investment. You can choose any integer point in between. When you click on the line, the green ball will move to the point you click on, and the corresponding numbers of BLUE investment and RED investment will be shown inside BLUE BOX and RED BOX above the line. You adjust your click until you arrive at your desired numbers, after which you click the submit button. Your decision in the round is then completed.
The two investment opportunities give different returns. The following shows returns from each investment.
BLUE investment: Each token you invest in the BLUE investment will earn you a return of 2 points.
RED investment: What you earn from the RED investment will depend on the total number of tokens that you and the other seven members of your group invest in the RED investment. Each token your group invest in the RED investment will earn you a return of 1.5 points.
More precisely,
Here are some examples:
Suppose that you invest 20 tokens in the BLUE investment and 30 tokens in the RED investment. Suppose that your group members (including yourself) together invest 90 tokens in the RED investment. Your income in this case is:
Suppose that you invest 50 tokens in the BLUE investment and 0 tokens in the RED investment. Suppose that your group members (including yourself) together invest 90 tokens in the RED investment. Your income in this case is:
Second 15 Rounds: Two-stage Investment Decision
Stage 1: Administrator Fund (AF)
At the beginning of each round, you will be endowed with 50 tokens and will be asked to decide how many tokens to spend on Administrator Fund (AF). Any integer amount between 0 and 50 (inclusive) is possible. In return to 1 token spending on AF, you will receive 1 lottery ticket with a ticket number on it. After all group members finish spending on AF, the computer randomly selects one winning lottery ticket (winning number). Each lottery ticket has equal chance to be selected.
If you have the winning lottery ticket (the winning number), then you become an administrator of your group in the round. After the 2nd stage, the administrator will monitor your group members’ RED investment and will have authority to impose a payoff deduction to one of the group members. More details will be provided later.
Stage 2: BLUE and RED Investment Decision
After the 1st stage Administrator Fund decision, no matter whether you become the administrator or not, you will be asked to decide how to divide remaining tokens (50 - Your Spending on AF) into two investment opportunities; BLUE investment and RED investment. The procedure of investment and returns from each investment are exactly the same as the first 15 rounds.
Administrator
The following screen shows how the administrator examines your RED investment.
The administrator may impose a deduction from your income subject to the following constraints:
The administrator needs to select only one of the group members to impose a payoff deduction.
The size of payoff deduction imposed to a group member should be no less than 0 and no more than three times the total size of the Administrator Fund, i. e. (3 × the sum of AF spending in a group).
Final Income
Here are some examples that show how to calculate your final income in each round:
Suppose that you spend 10 tokens on the Administrator Fund and get 10 lottery tickets with ticket number 11–20. It turns out that the winning lottery ticket number is 29. Then you are not an administrator. Next, you invest 10 tokens in the BLUE investment and 30 tokens in the RED investment. Your group members (including yourself) together invest 80 tokens in the RED investment. Suppose the size of AF in your group is 48 so that the power of administrator becomes 144. In the end, the administrator in your group imposes a payoff deduction of 30 to you. Your income in this round is:
Suppose that you spend 10 tokens on the Administrator Fund and get 10 lottery tickets with ticket number 11–20. It turns out that the winning lottery ticket number is 29. Then you are not an administrator. Next, you invest 10 tokens in the BLUE investment and 30 tokens in the RED investment. Your group members (including yourself) together invest 80 tokens in the RED investment. Suppose the size of AF in your group is 100 so that the power of administrator becomes 300. In the end, the administrator in your group imposes a payoff deduction of 200 to you. Your income in this round is:
Since your income is less than 0 in this case, you will just get 0 income.
Suppose that you spend 20 tokens in the Administrator Fund and get 20 lottery tickets with ticket number 26–45. It turns out that the winning lottery ticket number is 42. Then you become an administrator. Next, you invest 30 tokens in the BLUE investment and 0 tokens in the RED investment. Your group members (including yourself) together invest 50 tokens in the RED investment. Suppose the size of AF in your group is 60 so that the power of administrator becomes 180. In the end, the administrator (yourself) in your group imposes a payoff deduction of 0 to you. Your income in this round is:
Note. The amount taken by the administrator will disappear and no one, including the administrator, can get it.
Information Feedback
At the end of each round, the computer will provide a summary for the round: your AF spending, your BLUE investment, your group total RED investment, payoff deduction imposed to you, and your final income in the round.
Your Cash Payment
The experimenter randomly selects 2 rounds to calculate your cash payment, one from the first 15 rounds and one from the last 15 rounds. Each round has equal chance to be selected (So it is in your best interest to take each round seriously.) Your total payment will be the sum of your incomes in the two selected rounds divided by five plus a HK$30 show-up fee. Precisely,
Practice Rounds
To ensure your understanding of the instructions, we will provide you with a quiz and practice rounds. We will go through the quiz after you answer it on your own. You will then participate in 2 practice rounds, one for the first 15 round and one for the second 15 round. The practice rounds are part of the instructions which are not relevant to your cash payment; its objective is to get you familiar with the computer interface and the flow of the decisions in each round.
