Second-order Free-riders Research Articles

Evolutionary dynamics of public goods game with tax-based rewarding cooperators

In public goods games, rewards have been demonstrated as an effective mechanism for sustaining cooperation among individuals. Rewarding cooperators are willing to incur personal costs to incentivize cooperative behavior. However, pure cooperators become second-order free-riders because they are not willing to bear these additional costs. To address this issue and ensure the effectiveness of the reward strategy, we propose the introduction of a tax mechanism. We examine the performance of strong altruistic rewarding cooperators and weak altruistic rewarding cooperators separately, with the support of the tax mechanism. Through theoretical analysis and numerical calculations, our study reveals that tax-based rewarding cooperators possess an evolutionary advantage in maintaining cooperation. In addition, we found that strong altruistic rewarding cooperators were more effective than weak altruistic rewarding cooperators in solving the second-order free-riders problem. Our findings contribute to the understanding of cooperative behavior in public goods games and provide insights into the design of mechanisms that promote sustained cooperation. The introduction of a tax mechanism in combination with strong altruistic reward strategies can offer an effective solution to the second-order free-riders problem.

Social exclusion with antisocial punishment in spatial public goods game

In the spatial public goods game (SPGG), social exclusion is an effective strategy to quickly promote group cooperation. However, the second-order free riding occurs among cooperators who do not bear additional exclusion costs in the process of exclusion. To ensure that the exclusion strategy works while solving the second-order free-riding problem, we introduce an antisocial punishment strategy. The model employs four counterbalancing strategies: pure cooperators invest into the public pool; the defectors are the first-order free-riders of the cooperators; the excluders restrict the defectors from riding the cooperators with a certain probability, and the excluded defectors cannot share the benefits of the common pool; and the antisocial punishers punish the cooperators. Through the Monte Carlo simulations, we found that the cooperative excluders protected the cooperators from invasion by defectors and defective punishers, and more importantly, the second-order free-riding problem of the system was eliminated by the defective punishers.

The probabilistic pool punishment proportional to the difference of payoff outperforms previous pool and peer punishment

The public goods game is a multiplayer version of the prisoner’s dilemma game. In the public goods game, punishment on defectors is necessary to encourage cooperation. There are two types of punishment: peer punishment and pool punishment. Comparing pool punishment with peer punishment, pool punishment is disadvantageous in comparison with peer punishment because pool punishment incurs fixed costs especially if second-order free riders (those who invest in public goods but do not punish defectors) are not punished. In order to eliminate such a flaw of pool punishment, this study proposes the probabilistic pool punishment proportional to the difference of payoff. In the proposed pool punishment, each punisher pays the cost to the punishment pool with the probability proportional to the difference of payoff between his/her payoff and the average payoff of his/her opponents. Comparing the proposed pool punishment with previous pool and peer punishment, in pool punishment of previous studies, cooperators who do not punish defectors become dominant instead of pool punishers with fixed costs. However, in the proposed pool punishment, more punishers and less cooperators coexist, and such state is more robust against the invasion of defectors due to mutation than those of previous pool and peer punishment. The average payoff is also comparable to peer punishment of previous studies.

Egoistic punishment outcompetes altruistic punishment in the spatial public goods game

The evolution of costly punishment is a puzzle due to cooperators’ second-order free-riding. Previous studies have proposed many solutions mainly focused on reducing the punishment cost or punishing second-order free riders directly or indirectly. We attempt to explain this confusion from the perspective of punishment motivation, which is why the punisher is willing to pay the cost. The answer is that the punisher is egoistic. Egoistic punishment aims to protect punishers’ own cooperative benefits shared by the defectors. In such case, egoistic punishers would pay a cost in punishing defectors and retrieve lost payoffs from defectors. Here, we examined the evolution and performance of egoistic punishment and compared it with typical altruistic punishment using classic peer-punishment and pool-punishment modes. Results showed egoistic punishment can evolve and effectively promote cooperation within a large parameter range, whether in a well-mixed or structured population, or through peer-punishment or pool-punishment modes. This result is also robust to different strategy-updating rules. The evolution under the pool-punishment mechanism is more complicated. The influence of parameters is counter-intuitive because of cycle dominance; namely, the cost is the key factor to control the level of cooperation and the fine determines the ratio of the punishers and cooperators. Compared with altruistic punishment, egoistic punishment can promote cooperation in a lower-fine and higher-cost area, especially in the pool punishment mode, and the egoistic punishers have stronger survivability. Egoistic punishers represent the natural fairness in a social system. Results revealed that focusing on individual equity can significantly promote collective cooperation. This study provides another explanation for the evolution of costly 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.

