We study the evolution of cooperation in spatial public goods games where, besides the classical strategies of cooperation (C) and defection (D), we consider punishing cooperators (PC) or punishing defectors (PD) as an additional strategy. Using a minimalist modeling approach, our goal is to separately clarify and identify the consequences of the two punishing strategies. Since punishment is costly, punishing strategies loose the evolutionary competition in case of well-mixed interactions. When spatial interactions are taken into account, however, the outcome can be strikingly different, and cooperation may spread. The underlying mechanism depends on the character of the punishment strategy. In case of cooperating punishers, increasing the fine results in a rising cooperation level. In contrast, in the presence of the PD strategy, the phase diagram exhibits a reentrant transition as the fine is increased. Accordingly, the level of cooperation shows a non-monotonous dependence on the fine. Remarkably, punishing strategies can spread in both cases, but based on largely different mechanisms, which depend on the cooperativeness (or not) of punishers.
We have studied the evolution of strategies in spatial public goods games where both individual (peer) and institutional (pool) punishments are present beside unconditional defector and cooperator strategies. The evolution of strategy distribution is governed by imitation based on random sequential comparison of neighbors' payoff for a fixed level of noise. Using numerical simulations we have evaluated the strategy frequencies and phase diagrams when varying the synergy factor, punishment cost, and fine. Our attention is focused on two extreme cases describing all the relevant behaviors in suc…
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 sh…
Pro-social punishment, whereby cooperators punish defectors, is often suggested as a mechanism that maintains cooperation in large human groups. Importantly, models that support this idea have to date only allowed defectors to be the target of punishment. However, recent empirical work has demonstrated the existence of anti-social punishment in public goods games. That is, individuals that defect have been found to also punish cooperators. Some recent theoretical studies have found that such anti-social punishment can prevent the evolution of pro-social punishment and cooperation. However, the…
A large body of empirical evidence suggests that humans are willing to engage in costly punishment of defectors in public goods games. Based on such pieces of evidence, it is suggested that punishment serves an important role in promoting cooperation in humans, and possibly other species. Nevertheless, theoretical work has been unable to show how this is possible. The problem originates from the fact that punishment, being costly, is an altruistic act and its evolution is subject to the same problem that it tries to address. To suppress this so-called second-order free-rider problem, known the…
Cooperation in evolutionary biology means paying a cost, c, to enjoy benefits, b. A defector is one who does not pay any cost but enjoys the benefits of cooperators. Human societies, especially, have evolved a strategy to discourage defection, punishment. Costly punishment is a type of punishment where an agent in a biological network or some cooperative scheme pays a cost to ensure another agent incurs some cost. A previous study shows how parameters like diversity in neighbors across games, density of connectivity, and costly punishment influence the evolution of cooperation in non-regular n…
Identifying mechanisms able to sustain costly cooperation among self-interested agents is a central problem across social and biological sciences. One possible solution is peer punishment: when agents have an opportunity to sanction defectors, classical behavioral experiments suggest that cooperation can take root. Overlooked from standard experimental designs, however, is the fact that real-world human punishment -- the administration of justice -- is intrinsically noisy. Here we show that stochastic punishment falls short of sustaining cooperation in the repeated public good game. As punishm…
The efficiency of institutionalized punishment is studied by evaluating the stationary states in the spatial public goods game comprising unconditional defectors, cooperators, and cooperating pool-punishers as the three competing strategies. Fine and cost of pool-punishment are considered as the two main parameters determining the stationary distributions of strategies on the square lattice. Each player collects its payoff from five five-person public goods games, and the evolution of strategies is subsequently governed by imitation based on pairwise comparisons at a low level of noise. The im…
In explaining altruistic cooperation and punishment, the challenging riddle is how transcendental rules can emerge within the empirical world. Game-theoretical studies showed that pool punishment, particularly second-order punishment, plays a key role in understanding the evolution of cooperation. Second-order pool punishment, however, is tautological in nature; the punishment system itself is caused by its own effects. The emergence of pool punishment poses a logical conundrum that, to date, has been overlooked in the study of the evolution of social norms and institutions. Here, we tackle th…
Punishment and partner switching are two well-studied mechanisms that support the evolution of cooperation. Observation of human behaviour suggests that the extent to which punishment is adopted depends on the usage of alternative mechanisms, including partner switching. In this study, we investigate the combined effect of punishment and partner switching in evolutionary prisoner's dilemma games conducted on a network. In the model, agents are located on the network and participate in the prisoner's dilemma games with punishment. In addition, they can opportunistically switch interaction partn…