Once the practice rounds are over, the computer will tell you “The first 15 rounds begin now!” Once the first 15 rounds are over, the computer will tell you “The second 15 rounds begin now!” In each round, you will be randomly matched with seven other participants in this room.
Administration
Your decisions as well as your monetary payment will be kept confidential. Remember that you have to make your decisions entirely on your own; please do not discuss your decisions with any other participants. Upon finishing the experiment, you will receive your cash payment. You will be asked to sign your name to acknowledge your receipt of the payment (which will not be used for tax purposes). You are then free to leave.
If you have any question, please raise your hand now. We will answer your question individually. If there is no question, we will proceed to the quiz.
Quiz
True or False: I will be matched with the same seven other players in all 30 rounds.
In one of the first 15 rounds, suppose that you invest 20 tokens in BLUE investment and 30 tokens in RED investment. Your group total RED investment is 100 tokens. Calculate your income in this round.__________
In one of the second 15 rounds, suppose that you invest 20 tokens in BLUE investment and 10 tokens in RED investment. Your group total RED investment is 100 tokens. It turns out that the administrator imposes a payoff deduction of 40 tokens for you. Calculate your income in this round. __________
True or False: You spent 20 tokens for the AF. Your group members (including yourself) together spent 100 tokens for the AF. Then you have a 20 in 100 chance of being an administrator.
True or False: Your group members (including yourself) together spent 100 tokens for the AF. The administrator in your group can impose a payoff deduction for one of your group members no more than 300 tokens.
References
Anderson, Christopher M., and Louis Putterman. 2006. “Do Non-strategic Sanctions Obey the Law of demand? The Demand for Punishment in the Voluntary Contribution Mechanism.” Games and Economic Behavior 54: 1–24.10.1016/j.geb.2004.08.007Search in Google Scholar
Andreoni, James, and Laura K. Gee. 2012. “Gun for Hire: Delegated Enforcement and Peer Punishment in Public Goods Provision.” Journal of Public Economics 96: 1036–46.10.1016/j.jpubeco.2012.08.003Search in Google Scholar
Andreoni, James, William Harbaugh, and Lise Vesterlund. 2003. “The Carrot or the Stick: Rewards, Punishments, and Cooperation.” American Economic Review 93: 893–902.10.1257/000282803322157142Search in Google Scholar
Black, Sandra E., and Lisa M. Lynch. 2001. “How to Compete: The Impact of Workplace Practices and Information Technology on Productivity.” Review of Economics and Statistics 83: 434–45.10.3386/w6120Search in Google Scholar
Bonin, John P., Derek C. Jones, and Louis Putterman. 1993. “Theoretical and Empirical Studies of Producer Cooperatives: Will Ever the Twain Meet?” Journal of Economic Literature 31: 1290–320.Search in Google Scholar
Boyd, Robert, Herbert Gintis, and Samuel Bowles. 2010. “Coordinated Punishment of Defectors Sustains Cooperation and Can Proliferate When Rare.” Science 328: 617–20.10.1126/science.1183665Search in Google Scholar
Carpenter, Jeffrey P. 2007a. “The Demand for Punishment.” Journal of Economic Behavior & Organization 62: 522–42.10.1016/j.jebo.2005.05.004Search in Google Scholar
Carpenter, Jeffrey P. 2007b. “Punishing Free-Riders: How Group Size Affects Mutual Monitoring and the Provision of Public Goods.” Games and Economic Behavior 60: 31–51.10.1016/j.geb.2006.08.011Search in Google Scholar
Chen, Yan, and Charles R. Plott. 1996. “The Groves-Ledyard Mechanism: An Experimental Study of Institutional Design.” Journal of Public Economics 59: 335–64.10.1016/0047-2727(95)01506-XSearch in Google Scholar
Dal Bó, Pedro, Andrew Foster, and Louis Putterman. 2010. “Institutions and Behavior: Experimental Evidence on the Effects of Democracy.” American Economic Review 100: 2205–29.10.1257/aer.100.5.2205Search in Google Scholar
Denant-Boemont, Laurent, David Masclet, and Charles N. Noussair. 2007. “Punishment, Counterpunishment and Sanction Enforcement in a Social Dilemma Experiment.” Economic Theory 33: 145–67.10.1007/s00199-007-0212-0Search in Google Scholar