Effects of beliefs about sanctions on promoting cooperation in a public goods game

Cooperative behaviour among people facing social dilemmas remains an unsolved puzzle. Sanction systems such as punishment and reward are well-known solutions to social dilemmas. On the one hand, it is theorised that peer sanctions cannot maintain cooperation because of the intrusion of second-order free riders. On the other hand, experimental studies have widely reported that cooperation is sustainable by first-order sanction systems. To understand the divergence between theory and experimental results, we focus on the effects of beliefs about sanctions on promoting cooperation. While previous studies have revealed effects of beliefs about other people’s cooperation in public goods games (PGGs), the effect of beliefs about sanctions have not been considered. We conducted a scenario-based experiment using one-shot PGGs with and without sanction systems. The results revealed that beliefs about sanctions promote cooperation in a PGG when types of sanctions and some psychological attitudes to cooperation are controlled for. Our results indicate that the beliefs of actors promote cooperation despite the possible presence of second-order free riders. A belief about sanctions differs from a preference for cooperative behaviour and the amount a player pays to exercise a sanction. It is necessary to consider players’ beliefs about a sanction when studying its effectiveness.

Evolution of cooperation in a hierarchical society with corruption control

Punishment is widely recognized as a potential promoter in sustaining or even enhancing public cooperation, but it meanwhile induces the problem of second-order free-riders. Particularly, recent evidence shows that costly punishment can be maintained if punishers may engage in corruption. However, how to reduce or eliminate incidents of corruption has been the enduring conundrum in human society. As power asymmetries are associated with hierarchies, we investigate how costly punishment affects the evolution of cooperation in the cases without and with corruption control. In the absence of corruption control, altruistic punishers are incapable of punishing corrupt punishers. Corrupt punishment maintains civilian cooperation but undermines the evolution of altruistic punishment. Otherwise, altruistic punishers can enforce symmetrical or asymmetrical punishment on both corrupt punishers and civilian defectors. In this case, both civilian cooperation and altruistic punishment can be promoted. And as an instrument of corruption control, the policy of asymmetrical punishment is more effective in fostering public cooperation and improving social welfare than symmetrical punishment. Moreover, no matter whether corruption control is considered or not, spiteful corruption that non-cooperative punishers penalize defectors is a more effective form for enhancing cooperation compared with bribery. Our work may thus offer an insight into the effects of corruption on public cooperation and the policy of anti-corruption.

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.

Second-Order Free-Riding on Antisocial Punishment Restores the Effectiveness of Prosocial Punishment

Economic experiments have shown that punishment can increase public goods game contributions over time. However, the effectiveness of punishment is challenged by second-order freeriding and antisocial punishment. The latter implies that non-cooperators punish cooperators, while the former implies unwillingness to shoulder the cost of punishment. Here we extend the theory of cooperation in the spatial public goods game by considering four competing strategies, which are traditional cooperators and defectors, as well as cooperators who punish defectors and defectors who punish cooperators. We show that if the synergistic effects are high enough to sustain cooperation based on network reciprocity alone, antisocial punishment does not deter public cooperation. Conversely, if synergistic effects are low and punishment is actively needed to sustain cooperation, antisocial punishment does act detrimental, but only if the cost-to-fine ratio is low. If the costs are relatively high, cooperation again dominates as a result of spatial pattern formation. Counterintuitively, defectors who do not punish cooperators, and are thus effectively second-order freeriding on antisocial punishment, form an active layer around punishing cooperators, which protects them against defectors that punish cooperators. A stable three-strategy phase that is sustained by the spontaneous emergence of cyclic dominance is also possible via the same route. The microscopic mechanism behind the reported evolutionary outcomes can be explained by the comparison of invasion rates that determine the stability of subsystem solutions. Our results reveal an unlikely evolutionary escape from adverse effects of antisocial punishment, and they provide a rationale for why second-order freeriding is not always an impediment to the evolutionary stability of punishment.