Punishment may deter antisocial behavior. Yet to punish is costly, and the costs often do not offset the gains that are due to elevated levels of cooperation. However, the effectiveness of punishment depends not only on how costly it is, but also on the circumstances defining the social dilemma. Using the snowdrift game as the basis, we have conducted a series of economic experiments to determine whether severe punishment is more effective than mild punishment. We have observed that severe punishment is not necessarily more effective, even if the cost of punishment is identical in both cases. …
Previous studies suggest that punishment is a useful way to promote cooperation in the well-mixed public goods game, whereas it still lacks specific evidence that punishment maintains cooperation in spatial prisoner's dilemma game as well. To address this issue, we introduce a mechanism of recorded punishment, involved with memory and punishment, into spatial prisoner's dilemma game. We find that increasing punishment rate or memory length promotes the evolution of cooperation monotonously. Interestingly, compared with traditional version, recorded punishment will facilitate cooperation better…
Cooperation is crucial for the remarkable evolutionary success of the human species. Not surprisingly, some individuals are willing to bare additional costs in order to punish defectors. Current models assume that, once set, the fine and cost of punishment do not change over time. Here we show that relaxing this assumption by allowing players to adapt their sanctioning efforts in dependence on the success of cooperation can explain both, the spontaneous emergence of punishment, as well as its ability to deter defectors and those unwilling to punish them with globally negligible investments. By…
An open problem in evolutionary game dynamics is to understand the effect of peer pressure on cooperation in a quantitative manner. Peer pressure can be modeled by punishment, which has been proved to be an effective mechanism to sustain cooperation among selfish individuals. We investigate a symmetric punishment strategy, in which an individual will punish each neighbor if their strategies are different, and vice versa. Because of the symmetry in imposing the punishment, one might expect intuitively the strategy to have little effect on cooperation. Utilizing the prisoner's dilemma game as a …
We study the evolution of cooperation in spatial public goods games with four competing strategies: cooperators, defectors, punishing cooperators, and punishing defectors. To explore the robustness of the cooperation-promoting effect of costly punishment, besides the usual strategy adoption dynamics we also apply strategy mutations. As expected, frequent mutations create kind of well-mixed conditions, which support the spreading of defectors. However, when the mutation rate is small, the final stationary state does not significantly differ from the state of the mutation-free model, independent…
Collective actions, from city marathons to labor strikes, are often mass-driven and subject to the snowball effect. Motivated by this, we study evolutionary advantages of conditional punishment in the spatial public goods game. Unlike unconditional punishers who always impose the same fines on defectors, conditional punishers do so proportionally with the number of other punishers in the group. Phase diagrams in dependence on the punishment fine and cost reveal that the two types of punishers cannot coexist. Spontaneous coarsening of the two strategies leads to an indirect territorial competit…
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 emer…
Incomplete Reputation Information and Punishment in Indirect Reciprocity
Pukyong National University（釜庆国立大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Science (iTHEMS)（理化学研究所交叉理论数学科学中心（iTHEMS））；RIKEN Center for Computational Science（理化学研究所计算科学中心）
Finding ways to overcome the temptation to exploit one another is still a challenge in behavioural sciences. In the framework of evolutionary game theory, punishing strategies are frequently used to promote cooperation in competitive environments. Here, we introduce altruistic punishers in the spatial public goods game. This strategy acts as a cooperator in the absence of defectors, otherwise it will punish all defectors in their vicinity while bearing a cost to do so. We observe three distinct behaviours in our model: i) in the absence of punishers, cooperators (who don't punish defectors) ar…
Punishment is an effective way to sustain cooperation among selfish individuals. In most of previous studies, objects of punishment are set to be defectors. In this paper, we propose a mechanism of punishment, in which individuals with the majority strategy will punish those with the minority strategy in a public goods game group. Both theoretical analysis and simulation show that the cooperation level can be greatly enhanced by punishing minority. For no punishment or small values of punishment fine, the fraction of cooperators continuously increases with the multiplication factor. However, f…
Non-participant externalities reshape the evolution of altruistic punishment
School of Computing, Engineering and Digital Technologies, Teesside University（蒂赛德大学计算、工程与数字技术学院）；Faculty of Engineering Sciences, Kyushu University（九州大学工学研究院）；Department of Psychology, University of Milan Biccoca（米兰比可卡大学心理学系）
Strong reciprocity is a fundamental human characteristic associated with our extraordinary sociality and cooperation. Laboratory experiments on social dilemma games and many field studies have quantified well-defined levels of cooperation and propensity to punish/reward. The level of cooperation is observed to be strongly dependent on the availability of punishments and/or rewards. Here, we suggest that the propensity for altruistic punishment and reward is an emergent property that has co-evolved with cooperation by providing an efficient feedback mechanism through both biological and cultura…
