Punishment does not promote cooperation under exploration dynamics when anti-social punishment is possible

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.

Evolution of cooperation under punishment

Punishment has been considered as an effective mechanism for promoting and sustaining cooperation. In most existing models, punishment always comes as a third strategy alongside cooperation and defection, and it is commonly assumed to be executed based on individual decision rules rather than collective decision rules. Differently from previous works, we employ a democratic procedure by which cooperators cast votes independently and simultaneously for whether to impose punishment on defectors, and we establish a relationship between the cooperators' willingness to punish defectors (WTPD) and whether the punishment is inflicted on defectors. The results illustrate that the population can evolve to full cooperation under consensual punishment. It is noteworthy that, compared with autonomous punishment, whether consensual punishment is more in favor of cooperation crucially depends on the minimum number of votes required for punishment execution as well as the cooperators' WTPD. Our findings highlight the importance of collective decision making in the evolution of cooperation and may provide a mathematical framework for explaining the prevalence of democracy in modern societies.

Punishment: one tool, many uses

Humans are outstanding in their ability to cooperate with unrelated individuals, and punishment - paying a cost to harm others - is thought to be a key supporting mechanism. According to this view, cooperators punish defectors, who respond by behaving more cooperatively in future interactions. However, a synthesis of the evidence from laboratory and real-world settings casts serious doubts on the assumption that the sole function of punishment is to convert cheating individuals into cooperators. Instead, punishment often prompts retaliation and punishment decisions frequently stem from competitive, rather than deterrent motives. Punishment decisions often reflect the desire to equalise or elevate payoffs relative to targets, rather than the desire to enact revenge for harm received or to deter cheats from reoffending in future. We therefore suggest that punishment also serves a competitive function, where what looks like spiteful behaviour actually allows punishers to equalise or elevate their own payoffs and/or status relative to targets independently of any change in the target's behaviour. Institutions that reduce or remove the possibility that punishers are motivated by relative payoff or status concerns might offer a way to harness these competitive motives and render punishment more effective at restoring cooperation.

Modulating Activity in the Dorsolateral Prefrontal Cortex Changes Punishment in the 3-Player Prisoner's Dilemma: A Transcranial Direct Current Stimulation Study

Altruistic punishment of social norm violations plays a crucial role in maintaining widespread cooperation in human societies, and punitive behavior has been suggested to be related to the activity level of the dorsolateral prefrontal cortex (DLPFC). This study used unilateral and bilateral transcranial direct current stimulation (tDCS) to investigate how modulating the activity of the DLPFC affects cooperation and punishment in a 3-player prisoner's dilemma. We found that none of the unilateral stimulations changed the participants' cooperation behaviors, while left anodal/right cathodal stimulation increased the participants' cooperation. For punitive behavior, we found that all unilateral stimulations (i.e., right anodal, right cathodal, left anodal, left cathodal) and bilateral stimulations (i.e., right anodal/left cathodal, left anodal/right cathodal) significantly decreased the punishment imposed by the cooperators toward the defectors. In addition, right anodal stimulation significantly decreased the participant's third-party punishment (TPP) imposed by the cooperators toward the defectors. The other three unilateral stimulations also significantly decreased the participant's TPP imposed by the cooperators toward the defectors, but only when the punishment was revealed to the punished person. Our findings indicate that the mechanisms of selfishness and negative emotions suggested by previous studies probably interact with different stimulations: for anodal stimulations, the mechanism of negative emotions may overwhelm the mechanism of selfishness, while for cathodal stimulations, the mechanism of selfishness may be more dominant than the mechanism of negative emotions.

Invisible inequality leads to punishing the poor and rewarding the rich

Four experiments examine how lack of awareness of inequality affect behaviour towards the rich and poor. In Experiment 1, participants who became aware that wealthy individuals donated a smaller percentage of their income switched from rewarding the wealthy to rewarding the poor. In Experiments 2 and 3, participants who played a public goods game – and were assigned incomes reflective of the US income distribution either at random or on merit – punished the poor (for small absolute contributions) and rewarded the rich (for large absolute contributions) when incomes were unknown; when incomes were revealed, participants punished the rich (for their low percentage of income contributed) and rewarded the poor (for their high percentage of income contributed). In Experiment 4, participants provided with public education contributions for five New York school districts levied additional taxes on mostly poorer school districts when incomes were unknown, but targeted wealthier districts when incomes were revealed. These results shed light on how income transparency shapes preferences for equity and redistribution. We discuss implications for policy-makers.