Dickson, Eric S., Sanford C. Gordon, and Gregory A. Huber. 2017. “Identifying Legitimacy: Experimental Evidence on Compliance with Authority.” Technical report, Yale University: Working Paper. https://huber.research.yale.edu/materials?10.1126/sciadv.abj7377Search in Google Scholar
Diekmann, Andreas, and Wojtek Przepiorka. 2015. “Punitive Preferences, Monetary Incentives and Tacit Coordination in the Punishment of Defectors Promote Cooperation in Humans.” Scientific Reports 5: 10321.10.1038/srep10321Search in Google Scholar
Ertan, Arhan, Talbot Page, and Louis Putterman. 2009. “Who to Punish? Individual Decisions and Majority Rule in Mitigating the Free Rider Problem.” European Economic Review 53: 495–511.10.1016/j.euroecorev.2008.09.007Search in Google Scholar
Falkinger, Josef, Ernst Fehr, Simon Gächter, and Rudolf Winter-Ember. 2000. “A Simple Mechanism for the Efficient Provision of Public Goods: Experimental Evidence.” American Economic Review 90: 247–64.10.1257/aer.90.1.247Search in Google Scholar
Fehr, Ernst, and Simon Gachter. 2000. “Cooperation and Punishment In Public Goods Experiments.” American Economic Review 90: 980–94.10.1257/aer.90.4.980Search in Google Scholar
Fehr, Ernst, Holger Herz, and Tom Wilkening. 2013. “The Lure of Authority: Motivation and Incentive Effects of Power.” American Economic Review 103: 1325–59.10.1257/aer.103.4.1325Search in Google Scholar
Fehr, Ernst, and Tony Williams. 2018. Social Norms, Endogenous Sorting and the Culture of Cooperation. ECON – Working Papers 267, Department of Economics – University of Zurich.10.2139/ssrn.3198185Search in Google Scholar
Fischbacher, Urs. 2007. “z-Tree: Zurich Toolbox for Ready-Made Economic Experiments.” Experimental Economics 10: 171–78.10.1007/s10683-006-9159-4Search in Google Scholar
Fudenberg, Drew, and Parag A. Pathak. 2010. “Unobserved Punishment Supports Cooperation.” Journal of Public Economics 94: 78–86.10.1016/j.jpubeco.2009.10.007Search in Google Scholar
Gross, Jörg, Zsombor Z. Méder, Sanae Okamoto-Barth, and Arno Riedl. 2016. “Building the Leviathan–Voluntary Centralisation of Punishment Power Sustains Cooperation in Humans.” Scientific Reports 6: 20767.10.1038/srep20767Search in Google Scholar
Hamman, John R., Roberto A. Weber, and Jonathan Woon. 2011. “An Experimental Investigation of Electoral Delegation and the Provision of Public Goods.” American Journal of Political Science 55: 738–52.10.1111/j.1540-5907.2011.00531.xSearch in Google Scholar
Hillman, Arye L., and John G. Riley. 1989. “Politically Contestable Rents and Transfers.” Economics & Politics 1: 17–39.10.1007/978-3-540-79182-9_11Search in Google Scholar
Hung, Angela A., and Charles R. Plott. 2001. “Information Cascades: Replication and an Extension to Majority Rule and Conformity-Rewarding Institutions.” American Economic Review 91: 1508–20.10.1257/aer.91.5.1508Search in Google Scholar
Isaac, R. Mark, and James M. Walker. 1988. “Group Size Effects in Public Goods Provision: The Voluntary Contributions Mechanism.” The Quarterly Journal of Economics 103: 179–99.10.2307/1882648Search in Google Scholar
Isaac, R. Mark, James M. Walker, and Arlington W. Williams. 1994. “Group Size and the Voluntary Provision of Public Goods: Experimental Evidence Utilizing Large Groups.” Journal of public Economics 54: 1–36.10.1016/0047-2727(94)90068-XSearch in Google Scholar
Kamei, Kenju. 2016. “Democracy and Resilient Pro-Social Behavioral Change: An Experimental Study.” Social Choice and Welfare 47: 359–78.10.1007/s00355-016-0967-ySearch in Google Scholar
Kosfeld, Michael, Akira Okada, and Arno Riedl. 2009. “Institution Formation in Public Goods Games.” American Economic Review 99: 1335–55.10.1257/aer.99.4.1335Search in Google Scholar
Kroll, Stephan, Todd L. Cherry, and Jason F. Shogren. 2007. “Voting, Punishment, and Public Goods.” Economic Inquiry 45: 557–70.10.1111/j.1465-7295.2007.00028.xSearch in Google Scholar
Krueger, Anne O. 1974. “The Political Economy of the Rent-Seeking Society.” The American Economic Review 64: 291–303.10.1007/978-3-540-79247-5_8Search in Google Scholar
Levine, David I. 1990. “Participation, Productivity, and the Firm’s Environment.” California Management Review 32: 86–100.10.2307/41166630Search in Google Scholar