Punishing second-order free riders before first-order free riders: The effect of pool punishment priority on cooperation

Second-order free riders, who do not owe punishment cost to first-order free riders in public goods games, lead to low cooperation. Previous studies suggest that for stable cooperation, it is critical to have a pool punishment system with second-order punishment, which gathers resources from group members and punishes second-order free riders as well as first-order free riders. In this study, we focus on the priority of punishment. We hypothesize that the pool punishment system that prioritizes second-order punishment is more likely to achieve cooperation than the system that prioritizes first-order punishment, because the former is more likely to obtain sufficient punishment resources. In the experiments, we compare four pool punishment systems: 1To2 (first-order punishment to second-order punishment), 2To1 (second-order punishment to first-order punishment), 1ONLY (first-order punishment only), and 2ONLY (second-order punishment only). We find that the 2To1 and 2ONLY systems can receive more support than the 1To2 and 1ONLY systems and only the 2To1 system can achieve high cooperation. However, the effect of priority of second-order punishment is observed only when the punishment ratio (PR) is low (Experiment 1), not high (Experiment 2), in which the punishment resource is relatively abundant.

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.

How to keep punishment to maintain cooperation: Introducing social vaccine

Although there is much support for the punishment system as a sophisticated approach to resolving social dilemmas, more than a few researchers have also pointed out the limitations of such an approach. Second-order free riding is a serious issue facing the punishment system. Various pioneering works have suggested that an anti-social behavior or noise stemming from a mutation may, surprisingly, be helpful for avoiding second-order freeloaders. In this work, we show through mathematical analysis and an agent-based simulation of a model extending the meta-norms game that the coercive introduction of a small number of non-cooperators can maintain a cooperative regime robustly. This paradoxical idea was inspired by the effect of a vaccine, which is a weakened pathogen injected into a human body to create antibodies and ward off infection by that pathogen. Our expectation is that the coercive introduction of a few defectors, i.e., a social vaccine, will help maintain a highly cooperative regime because it will ensure that the punishment system works.

How the indirect reciprocity with co-evolving norm and strategy for 2 [formula omitted] 2 prisoner’s dilemma game works for emerging cooperation

We built a new indirect reciprocity model based on binary image scores, where an agent’s strategy and norm co-evolve. The norm, meaning what behavior is evaluated as “good” or “bad,” stipulates how image scores of two agents playing a game is altered, which has been presumed to be a fixed value in most previous studies. Also, unlike former studies, our model allows an agent to play with an agent who has a different norm. This point of relaxing the freedom of the model pulls down cooperation level vis-à-vis the case where an agent always plays with another one having same norm. However, it is observed that a rather larger dilemma shows robust cooperation establishing compared with a smaller dilemma, since a norm that punishes a so-called second-order free-rider is prompted. To encourage the evolution of norms to be able to punish second-order free-riders, a society needs a small number of defectors. This is elucidated by the fact that cases with action error are more cooperative than those without action error.

Social exclusion in finite populations.

Social exclusion, keeping free riders from benefit sharing, plays an important role in sustaining cooperation in our world. Here we propose two different exclusion regimes, namely, peer exclusion and pool exclusion, to investigate the evolution of social exclusion in finite populations. In the peer exclusion regime, each excluder expels all the defectors independently, and thus bears the total cost on his own, while in the pool exclusion regime, excluders spontaneously form an institution to carry out rejection of the free riders, and each excluder shares the cost equally. In a public goods game containing only excluders and defectors, it is found that peer excluders outperform pool excluders if the exclusion costs are small, and the situation is converse once the exclusion costs exceed some critical points, which holds true for all the selection intensities and different update rules. Moreover, excluders can dominate the whole population under a suitable parameters range in the presence of second-order free riders (cooperators), showing that exclusion has prominent advantages over common costly punishment. More importantly, our finding indicates that the group exclusion mechanism helps the cooperative union to survive under unfavorable conditions. Our results may give some insights into better understanding the prevalence of such a strategy in the real world and its significance in sustaining cooperation.

Group Cooperation without Group Selection: Modest Punishment Can Recruit Much Cooperation.

Humans everywhere cooperate in groups to achieve benefits not attainable by individuals. Individual effort is often not automatically tied to a proportionate share of group benefits. This decoupling allows for free-riding, a strategy that (absent countermeasures) outcompetes cooperation. Empirically and formally, punishment potentially solves the evolutionary puzzle of group cooperation. Nevertheless, standard analyses appear to show that punishment alone is insufficient, because second-order free riders (those who cooperate but do not punish) can be shown to outcompete punishers. Consequently, many have concluded that other processes, such as cultural or genetic group selection, are required. Here, we present a series of agent-based simulations that show that group cooperation sustained by punishment easily evolves by individual selection when you introduce into standard models more biologically plausible assumptions about the social ecology and psychology of ancestral humans. We relax three unrealistic assumptions of past models. First, past models assume all punishers must punish every act of free riding in their group. We instead allow punishment to be probabilistic, meaning punishers can evolve to only punish some free riders some of the time. This drastically lowers the cost of punishment as group size increases. Second, most models unrealistically do not allow punishment to recruit labor; punishment merely reduces the punished agent’s fitness. We instead realistically allow punished free riders to cooperate in the future to avoid punishment. Third, past models usually restrict agents to interact in a single group their entire lives. We instead introduce realistic social ecologies in which agents participate in multiple, partially overlapping groups. Because of this, punitive tendencies are more expressed and therefore more exposed to natural selection. These three moves toward greater model realism reveal that punishment and cooperation easily evolve by direct selection—even in sizeable groups.