Changes in political party systems arising from conflict and transfer among political parties

Conflict that arises between two groups of different paradigms is an inevitable phenomenon, and a representative example of the conflict among different groups is a conflict phenomenon caused by competition among political parties. In this paper, we study the dynamical behavior of a political party system. Considering three major political parties, we investigate how political party systems can be changed by employing a mathematical model. By considering the transfer mechanism of recruitment as well as conflict of competition between political parties, we found that all parties are likely to coexist when both the competition and transfer between the parties are weak, or if either mechanism can occur at a relatively low level. Otherwise, a political party system is changed to a single-party system. In addition, we found that when a party system was changed into a single-party system, it appeared to be either bistable or multistable, and has been elucidate by linear stability analysis. Our results may provide insights to understand mechanisms how political party systems can be changed by conflict and transfer.

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.

Competitions between prosocial exclusions and punishments in finite populations

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 matter whether second-order sanctioning is considered or not. Furthermore, peer exclusion does better than pool exclusion both in the optional and in the compulsory game, but the situation is reversed in the presence of second-order exclusion. Finally, we extend the competition among all possible sanctioning strategies and find that peer exclusion can outperform all other strategies in the absence of second-order exclusion and punishment, while pool exclusion prevails when second-order sanctioning is possible. Our results demonstrate that exclusion is a more powerful strategy than punishment for the resolution of social dilemmas.

Sadism, the Intuitive System, and Antisocial Punishment in the Public Goods Game

In public goods situations, a specific destructive behavior emerges when individuals face the possibility of punishing others: antisocial punishment, that is, costly punishing cooperative individuals. So far, little is known about the (intuitive or reflective) processes underlying antisocial punishment. Building on the Social Heuristics Hypothesis and arguing that antisocial punishment reflects the basic characteristics of sadism, namely, aggressive behavior to dominate and to harm other individuals it is assumed that everyday sadists intuitively engage in antisocial punishment. Two studies document that activating (Study 1) and inhibiting (Study 2) the intuitive system when a punishment option can be realized in one-shot iterated public goods games increased (Study 1) and reduced (Study 2) antisocial punishment, in particular among individuals who reported a proneness to sadism. In sum, the present research suggests that sadistic tendencies executed intuitively play a crucial role regarding antisocial punishment in public goods situations.

Evolution of cooperation under indirect reciprocity and arbitrary exploration rates

Cooperation has been recognized as an evolutionary puzzle since Darwin, and remains identified as one of the biggest challenges of the XXIst century. Indirect Reciprocity (IR), a key mechanism that humans employ to cooperate with each other, establishes that individual behaviour depends on reputations, which in turn evolve depending on social norms that classify behaviours as good or bad. While it is well known that different social norms give rise to distinct cooperation levels, it remains unclear how the performance of each norm is influenced by the random exploration of new behaviours, often a key component of social dynamics where a plethora of stimuli may compel individuals to deviate from pre-defined behaviours. Here we study, for the first time, the impact of varying degrees of exploration rates - the likelihood of spontaneously adopting another strategy, akin to a mutation probability in evolutionary dynamics - in the emergence of cooperation under IR. We show that high exploration rates may either improve or harm cooperation, depending on the underlying social norm at work. Regarding some of the most popular social norms studied to date, we find that cooperation under Simple-standing and Image-score is enhanced by high exploration rates, whereas the opposite occurs for Stern-judging and Shunning.