Economic studies have shown that there are two types of regulation schemes which can be considered as a vital part of today's global economy: self-regulation enforced by self-regulation organizations to govern industry practices, and government regulation which is considered as another scheme to sustain corporate adherence. An outstanding problem of particular interest is to understand quantitatively the role of these regulation schemes in evolutionary dynamics. Typically, punishment usually occurs for enforcement of regulations. Taking into account both types of punishments to curve the regul…
Pro-social punishment and exclusion are common means to elevate the level of cooperation among unrelated individuals. Indeed, it is worth pointing out that the combined use of these two strategies is quite common across human societies. However, it is still not known how a combined strategy where punishment and exclusion are switched can promote cooperation from the theoretical perspective. In this paper, we thus propose two different switching strategies, namely peer switching that is based on peer punishment and peer exclusion, and pool switching that is based on pool punishment and pool exc…
Failures of cooperation cause many of society's gravest problems. It is well known that cooperation among many players faced with a social dilemma can be maintained thanks to the possibility of punishment, but achieving the initial state of widespread cooperation is often much more difficult. We show here that there exist strategies of `targeted punishment' whereby a small number of punishers can shift a population of defectors into a state of global cooperation. The heterogeneity of players, often regarded as an obstacle, can in fact boost the mechanism's effectivity. We conclude by outlining…
Monitoring with implicated punishment is common in human societies to avert freeriding on common goods. But is it effective in promoting public cooperation? We show that the introduction of monitoring and implicated punishment is indeed effective, as it transforms the public goods game to a coordination game, thus rendering cooperation viable in infinite and finite well-mixed populations. We also show that the addition of within-group enforcement further promotes the evolution of public cooperation. However, although the group size in this context has nonlinear effects on collective action, an…
Punishment, especially selfish punishment, has recently been identified as a potent promoter in sustaining or even enhancing the cooperation among unrelated individuals. However, without other key mechanisms, the first-order social dilemma and second-order social dilemma are still two enduring conundrums in biology and the social sciences even with the presence of punishment. In the present study, we investigate a spatial evolutionary four-strategy prisoner's dilemma game model with avoiding mechanism, where the four strategies are cooperation, defection, altruistic and selfish punishment. By …
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 str…
Utilizing common resources is always a dilemma for community members. While cooperator players restrain themselves and consider the proper state of resources, defectors demand more than their supposed share for a higher payoff. To avoid the tragedy of the common state, punishing the latter group seems to be an adequate reaction. This conclusion, however, is less straightforward when we acknowledge the fact that resources are finite and even a renewable resource has limited growing capacity. To clarify the possible consequences, we consider a coevolutionary model where beside the payoff-driven …
As a simple model for criminal behavior, the traditional two-strategy inspection game yields counterintuitive results that fail to describe empirical data. The latter shows that crime is often recurrent, and that crime rates do not respond linearly to mitigation attempts. A more apt model entails ordinary people who neither commit nor sanction crime as the third strategy besides the criminals and punishers. Since ordinary people free-ride on the sanctioning efforts of punishers, they may introduce cyclic dominance that enables the coexistence of all three competing strategies. In this setup or…
The mitigation of the effects of climate change on humankind is one of the most pressing and important collective governance problems nowadays$^{1-4}$. To explore different solutions and scenarios, previous works have framed this problem into a Public Goods Game (PGG), where a dilemma between short-term interests and long-term sustainability arises$^{5-9}$. In such a context, subjects are placed in groups and play a PGG with the aim of avoiding dangerous climate change impact. Here we report on a lab experiment designed to explore two important ingredients: costly punishment to free-riders and…
Peer punishment of free-riders (defectors) is a key mechanism for promoting cooperation in society. However, it is highly unstable since some cooperators may contribute to a common project but refuse to punish defectors. Centralized sanctioning institutions (for example, tax-funded police and criminal courts) can solve this problem by punishing both defectors and cooperators who refuse to punish. These institutions have been shown to emerge naturally through social learning and then displace all other forms of punishment, including peer punishment. However, this result provokes a number of que…
Typical arguments against scientific misconduct generally fail to support current policies on research fraud: they may not prove wrong what is usually considered research misconduct and they tend to make wrong things that are not normally seen as scientific fraud, in particular honest errors. I also point out that sanctions are not consistent with the reasons why scientific fraud is supposed to be wrong either. Moreover honestly seeking truth should not be contrived as a moral rule -- it is instead a necessary condition for work to qualify as scientific. Keywords: cheating; ethics; fabrication…
