Punishment of non-cooperators—free riders—can lead to high cooperation in public goods games (PGG). However, second-order free riders, who do not pay punishment costs, reduce the effectiveness of punishment. Here we introduce a “leader support system,” in which one group leader can freely punish group followers using capital pooled through the support of group followers. In our experiment, participants engage in three stages repeatedly: a PGG stage in which followers decide to cooperate for their group; a support stage in which followers decide whether to support the leader; and a punishment stage in which the leader can punish any follower. We compare a support-present condition with a no-support condition, in which there is an external source for the leader’s punishment. The results show that punishment occurs more frequently in the support-present condition than the no-support condition. Within the former, both higher cooperation and higher support for a leader are achieved under linkage-type leaders—who punish both non-cooperators and non-supporters. In addition, linkage-type leaders themselves earn higher profits than other leader types because they withdraw more support. This means that leaders who effectively punish followers could increase their own benefits and the second-order free rider problem would be solved. 1579 scirep Scientific Reports Sci Rep Nature Publishing Group PMC5146942 5146942 5146942 27934871 10.1038/srep38349 Solving the second-order free rider problem in a public goods game: An experiment using a leader support system Ozono Hiroki 1 a Jin Nobuhito 2 Watabe Motoki 3 Shimizu Kazumi 4 1 Faculty of Law, Economics and Humanities, Kagoshima University, 1-21-30, Korimoto, Kagoshima 890-0065, Japan 2 School of Psychology Practices, College of Integrated Human and Social Welfare Studies, Shukutoku University, 200, Daiganji-cho, Chuo-ku, Chiba 260-8701, Japan 3 School of Business, MonashUniversity, Malaysia, Jalan Lagoon Selatan, 46150 Bandar Sunway, Selangor Darul Ehsan, Malaysia 4 School of Political Science and Economics, Waseda University, Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan a Email: Hiroki.ozono@gmail.com 9 12 2016 6 38349 38349 16 12 2016 Copyright © 2016, The Author(s) This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ Abstract Punishment of non-cooperators—free riders—can lead to high cooperation in public goods games (PGG). However, second-order free riders, who do not pay punishment costs, reduce the effectiveness of punishment. The difficulties of constructing a cooperative relationship are formulized as a public goods problem 1 , 2 , and many such studies are conducted in the social sciences. In a typical public goods game (PGG), group members decide how much of their own resources to contribute to the common pool and the resources gathered in the pool benefit members equally. The entire group earns the highest profit when all members contribute all their resources. Free riders, however, can increase their own payoff if they contribute nothing and still benefit from the common pool. This results in a socially inefficient situation. This is called the free rider problem. Despite several laboratory experiments indicating that peer punishment solves the free rider problem 3 , 4 , 5 , 6 , several theoretical and empirical questions have been posed. The biggest theoretical issue is the second-order free rider problem 8 , 9 . Because punishing someone incurs cost, owing the punishment cost to maintain group cooperation is a second-order cooperative action. However, because the individual’s profits increase if s/he punishes nobody, second-order free riders emerge. Thus, in theory, peer punishment should not evolve. The reasons people punish, even if they have to pay the cost, have been proposed using multi-level selection theory 10 and reputational benefits for punishers 11 , 12 . However, both theories have been criticized (Pinker’s criticism 13 for multi-level selection; Raihani and Bshary’s criticism 14 for punishers’ reputations) and there is no sufficient answer yet. Furthermore, an anthropological survey showed that punishment between individuals is rare in a small society, which is similar to an evolved environment 15 . As such, there is much doubt as to Other than the peer punishment system, the pool punishment system has been proposed to solve the public goods problem 16 , 17 , 18 , 19 , 20 . Sigmund et al . 18 compares peer punishment with pool punishment, in which group members pay costs to a punishment-executing system (e.g., a police force) and the system uses these resources as capital to punish free riders. The authors mathematically show that the pool punishment system is more stable than peer punishment only when the system punishes both the first- and second-order free riders (the latter do not bear the cost of the punishment system). Traulsen et al . Solving the second-order free rider problem in a public goods game: An experiment using a leader support system. Sci. Rep. 6 , 38349; doi: 10.1038/srep38349 (2016). Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Supplementary Material Supplementary Information Acknowledgments This work was supported by JS PSKAKENHI Grant Number 25885057. Footnotes Author Contributions H.O. & N.J. designed research and H.O. & K.S. performed the experiment; H.O. & M.W. analyzed the data and wrote the paper; all authors interpreted the results and reviewed and approved the manuscript.

