Second-order Free-rider Problem Research Articles

Indirect reciprocity undermines indirect reciprocity destabilizing large-scale cooperation

Previous models suggest that indirect reciprocity (reputation) can stabilize large-scale human cooperation [K. Panchanathan, R. Boyd, Nature 432, 499-502 (2004)]. The logic behind these models and experiments [J. Gross et al., Sci. Adv. 9, eadd8289 (2023) and O. P. Hauser, A. Hendriks, D. G. Rand, M. A. Nowak, Sci. Rep. 6, 36079 (2016)] is that a strategy in which individuals conditionally aid others based on their reputation for engaging in costly cooperative behavior serves as a punishment that incentivizes large-scale cooperation without the second-order free-rider problem. However, these models and experiments fail to account for individuals belonging to multiple groups with reputations that can be in conflict. Here, we extend these models such that individuals belong to a smaller, "local" group embedded within a larger, "global" group. This introduces competing strategies for conditionally aiding others based on their cooperative behavior in the local or global group. Our analyses reveal that the reputation for cooperation in the smaller local group can undermine cooperation in the larger global group, even when the theoretical maximum payoffs are higher in the larger global group. This model reveals that indirect reciprocity alone is insufficient for stabilizing large-scale human cooperation because cooperation at one scale can be considered defection at another. These results deepen the puzzle of large-scale human cooperation.

Evolution of prosocial punishment in unstructured and structured populations and in the presence of antisocial punishment.

A large body of empirical evidence suggests that altruistic punishment abounds in human societies. Based on such evidence, it is suggested that punishment serves an important role in promoting cooperation in humans and possibly other species. However, as punishment is costly, its evolution is subject to the same problem that it tries to address. To suppress this so-called second-order free-rider problem, known theoretical models on the evolution of punishment resort to one of the few established mechanisms for the evolution of cooperation. This leaves the question of whether altruistic punishment can evolve and give rise to the evolution of cooperation in the absence of such auxiliary cooperation-favoring mechanisms unaddressed. Here, by considering a population of individuals who play a public goods game, followed by a public punishing game, introduced here, we show that altruistic punishment indeed evolves and promotes cooperation in the absence of a cooperation-favoring mechanism. In our model, the punishment pool is considered a public resource whose resources are used for punishment. We show that the evolution of a punishing institution is facilitated when resources in the punishment pool, instead of being wasted, are used to reward punishers when there is nobody to punish. Besides, we show that higher returns to the public resource or punishment pool facilitate the evolution of prosocial instead of antisocial punishment. We also show that an optimal cost of investment in the punishment pool facilitates the evolution of prosocial punishment. Finally, our analysis shows that being close to a physical phase transition facilitates the evolution of altruistic punishment.

The Singaporean model in public goods dilemmas with benevolent leaders and bribery

Public goods dilemmas are at the heart of some of the greatest challenges of our time, including climate inaction, growing inequality, and the overuse of natural resources. The public goods game in which cooperators contribute to a common pool that is then shared equally with defectors who contribute nothing captures the gist of the problem. Cooperators therefore cannot prevail, which ultimately leads to the tragedy of the commons. Actions such as punishment, rewards, and exclusion have been shown to help, but they are costly, therefore rendering cooperators second-order free-riders due to their lack of participation in these actions. In the search for a remedy, we study the public goods game with benevolent leaders who, at a personal cost, have the ability to exclude defectors from using common pool resources. We also consider bribers who can pay the leaders to relax their exclusion efforts. In a traditional setting, this setup yields the standard second-order free-rider problem, where, ironically, the leaders are overcome by cooperators, who then themselves succumb to defectors. We show, however, that the Singaporean model – where a leader’s payoff is determined not only by the regular sharing income from the firm production but also by the success of gross firm production as an incentive – can resolve the second-order free-rider problem. We also show that the detrimental effect of bribery can always be, no matter how high the bribe, held in check as long as the number of individuals engaged in this activity is low compared to the number of benevolent leaders. Otherwise, an abrupt transition to a cooperator-less state becomes unavoidable. We discuss the implications of our research for designing successful cooperation and anti-corruption strategies in public goods dilemmas.