Mean field Master equations for the norm game are investigated. The strategies are: to obey the norm or not and to punish those who break it or not. The punishment, the temptation, the punishment cost and the relaxation of vengeance are modeled by four parameters; for the fixed points, only two ratios of these parameters are relevant. The analysis reveals two phases; in one of them, nobody obeys the norm and nobody punishes. This phase is stable if the punishment is small enough. In the other phase, the proportion of defectors depends on the parameters and in some cases it can be arbitrarily s…
Trust plays an essential role in the development of human society. According to the standard trust game, an investor decides whether to keep or transfer a certain portion of initial stake to a trustee. In the latter case, the stake is enhanced to signal the value of trust. The trustee then chooses how much to return to the investor. We here distinguish two types of investors and two types of trustees who can learn from each other. While a trustee can be trustworthy or untrustworthy, an investor could be normal or punishing one. The latter strategy punishes both untrustworthy trustees and norma…
The public goods game is a famous example illustrating the tragedy of the commons. In this game cooperating individuals contribute to a pool, which in turn is distributed to all members of the group, including defectors who reap the same rewards as cooperators without having made a contribution before. The question is now, how to incentivize group members to all cooperate as it maximizes the common good. While costly punishment presents one such method, the cost of punishment still reduces the common good. Here we show how group-level selection can be such an incentive, and specifically how ev…
Empirical studies have shown that individuals' behaviors are largely influenced by social conformity, including punishment. However, a coevolutionary theoretical framework that takes into account effects of conformity on individuals' punishment behaviors has not been put forward yet. Herein we propose a coevolutionary game model to extend the theory of cooperation with conformity in spatial public goods game by considering pool punishment, as well as two converse feedback modes of conformity that strongly affect cooperators' punishment behaviors. We focus on how different parameters and spatia…
Reputation is one of key mechanisms to maintain human cooperation, but its analysis gets complicated if we consider the possibility that reputation does not reach consensus because of erroneous assessment. The difficulty is alleviated if we assume that reputation and cooperation do not take binary values but have continuous spectra so that disagreement over reputation can be analysed in a perturbative way. In this work, we carry out the analysis by expanding the dynamics of reputation to the second order of perturbation under the assumption that everyone initially cooperates with good reputati…
Societies consisting of cooperative individuals seem to require for their continuing success that defectors be policed. The precise connection between punishers and benefits, population structure, and division of labour, however, remains ill-understood. Many models assume costly "peer punishment" to enforce cooperation, but results in the economics literature suggest that this assumption may not be generally valid. In many human and animal societies, there is a division of labour between a purely supportive majority and a dedicated minority of police-like enforcers. Here we present several ext…
Spending by the UK's National Health Service (NHS) on independent healthcare treatment has been increased in recent years and is predicted to sustain its upward trend with the forecast of population growth. Some have viewed this increase as an attempt not to expand the patients' choices but to privatize public healthcare. This debate poses a social dilemma whether the NHS should stop cooperating with Private providers. This paper contributes to healthcare economic modelling by investigating the evolution of cooperation among three proposed populations: Public Healthcare Providers, Private Heal…
The promise of punishment and reward in promoting public cooperation is debatable. While punishment is traditionally considered more successful than reward, the fact that the cost of punishment frequently fails to offset gains from enhanced cooperation has lead some to reconsider reward as the main catalyst behind collaborative efforts. Here we elaborate on the "stick versus carrot" dilemma by studying the evolution of cooperation in the spatial public goods game, where besides the traditional cooperators and defectors, rewarding cooperators supplement the array of possible strategies. The lat…
Inspired by the fact that people have diverse propensities to punish wrongdoers, we study a spatial public goods game with defectors and different types of punishing cooperators. During the game, cooperators punish defectors with class-specific probabilities and subsequently share the associated costs of sanctioning. We show that in the presence of different punishing cooperators the highest level of public cooperation is always attainable through a selection mechanism. Interestingly, the selection not necessarily favors the evolution of punishers who would be able to prevail on their own agai…
Pro-social punishment is a key driver of harmonious and stable society. However, this institution is vulnerable to corruption since law-violators can avoid sanctioning by paying bribes to corrupt law-enforcers. Consequently, to understand how altruistic behavior survives in a corrupt environment is an open question. To reveal potential explanations here we introduce corrupt enforcers and violators into the public goods game with pool punishment, and assume that punishers, as corrupt enforcers, may select defectors probabilistically to take a bribe from, and meanwhile defectors, as corrupt viol…
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 distingui…
Entanglement: Balancing Punishment and Compensation, Repeated Dilemma Game-Theoretic Analysis of Maximum Compensation Problem for Bypass and Least Cost Paths in Fact-Checking, Case of Fake News with Weak Wallace's Law
Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionary advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding and punishment, a fourth …