Voluntary rewards mediate the evolution of pool punishment for maintaining public goods in large populations.

Punishment is a popular tool when governing commons in situations where free riders would otherwise take over. It is well known that sanctioning systems, such as the police and courts, are costly and thus can suffer from those who free ride on other's efforts to maintain the sanctioning systems (second-order free riders). Previous game-theory studies showed that if populations are very large, pool punishment rarely emerges in public good games, even when participation is optional, because of second-order free riders. Here we show that a matching fund for rewarding cooperation leads to the emergence of pool punishment, despite the presence of second-order free riders. We demonstrate that reward funds can pave the way for a transition from a population of free riders to a population of pool punishers. A key factor in promoting the transition is also to reward those who contribute to pool punishment, yet not abstaining from participation. Reward funds eventually vanish in raising pool punishment, which is sustainable by punishing the second-order free riders. This suggests that considering the interdependence of reward and punishment may help to better understand the origins and transitions of social norms and institutions.

The evolution of sanctioning institutions: an experimental approach to the social contract

A vast amount of empirical and theoretical research on public good games indicates that the threat of punishment can curb free-riding in human groups engaged in joint enterprises. Since punishment is often costly, however, this raises an issue of second-order free-riding: indeed, the sanctioning system itself is a common good which can be exploited. Most investigations, so far, considered peer punishment: players could impose fines on those who exploited them, at a cost to themselves. Only a minority considered so-called pool punishment. In this scenario, players contribute to a punishment pool before engaging in the joint enterprise, and without knowing who the free-riders will be. Theoretical investigations (Sigmund et al., Nature 466:861–863, 2010) have shown that peer punishment is more efficient, but pool punishment more stable. Social learning, i.e., the preferential imitation of successful strategies, should lead to pool punishment if sanctions are also imposed on second-order free-riders, but to peer punishment if they are not. Here we describe an economic experiment (the Mutual Aid game) which tests this prediction. We find that pool punishment only emerges if second-order free riders are punished, but that peer punishment is more stable than expected. Basically, our experiment shows that social learning can lead to a spontaneously emerging social contract, based on a sanctioning institution to overcome the free rider problem.

The evolution of cooperation by social exclusion

The exclusion of freeriders from common privileges or public acceptance is widely found in the real world. Current models on the evolution of cooperation with incentives mostly assume peer sanctioning, whereby a punisher imposes penalties on freeriders at a cost to itself. It is well known that such costly punishment has two substantial difficulties. First, a rare punishing cooperator barely subverts the asocial society of freeriders, and second, natural selection often eliminates punishing cooperators in the presence of non-punishing cooperators (namely, ‘second-order’ freeriders). We present a game-theoretical model of social exclusion in which a punishing cooperator can exclude freeriders from benefit sharing. We show that such social exclusion can overcome the above-mentioned difficulties even if it is costly and stochastic. The results do not require a genetic relationship, repeated interaction, reputation or group selection. Instead, only a limited number of freeriders are required to prevent the second-order freeriders from eroding the social immune system.

An economic experiment reveals that humans prefer pool punishment to maintain the commons

Punishment can stabilize costly cooperation and ensure the success of a common project that is threatened by free-riders. Punishment mechanisms can be classified into pool punishment, where the punishment act is carried out by a paid third party, (e.g. a police system or a sheriff), and peer punishment, where the punishment act is carried out by peers. Which punishment mechanism is preferred when both are concurrently available within a society? In an economic experiment, we show that the majority of subjects choose pool punishment, despite being costly even in the absence of defectors, when second-order free-riders, cooperators that do not punish, are also punished. Pool punishers are mutually enforcing their support for the punishment organization, stably trapping each other. Our experimental results show how organized punishment could have displaced individual punishment in human societies.