Replicator dynamics for public goods game with resource allocation in large populations

Costly punishment can promote human cooperation, but the effectiveness of punishment is reduced because of the existence of second-order free-rider problem. How to solve the problem remains a challenge for the emergence of costly punishment. Motivated by the regimes of resource allocation in human society, in this work we consider the resource allocation with threshold for the common pool in the public goods game with an additional strategy of peer punishment, and aim to explore whether such proposed resource allocation can solve the problem of second-order free-riders by using replicator equations in infinite well-mixed populations. We assume that if contributing resources in the common pool exceed the threshold, the contributing resources will be divided into two parts: the first part will be equally allocated by all the players, and the second part will be allocated by all the players based on their strategy choices. Otherwise all the contributing resources are equally allocated by all the players. We find that the second-order free-rider problem can be effectively solved by this regime of resource allocation even when most of contributing resources are equally allocated among individuals. In addition, we find that punishment is the dominant strategy in a broad region of allocation parameters. Our work may thus suggest an effective approach about resource allocation for resisting second-order free-riders in the public goods dilemma.

Conditional punishment is a double-edged sword in promoting cooperation

Punishment is widely recognized as an effective approach for averting from exploitation by free-riders in human society. However, punishment is costly, and thus rational individuals are unwilling to take the punishing action, resulting in the second-order free-rider problem. Recent experimental study evidences that individuals prefer conditional punishment, and their punishing decision depends on other members’ punishing decisions. In this work, we thus propose a theoretical model for conditional punishment and investigate how such conditional punishment influences cooperation in the public goods game. Considering conditional punishers only take the punishing action when the number of unconditional punishers exceeds a threshold number, we demonstrate that such conditional punishment induces the effect of a double-edged sword on the evolution of cooperation both in well-mixed and structured populations. Specifically, when it is relatively easy for conditional punishers to engage in the punishment activity corresponding to a low threshold value, cooperation can be promoted in comparison with the case without conditional punishment. Whereas when it is relatively difficult for conditional punishers to engage in the punishment activity corresponding to a high threshold value, cooperation is inhibited in comparison with the case without conditional punishment. Moreover, we verify that such double-edged sword effect exists in a wide range of model parameters and can be still observed in other different punishment regimes.

How the Second-Order Free Rider Problem Is Solved in a Small-Scale Society

Moralistic punishment enables human cooperation, but an outstanding question is why people voluntarily sanction when they can obtain the benefits of punishment without being enforcers themselves. To address how decentralized societies solve this second-order free rider issue, I examine why people punish among the Turkana, a population in Kenya in which informal peer sanctioning sustains participation in high-stakes interethnic warfare. Using vignette experiments I show that Turkana subjects express punitive sentiments toward second-order free riders and those who sanction irresponsibly. The prevalence of such meta norms regulating punishment reveal a possible pathway by which moralistic punishment could have evolved.

Solving the second-order free rider problem in a public goods game: An experiment using a leader support system.

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.

The Sanctioning Dilemma: A Quasi-Experiment on Social Norm Enforcement in the Train

Numerous laboratory experiments have established peer-sanctioning as an important driver of norm compliance and cooperation in human groups. However, systematic evidence of peer-sanctioning occurring in the field is still rare. Here we present results from a quasi-experimental field study investigating the enforcement of the silence norm in the train. We let a confederate play music on his/her mobile phone in an open-plan train car and measure the time until a negative sanction occurs (if any). The silence norm is enforced in 45 of 90 cases, enforcement rates do not differ across silent- and non-silent-area cars, and the more passengers are in a car, the more likely is the silence norm enforced. Passengers’ propensities to enforce the silence norm are in line with predictions derived from the asymmetric volunteer’s dilemma (VOD). The higher a passenger’s net benefit from enforcing the silence norm is, the more likely is the passenger to negatively sanction the norm breaker. Our findings extend the validity of results from laboratory experiments which conceive the second-order free-rider problem as a VOD.

Collective punishment is more effective than collective reward for promoting cooperation.

Collective punishment and reward are usually regarded as two potential mechanisms to explain the evolution of cooperation. Both scenarios, however, seem problematic to understand cooperative behavior, because they can raise the second-order free-rider problem and many organisms are not able to discriminate less cooperating individuals. Even though they have been proved to increase cooperation, there has been a debate about which one being more effective. To address this issue, we resort to the N-player evolutionary snowdrift game (NESG), where a collective punishment/reward mechanism is added by allowing some players to display punishment/reward towards all remaining players. By means of numerous simulations and analyses, we find that collective punishment is more effective in promoting cooperation for a relatively high initial frequency of cooperation or for a relatively small group. When the intensity of punishment exceeds a certain threshold, a stable state of full cooperation emerges for both small and large groups. In contrast, such state does not appear for large groups playing a NESG with reward mechanism. In the case of mutualistic interactions, finally, our results show the new payoff with collective punishment/reward can lead to the coexistence of cooperators and defectors when discrimination between these two is not possible.