Altruistic punishment does not increase with the severity of norm violations in the field

The degree of human cooperation among strangers is a major evolutionary puzzle. A prominent explanation is that cooperation is maintained because many individuals have a predisposition to punish those violating group-beneficial norms. A critical condition for cooperation to evolve in evolutionary models is that punishment increases with the severity of the violation. Here we present evidence from a field experiment with real-life interactions that, unlike in lab experiments, altruistic punishment does not increase with the severity of the violation, regardless of whether it is direct (confronting a violator) or indirect (withholding help). We also document growing concerns for counter-punishment as the severity of the violation increases, indicating that the marginal cost of direct punishment increases with the severity of violations. The evidence suggests that altruistic punishment may not provide appropriate incentives to deter large violations. Our findings thus offer a rationale for the emergence of formal institutions for promoting large-scale cooperation among strangers.

Lab experiments have shown that people will punish violators of social norms, with the severity of punishment increasing with the degree of violation. Here, Balafoutas et al. show that, outside of the lab, larger violations are not punished more severely and are associated with a greater risk of reprisal.

Social image concerns promote cooperation more than altruistic punishment

Human cooperation is enigmatic, as organisms are expected, by evolutionary and economic theory, to act principally in their own interests. However, cooperation requires individuals to sacrifice resources for each other's benefit. We conducted a series of novel experiments in a foraging society where social institutions make the study of social image and punishment particularly salient. Participants played simple cooperation games where they could punish non-cooperators, promote a positive social image or do so in combination with one another. We show that although all these mechanisms raise cooperation above baseline levels, only when social image alone is at stake do average economic gains rise significantly above baseline. Punishment, either alone or combined with social image building, yields lower gains. Individuals' desire to establish a positive social image thus emerges as a more decisive factor than punishment in promoting human cooperation.

Cooperation requires individuals to sacrifice individual rewards for group benefits. Here, Grimalda, Pondorfer and Tracer show in a foraging society of Papua New Guinea that social image building is a more powerful motivator of social cooperation than altruistic punishment.

Antisocial pool rewarding does not deter public cooperation

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 free-riders 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. Contrary to a naive expectation, we show that the ability of defectors to distribute rewards to their like does not deter public cooperation as long as cooperators are able to do the same. Even in the presence of antisocial rewarding, the spatial selection for cooperation in evolutionary social dilemmas is enhanced. Since the administration of rewards to either strategy requires a considerable degree of aggregation, cooperators can enjoy the benefits of their prosocial contributions as well as the corresponding rewards. Defectors when aggregated, on the other hand, can enjoy antisocial rewards, but due to their lack of contributions to the public good they ultimately succumb to their inherent inability to secure a sustainable future. Strategies that facilitate the aggregation of akin players, even if they seek to promote antisocial behaviour, thus always enhance the long-term benefits of cooperation.

Promote or hinder? The role of punishment in the emergence of cooperation

Investigation of anti-social punishment has shaken the positive role of punishment in the evolution of cooperation. However, punishment is ubiquitous in nature, and the centralized, apposed to decentralized, punishment is more favored by certain modern societies in particular. To explore the underlying principle of such phenomenon, we study the evolution of cooperation in the context of pro- and anti-social punishments subject to two distinct patterns: costly centralized and decentralized punishments. The results suggest that the pattern of punishment has a great effect on the role of punishment in the evolution of cooperation. In the absence of anti-social punishment, the costly centralized punishment is more effective in promoting the emergence of cooperation. Anti-social punishment can subvert the positive role of punishment when anti- and pro-social punishments are in the same pattern. However, driven by centralized pro-social punishment, cooperation can be more advantageous than defection even in the presence of decentralized anti-social punishment.

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.

Antisocial punishment in two social dilemmas

The effect of sanctions on cooperation depends on social and cultural norms. While free riding is kept at bay by altruistic punishment in certain cultures, antisocial punishment carried out by free riders pushes back cooperation in others. In this paper we analyze sanctions in both a standard public goods game with a linear production function and an otherwise identical social dilemma in which the minimum contribution determines the group outcome. Experiments were run in a culture with traditionally high antisocial punishment (Southern Europe). We replicate the detrimental effect of antisocial sanctions on cooperation in the linear case. However, we find that punishment is still widely effective when actions are complementary: the provision of the public good significantly and substantially increases with sanctions, participants punish significantly less and sanctions radically transform conditional cooperation patterns to generate significant welfare gains.