Levine, David K. and Thomas R. Palfrey. 2007. “The Paradox of Voter Participation? A Laboratory Study.” American Political Science Review 101: 143–58.10.1017/S0003055407070013Search in Google Scholar
Loken, Eric, and Andrew Gelman. 2017. “Measurement Error and the Replication Crisis.” Science 355: 584–85.10.1126/science.aal3618Search in Google Scholar
Markussen, Thomas, Louis Putterman, and Jean-Robert Tyran. 2013. “Self-organization for Collective Action: An Experimental Study of Voting on Sanction Regimes.” Review of Economic Studies 81: 301–24.10.1093/restud/rdt022Search in Google Scholar
Masclet, David, Charles Noussair, Steven Tucker, and Marie-Claire Villeval. 2003. “Monetary and Nonmonetary Punishment in the Voluntary Contributions Mechanism.” American Economic Review 93: 366–80.10.1257/000282803321455359Search in Google Scholar
Morgan, John. 2000. “Financing Public Goods by Means of Lotteries.” The Review of Economic Studies 67: 761–84.10.1111/1467-937X.00153Search in Google Scholar
Muthukrishna, Michael, Patrick Francois, Shayan Pourahmadi, and Joseph Henrich. 2017. “Corrupting Cooperation and How Anti-corruption Strategies May Backfire.” Nature Human Behaviour 1: 0138.10.1038/s41562-017-0138Search in Google Scholar
Nicklisch, Andreas, Kristoffel Grechenig, and Christian Thöni. 2016. “Information-Sensitive Leviathans.” Journal of Public Economics 144: 1–13.10.1016/j.jpubeco.2016.09.008Search in Google Scholar
Nikiforakis, Nikos. 2008. “Punishment and Counter-Punishment in Public Good Games: Can we Really Govern Ourselves?” Journal of Public Economics 92: 91–112.10.1016/j.jpubeco.2007.04.008Search in Google Scholar
O’Gorman, Rick, Joseph Henrich, and Mark Van Vugt. 2008. “Constraining Free Riding in Public Goods Games: Designated Solitary Punishers Can Sustain Human Cooperation.” Proceedings of the Royal Society B: Biological Sciences 276: 323–29.10.1098/rspb.2008.1082Search in Google Scholar
Ostrom, Elinor, James Walker, and Roy Gardner. 1992. “Covenants with and Without a Sword: Self-Governance is Possible.” American Political Science Review 86: 404–17.10.2307/1964229Search in Google Scholar
Ozono, Hiroki, Nobuhito Jin, Motoki Watabe, and Kazumi Shimizu. 2016. “Solving the Second-Order Free Rider Problem in a Public Goods Game: An Experiment using a Leader Support System.” Scientific Reports 6: 38349.10.1038/srep38349Search in Google Scholar
Przepiorka, Wojtek, and Andreas Diekmann. 2013. “Individual Heterogeneity and Costly Punishment: A Volunteer’s Dilemma.” Proceedings of the Royal Society B: Biological Sciences 280: 20130247.10.1098/rspb.2013.0247Search in Google Scholar
Sigmund, Karl, Hannelore De Silva, Arne Traulsen, and Christoph Hauert. 2010. “Social Learning Promotes Institutions for Governing the Commons.” Nature 466: 861.10.1038/nature09203Search in Google Scholar
Spindler, Zane A. 1990. “Constitutional Design for a Rent-Seeking Society: Voting Rule Choice.” Constitutional Political Economy 1: 73–82.10.1007/BF02393241Search in Google Scholar
Sutter, Matthias, Stefan Haigner, and Martin G. Kocher. 2010. “Choosing the Carrot or the Stick? Endogenous Institutional Choice in Social Dilemma Situations.” The Review of Economic Studies 77: 1540–66.10.1111/j.1467-937X.2010.00608.xSearch in Google Scholar
Traulsen, Arne, Torsten Röhl, and Manfred Milinski. 2012. “An Economic Experiment Reveals that Humans Prefer Pool Punishment to Maintain the Commons.” Proceedings of the Royal Society B: Biological Sciences 279: 3716–21.10.1098/rspb.2012.0937Search in Google Scholar
Tullock, G. 2001. “Efficient Rent Seeking.” In Efficient Rent-Seeking, edited by A.A. Lockard, G. Tullock. Boston, MA: Springer.10.1007/978-1-4757-5055-3_2Search in Google Scholar
Tyran, Jean-Robert, and Lars P. Feld. 2006. “Achieving Compliance When Legal Sanctions are Non-deterrent.” Scandinavian Journal of Economics 108: 135–56.10.1111/j.1467-9442.2006.00444.xSearch in Google Scholar
Yamagishi, Toshio. 1986. “The Provision of a Sanctioning System as a Public Good.” Journal of Personality and Social Psychology 51: 110.10.1037/0022-3514.51.1.110Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