The Effect of Incentives and Meta-incentives on the Evolution of Cooperation.

Although positive incentives for cooperators and/or negative incentives for free-riders in social dilemmas play an important role in maintaining cooperation, there is still the outstanding issue of who should pay the cost of incentives. The second-order free-rider problem, in which players who do not provide the incentives dominate in a game, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players’ incentives. The critical assumption of our model is that players who tend to provide incentives to other players for their cooperative or non-cooperative behavior also tend to provide incentives to their incentive behaviors. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We find that the second-order free-rider problem is completely resolved without any third-order or higher (meta) incentive under the assumption. To do so, a second-order costly incentive, which is given individually (peer-to-peer) after playing donation games, is needed. The paper concludes that (1) second-order incentives for first-order reward are necessary for cooperative regimes, (2) a system without first-order rewards cannot maintain a cooperative regime, (3) a system with first-order rewards and no incentives for rewards is the worst because it never reaches cooperation, and (4) a system with rewards for incentives is more likely to be a cooperative regime than a system with punishments for incentives when the cost-effect ratio of incentives is sufficiently large. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives.

Probabilistic sharing solves the problem of costly punishment

Cooperators that refuse to participate in sanctioning defectors create the second-order free-rider problem. Such cooperators will not be punished because they contribute to the public good, but they also eschew the costs associated with punishing defectors. Altruistic punishers—those that cooperate and punish—are at a disadvantage, and it is puzzling how such behaviour has evolved. We show that sharing the responsibility to sanction defectors rather than relying on certain individuals to do so permanently can solve the problem of costly punishment. Inspired by the fact that humans have strong but also emotional tendencies for fair play, we consider probabilistic sanctioning as the simplest way of distributing the duty. In well-mixed populations the public goods game is transformed into a coordination game with full cooperation and defection as the two stable equilibria, while in structured populations pattern formation supports additional counterintuitive solutions that are reminiscent of Parrondoʼs paradox.

協同セルフヘルプ型 (「クラブ財型」) 集合行為におけるコミットメントと忠誠

We can hypothetically formulate a model to analyze a category of collective action that may be called “collective self-help social movements.” The thesis of “collective action problem” that M. Olson posits for collective actions that produce public goods does not apply to that category of actions, because the goods they produce are “club goods,” which are characterized by excludability (and nonrivalrousness). However, the cost of administrating and managing collective action (that corresponds to “second-order free-rider problem” for collective actions that produce public goods) tends to be remarkably higher than that of “first-order” activities that produce club goods themselves in those collective actions, and it tends to be covered by a limited number of members that form the leadership, who are characterized by “irrational” commitment and loyalty to the causes, ideologies, or goals of the movements they lead, and/or to the groups to which they suppose that they belong to (or, identities). We can hypothesize that that kind of collective actions tend to succeed where two conditions exist: where (1) there are committed or loyal leaders, and (2) the benefit from participating in those actions (the utility of the club goods produced by those actions) is high for a substantial part of the population. It is shown that Hirschman's findings on social movements for grassroots development in Latin America can be re-interpreted by that hypothesis and that the rise and fall of the “barter club” movements in Argentina can be interpreted (if not explained) by the same hypothesis. We might suppose that plausibility of the hypothesis presented in this essay would show that “irrational” elements play a substantial role in politics.

Evolutionary establishment of moral and double moral standards through spatial interactions.

Situations where individuals have to contribute to joint efforts or share scarce resources are ubiquitous. Yet, without proper mechanisms to ensure cooperation, the evolutionary pressure to maximize individual success tends to create a tragedy of the commons (such as over-fishing or the destruction of our environment). This contribution addresses a number of related puzzles of human behavior with an evolutionary game theoretical approach as it has been successfully used to explain the behavior of other biological species many times, from bacteria to vertebrates. Our agent-based model distinguishes individuals applying four different behavioral strategies: non-cooperative individuals (“defectors”), cooperative individuals abstaining from punishment efforts (called “cooperators” or “second-order free-riders”), cooperators who punish non-cooperative behavior (“moralists”), and defectors, who punish other defectors despite being non-cooperative themselves (“immoralists”). By considering spatial interactions with neighboring individuals, our model reveals several interesting effects: First, moralists can fully eliminate cooperators. This spreading of punishing behavior requires a segregation of behavioral strategies and solves the “second-order free-rider problem”. Second, the system behavior changes its character significantly even after very long times (“who laughs last laughs best effect”). Third, the presence of a number of defectors can largely accelerate the victory of moralists over non-punishing cooperators. Fourth, in order to succeed, moralists may profit from immoralists in a way that appears like an “unholy collaboration”. Our findings suggest that the consideration of punishment strategies allows one to understand the establishment and spreading of “moral behavior” by means of game-theoretical concepts. This demonstrates that quantitative biological modeling approaches are powerful even in domains that have been addressed with non-mathematical concepts so far. The complex dynamics of certain social behaviors become understandable as the result of an evolutionary competition between different behavioral strategies.