Humans are considered a highly cooperative species. Through cooperation, we can tackle shared problems like climate change or pandemics and cater for shared needs like shelter, mobility, or healthcare. However, cooperation invites free-riding and can easily break down. Maybe because of this reason, societies also enable individuals to solve shared problems individually, like in the case of private healthcare plans or private retirement planning. Such "self-reliance" allows individuals to avoid problems related to public goods provision, like free-riding or underprovision, and decreases social interdependence. However, not everyone can equally afford to be self-reliant, and amid shared problems, self-reliance may lead to conflicts within groups on how to solve shared problems. In two preregistered studies, we investigate how the ability of self-reliance influences collective action and cooperation. We show that self-reliance crowds out cooperation and exacerbates inequality, especially when some heavily depend on collective action while others do not. However, we also show that groups are willing to curtail their ability of self-reliance. When given the opportunity, groups overwhelmingly vote in favor of abolishing individual solutions to shared problems, which, in turn, increases cooperation and decreases inequality, particularly between group members that differ in their ability to be self-reliant. The support for such endogenously imposed interdependence, however, reduces when individual solutions become more affordable, resonating with findings of increased individualism in wealthier societies and suggesting a link between wealth inequality and favoring individual independence and freedom over communalism and interdependence. #28,383 | AsPredicted ' Self-imposed interdependence ' Download PDF AsPredicted #: 28,383 Author(s) Jörg Gross (Leiden University) - gross@psychologie.uzh.ch Robert Böhm (RWTH Aachen University) - robert.boehm@univie.ac.at Pre-registered on 2019/09/26 02:47 (PT) 1) Have any data been collected for this study already? No, no data have been collected for this study yet. 2) What's the main question being asked or hypothesis being tested in this study? Research question: Do groups of individuals coordinate on abandoning individual solutions to shared social problems in order to increase group interdependence and achieve greater social welfare? Or, alternatively, do they prefer to maintain individual solutions at the cost of social welfare? Hypotheses: 1. Having individual solutions (in addition to a collective solution) will lead to less cooperation and more coordination failure. 2. With increasing costs for individual solutions (relative to collective solutions), group members will more likely choose to abolish individual solutions. 3. This will lead to increased social welfare compared to the control treatment in which groups have no mean to abolish individual solutions to shared problems. 3) Describe the key dependent variable(s) specifying how they will be measured. Key DVs: 1. Individual choice to abolish individual solutions (in the voting treatment only). 2. Individual contribution decision to private pool (individual solution), shared public pool (collective solution), and tokens kept (free-riding) 4) How many and which conditions will participants be assigned to? Two-factorial mixed design; Between-subjects factor: 1. Control treatment: Individuals have no choice regarding whether to abolish the individual solution or not (i.e., they play the game with the individual and the collective solution) 2. Voting treatment: Individuals can vote after every third round on whether to maintain or abolish the individual solution as a potential behavioral strategy in the following three rounds; the outcome is determined by the majority voting rule in the 5-person group. Within-subject factor: The game is played repeatedly for 54 rounds in three blocks, each with 18 rounds. The order of the blocks is counter-balanced and varies the costs of the individual solution (i.e., 40 vs. 60 vs. 80) at a fixed cost for the collective solution (i.e., 200). 5) Specify exactly which analyses you will conduct to examine the main question/hypothesis.

We argue that the incentive structure of all individual and coordinated measures across countries to contain the corona-pandemic is that of a weakest-link public good game. We discuss a selection of theoretical and experimental key results of weakest-link games and interpret them in the light of the corona-pandemic. First, we highlight that experimental evidence does not support the assumption that coordination can be trivially solved, even among symmetric players. Second, we argue that for asymmetric countries the weakest-link game does not only pose a problem of coordination, but also a problem of cooperation. Third, we show how and under which conditions self-enforcing treaties can foster coordination and cooperation. We account for the possibility that countries make mistakes when choosing their actions. Our discussion shows that North-South cooperation is relevant and likely to be self-enforcing and that regional cooperation, e.g., within the EU, will also be important.

Uniform punishment policies can sustain cooperation in social dilemmas but impose severe costs on enforcers, creating a second-order free-rider problem that undermines the very mechanism designed to prevent exploitation. We show that the remedy is not a harsher stick but a smarter one. In a four-strategy spatial public-goods game we pit conventional punishers, who levy a fixed fine, against norm-responsive punishers that double both fine and cost only when at least half of their current group already cooperates. Extensive large scale Monte Carlo simulations on lattices demonstrate that context-sensitive punishment achieves complete defector elimination at fine levels 15\% lower than uniform enforcement, despite identical marginal costs per sanctioning event. The efficiency gain emerges because norm-responsive punishers conserve resources in defector-dominated regions while concentrating intensified sanctions at cooperative-defector boundaries, creating self-reinforcing fronts that amplify the spread of prosocial behavior. These findings reveal that enforcement efficiency can be dramatically improved by targeting punishment at cooperative-defector interfaces rather than applying uniform sanctions, offering quantitative guidelines for designing adaptive regulatory mechanisms that maximize compliance while minimizing institutional costs.

Background/Objectives: Free riding in healthcare occurs when actors benefit from health-related public goods, risk-pooling arrangements, common resources, or cooperative institutions while contributing less than is socially optimal. This review clarifies how free-rider dynamics differ across vaccination, health insurance and universal health coverage, antimicrobial resistance, organ donation and transplant allocation, and global health cooperation. Methods: A narrative review with conceptual synthesis was conducted. Searches of PubMed and Scopus were complemented by citation tracking and targeted inclusion of foundational economics, game theory, public-health ethics, and market-design sources. Sources were mapped by domain, actors, strategies, payoff structure, information conditions, time horizon, enforcement mechanism and policy relevance. Results: Across domains, free riding arises when private payoffs diverge from collective welfare, but the underlying game differs: threshold public-good and coordination games in vaccination, adverse-selection and participation games in insurance, common-pool-resource dilemmas in antimicrobial use, donor-registration and matching-market problems in transplantation, and repeated public-goods games in global health. The review identifies three policy functions: altering payoffs, altering information and beliefs, and changing the structure, repetition, or enforceability of the game. Conclusions: Game theory is most useful as a mechanism-based framework rather than a stand-alone policy prescription. Its policy value depends on empirical calibration, institutional context, ethical legitimacy, and attention to equity, incomplete information, behavioral responses, and enforcement capacity. The synthesis also emphasizes boundary conditions: game-theoretic prescriptions can fail when political economy, asymmetric power, implementation capacity, access barriers, or trust-related drivers are ignored.