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 impact of pool-punishment on the evolution of cooperation in structured populations is significantly different from that reported previously for peer-punishment. Representative phase diagrams reveal remarkably rich behavior, depending also on the value of the synergy factor that characterizes the efficiency of investments payed into the common pool. Besides traditional single and two-strategy stationary states, a rock-paper-scissors type cyclic dominance can emerge in strikingly different ways.
Although empirical and theoretical studies affirm that punishment can elevate collaborative efforts, its emergence and stability remain elusive. By peer-punishment the sanctioning is something an individual elects to do depending on the strategies in its neighborhood. The consequences of unsustainable efforts are therefore local. By pool-punishment, on the other hand, where resources for sanctioning are committed in advance and at large, the notion of sustainability has greater significance. In a population with free-riders, punishers must be strong in numbers to keep the "punishment pool" fro…
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…
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…
Prosocial punishment has been proved to be a powerful mean to promote cooperation. Recent studies have found that social exclusion, which indeed can be regarded as a kind of punishment, can also support cooperation. However, if prosocial punishment and exclusion are both present, it is still unclear which strategy is more advantageous to curb free-riders. Here we first study the direct competition between different types of punishment and exclusion. We find that pool (peer) exclusion can always outperform pool (peer) punishment both in the optional and in the compulsory public goods game, no m…
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…
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…
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…
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 c…
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…
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…
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…
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…
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…
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）
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…
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…
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…
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…
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…
Properly coordinating cooperation is relevant for resolving public good problems such as clean energy and environmental protection. However, little is known about how individuals can coordinate themselves for a certain level of cooperation in large populations of strangers. In a typical situation, a consensus-building process hardly succeeds due to lack of face and standing. The evolution of cooperation in this type of situation is studied using threshold public good games in which cooperation prevails when it is initially sufficient, or otherwise, it perishes. While punishment is a powerful t…
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…
In this work, we aim to answer the question: what triggers cooperative behavior in the thermodynamic limit by taking recourse to the Public goods game. Using the idea of mapping the 1D Ising model Hamiltonian with nearest neighbor coupling to payoffs in the game theory we calculate the Magnetisation of the game in the thermodynamic limit. We see a phase transition in the thermodynamic limit of the two player Public goods game. We observe that punishment acts as an external field for the two player Public goods game triggering cooperation or provide strategy, while cost can be a trigger for sup…
Theoretical models suggest that social networks influence the evolution of cooperation, but to date there have been few experimental studies. Observational data suggest that a wide variety of behaviors may spread in human social networks, but subjects in such studies can choose to befriend people with similar behaviors, posing difficulty for causal inference. Here, we exploit a seminal set of laboratory experiments that originally showed that voluntary costly punishment can help sustain cooperation. In these experiments, subjects were randomly assigned to a sequence of different groups in orde…
Rewarding cooperation is in many ways expected behaviour from social players. However, strategies that promote antisocial behaviour are also surprisingly common, not just in human societies, but also among eusocial insects and bacteria. Examples include sanctioning of individuals who behave prosocially, or rewarding of freeriders who do not contribute to collective enterprises. We therefore study the public goods game with antisocial and prosocial pool rewarding in order to determine the potential negative consequences on the effectiveness of positive incentives to promote cooperation. Contrar…
We propose an extended public goods interaction model to study the evolution of cooperation in heterogeneous population. The investors are arranged on the well known scale-free type network, the Barabási-Albert model. Each investor is supposed to preferentially distribute capital to pools in its portfolio based on the knowledge of pool sizes. The extent that investors prefer larger pools is determined by investment strategy denoted by a tunable parameter $α$, with larger $α$ corresponding to more preference to larger pools. As comparison, we also study this interaction model on square lattice,…
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
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…
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 …
Rewards and penalties are common practical tools that can be used to promote cooperation in social institutions. The evolution of cooperation under reward and punishment incentives in joint enterprises has been formalized and investigated, mostly by using compulsory public good games. Recently, Sasaki et al. (2012, Proc Natl Acad Sci USA 109:1165-1169) considered optional participation as well as institutional incentives and described how the interplay between these mechanisms affects the evolution of cooperation in public good games. Here, we present a full classification of these evolutionar…
Repeated interaction promotes cooperation among rational individuals under the shadow of future, but it is hard to maintain cooperation when a large number of error-prone individuals are involved. One way to construct a cooperative Nash equilibrium is to find a `friendly-rivalry' strategy, which aims at full cooperation but never allows the co-players to be better off. Recently it has been shown that for the iterated Prisoner's Dilemma in the presence of error, a friendly rival can be designed with the following five rules: Cooperate if everyone did, accept punishment for your own mistake, pun…
Cooperation and defection may be considered as two extreme responses to a social dilemma. Yet the reality is much less clear-cut. Between the two extremes lies an interval of ambivalent choices, which may be captured theoretically by means of continuous strategies defining the extent of the contributions of each individual player to the common pool. If strategies are chosen from the unit interval, where 0 corresponds to pure defection and 1 corresponds to the maximal contribution, the question is what is the characteristic level of individual investments to the common pool that emerges if the …
Prosocial incentive can promote cooperation, but providing incentive is costly. Institutions in human society may prefer to use an incentive strategy which is able to promote cooperation at a reasonable cost. However, thus far few works have explored the optimal institutional incentives which minimize related cost for the benefit of public cooperation. In this work, in combination with optimal control theory we thus formulate two optimal control problems to explore the optimal incentive strategies for institutional reward and punishment respectively. By using the approach of Hamilton-Jacobi-Be…
The basic social dilemma is frequently captured by a public goods game where participants decide simultaneously whether to support a common pool or not and after the enhanced contributions are distributed uniformly among all competitors. What if the result of common efforts is {\it not} distributed immediately, but it is reinvested and added to the pool for a next round? This extension may not only result in an enhanced benefit for group members but also opens new strategies for involved players because they may act in distinct rounds differently. In this work we focus on the simplest case whe…