Second-order free-riding problem solved? (reply)

We have shown that, if a system of indirect reciprocity is stable, exclusion from that system could deter collective-action cheats1. Unlike direct punishment2,3,4,5, indirect punishers benefit by avoiding donation, obviating the second-order free-rider problem. Fowler claims6, however, that we assume away the second-order free-rider problem, and (by adding a new error term) argues that indirect-reciprocity defectors undermine cooperation.

Fehr on Altruism, Emotion, and Norms

Abstract I discuss recent work by Ernst Fehr and his collaborators on cooperation and reciprocity. (i) Their work demonstrates conclusively the reality and importance of non-self-interested motivations. (ii) It allows for a useful distinction between trust and blind trust. (iii) It points to a category of quasi-moral norms, distinct both from social norms and moral norms. (iv) It demonstrates how social interactions can generate irrational belief formation. (v) It shows the potential of punishment for sustaining social norms and for overcoming the second-order free rider problem as well as obstacles to group selection. (vi) It offers a provocative experimental basis for the ‘warm-glow’ explanation of altruistic behavior. I conclude by suggesting some experiments that might allow for further developments of the theory.

Indirect reciprocity can stabilize cooperation without the second-order free rider problem

Models of large-scale human cooperation take two forms. 'Indirect reciprocity' occurs when individuals help others in order to uphold a reputation and so be included in future cooperation. In 'collective action', individuals engage in costly behaviour that benefits the group as a whole. Although the evolution of indirect reciprocity is theoretically plausible, there is no consensus about how collective action evolves. Evidence suggests that punishing free riders can maintain cooperation, but why individuals should engage in costly punishment is unclear. Solutions to this 'second-order free rider problem' include meta-punishment, mutation, conformism, signalling and group-selection. The threat of exclusion from indirect reciprocity can sustain collective action in the laboratory. Here, we show that such exclusion is evolutionarily stable, providing an incentive to engage in costly cooperation, while avoiding the second-order free rider problem because punishers can withhold help from free riders without damaging their reputations. However, we also show that such a strategy cannot invade a population in which indirect reciprocity is not linked to collective action, thus leaving unexplained how collective action arises.

Social Relations and Cooperation in Organizations

The paper addresses the effects of social relations on cooperation (or collusion) in organizations and communities. and production relations are modeled as separate repeated strategic interactions. Linking them--by employing members of the same community or by encouraging social interaction between employees--is shown to facilitate cooperation in production: (a) because of available Social Capital, the slack of net expected gains from cooperation in the social relations which can be credibly transferred to discipline behavior in the workplace; (b) because payoffs from the social and production relations tend to be substitutes, in which case the linkage of more relations endogenously generates (a sort of increasing returns in cooperation); (c) because the linkage generates transfers of trust, reputation spillovers from a cooperative social background to newly started production relations; and (d) because agents who share social relations have access to additional information about each other's situations. The model provides a microfoundation for Putnam's concept of Social Capital and for Granovetter's idea of embeddedness for the employment relation. It shows that Kandel and Lazear's peer pressures are a credible effort-enforcing mechanism even when teams' members are fully self-interested, and that the threat of social sanctions can credibly enforce social norms independent of agents' moral constraints (that is, no second-order free rider problem exists). It provides an explanation for Japanese firms' investments in employees' free-time activities, for the Grameen Bank's requirement that group members belong to the same village and participate in social activities, for the ambiguous empirical results on the effectiveness of group-incentives, for markets' tendency to crowd out cooperative institutions, and for the sudden breakdown in trust and cooperation observed in communities after a war ends and peace is established.

Modeling the Second-Order Free-Rider Problem

Modeling the Second-Order Free-Rider Problem

Collective Action and the Second-Order Free-Rider Problem

This article examines the relationship between the first- and second-order free-rider problems in collective sanction systems, with special emphasis on the relative robustness of cooperation in the first and second levels. The results indicate that second-order cooperation exhibits surprising robustness relative to first-order cooperation. The implication is that hypocrisy, though universally maligned, may play a crucial transitional role both in the emergence of collective action and in the continuity of collective action under adverse circumstances.