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Overpunishing is not necessary to fix cooperation in voluntary public goods games
Abstract
The fixation of cooperation among unrelated individuals is one of the fundamental problems in biology and social sciences. It is investigated by means of public goods games, the generalization of the prisoner's dilemma to more than two players. In compulsory public goods games, defect is the dominant strategy, while voluntary participation overcomes the social dilemma by allowing a cyclic coexistence of cooperators, defectors, and non-participants. Experimental and theoretical research has shown how the combination of voluntary participation and altruistic punishment-punishing antisocial behaviors at a personal cost-provides a solution to the problem, as long as antisocial punishment-the punishing of cooperators-is not allowed. Altruistic punishment can invade at low participation and pave the way to the fixation of cooperation. Specifically, defectors are overpunished, in the sense that their payoff is reduced by a sanction proportional to the number of punishers in the game. Here we show that qualitatively equivalent results can be achieved with a milder punishing mechanism, where defectors only risk a fixed penalty per round-as in many real situations-and the cost of punishment is shared among the punishers. The payoffs for the four strategies-cooperate, defect, abstain, and cooperate-&-punish-are derived and the corresponding replicator dynamics analyzed in full detail.
... Given the undeniably important role that institutional punishment plays in curbing defection in the real world, we consider here some realistic improvements to the standard N -person prisoner's dilemma formulation with pool punishment [15]. In particular, we eliminate overpun-ishment (i.e., penalties for different types of offenses are fixed and do not depend on the wealth of the sanctioning institution [19]), but account for the high costs of creating and maintaining a sanctioning institution by requiring a minimum number of punishers to establish it. However, the maintenance costs are divided among the punishers once this minimum number is reached. ...
... This threshold has a non-trivial dependence on the size of the community. These findings are consistent with the results of other implementations of institutional punishment where both cooperators and defectors are punished [16,17,19]. ...
... This penalty is a fraction α ∈ [0, 1] of the penalty applied to defectors (see below) and it is only effective if there are at least K m < N individuals (i.e., punishers) contributing to the sanctioning institution. Once this minimum number of punishers is reached, the penalty term becomes constant, in contrast to previous formulations of institutional punishment where the penalty increases linearly with the number of individuals contributing to the sanctioning institution [14,15], resulting in overpunishment [19]. In fact, the constant punishment term with K m = 1 was proposed in the original study that showed the non-necessity of overpunishment for the establishment of public goods contributors in the institutional punishment scenario [19]. ...
The conflict between individual and collective interests makes fostering cooperation in human societies a challenging task, requiring drastic measures such as the establishment of sanctioning institutions. These institutions are costly because they have to be maintained regardless of the presence or absence of offenders. Here, we propose realistic improvements to the standard $N$-person prisoner's dilemma formulation with institutional punishment by eliminating overpunishment, requiring a minimum number of contributors to establish the sanctioning institution, and sharing the cost among them once this minimum number is reached. In addition, we focus on large groups or communities for which sanctioning institutions are ubiquitous. Using the replicator equation framework for an infinite population, we find that by sufficiently fining players who fail to contribute either to the public good or to the sanctioning institution, a population of contributors immune to invasion by these free riders can be established, provided that the contributors are sufficiently numerous. In a finite population, we use finite-size scaling to show that, for some parameter settings, demographic noise helps to fixate the strategy that contributes to the public good but not to the sanctioning institution even for infinitely large populations when, somewhat counterintuitively, its proportion in the initial population vanishes with a small power of the population size.
... Hundreds of published studies have been conducted analyzing these strategies under social dilemmas 11,19,[29][30][31][32][33][34][35][36][37] . The literature reviewed reveals two institutional arrangements for incentive strategies 38 : a decentralized system (peer-punishment) 29,39 , in which each player monitors and sanctions/rewards defectors, and a centralized system (pool-punishment), in which the power to administer the incentives is concentrated in a restricted punishment institution 38,[40][41][42][43][44] . ...
... Recently, various researchers have investigated other innovative methods to impose penalties on free riders, drawing inspiration from real-world scenarios. Dercole et al. 34 examined a model where defectors are fined a predetermined amount. Sasaki et al. 19 explored the prevention of second-order free riding through the implementation of an entry fee. ...
In Public Goods Games (PGG), the temptation to free-ride on others’ contributions poses a significant threat to the sustainability of cooperative societies. Therefore, societies strive to mitigate this through incentive systems, employing rewards and punishments to foster cooperative behavior. Thus, peer punishment, in which cooperators sanction defectors, as well as pool punishment, where a centralized punishment institution executes the punishment, is deeply analyzed in previous works. Although the literature indicates that these methods may enhance cooperation on social dilemmas under particular contexts, there are still open questions, for instance, the structural connection between graduated punishment and the monitoring of public goods games. Our investigation proposes a compulsory PGG framework under Panoptical surveillance. Inspired by Foucault’s theories on disciplinary mechanisms and biopower, we present a novel mathematical model that scrutinizes the balance between the severity and scope of punishment to catalyze cooperative behavior. By integrating perspectives from evolutionary game theory and Foucault’s theories of power and discipline, this research uncovers the theoretical foundations of mathematical frameworks involved in punishment and discipline structures. We show that well-calibrated punishment and discipline schemes, leveraging the panoptical effect for universal oversight, can effectively mitigate the free-rider dilemma, fostering enhanced cooperation. This interdisciplinary approach not only elucidates the dynamics of cooperation in societal constructs but also underscores the importance of integrating diverse methodologies to address the complexities of fostering cooperative evolution.
... Traditional incentivizing mechanisms 5 either make cooperation conditional-such as reciprocal altruism 1, 2 (also known as direct reciprocity), the establishment of reputations 6 (also known as indirect reciprocity), and mechanisms of kin 7 or group selection 8 (or other forms of assortment 9, 10 )-or change the rules of the game, as by introducing volunteering (optional participation) 11 and punishment of antisocial behaviors. 12,13 All these mechanisms add degrees of strategical complexity, either in terms of players' cognitive abilities and/or information flows, or due to extra options in the underlying game. ...
... The resulting network is however disconnected if k /N is too small (it is disconnected with probability 1 if p < ln N/N, a condition that is met in our simulations with N = 1000 and k = 4). Though connectivity can be easily forced, the effects on the degree 13 ...
Since Nowak & May's (1992) influential paper, network reciprocity--the fact that individuals' interactions repeated within a local neighborhood support the evolution of cooperation--has been confirmed in several theoretical models. Essentially, local interactions allow cooperators to stay protected from exploiters by assorting into clusters, and the heterogeneity of the network of contacts--the co-presence of low- and high-connected nodes--has been shown to further favor cooperation. The few available large-scale experiments on humans have however missed these effects. The reason is that, while models assume that individuals update strategy by imitating better performing neighbors, experiments showed that humans are more prone to reciprocate cooperation than to compare payoffs. Inspired by the empirical results, we rethink network reciprocity as a rational form of direct reciprocity on networks--networked rational reciprocity--indeed made possible by the locality of interactions. We show that reciprocal altruism in a networked prisoner's dilemma can invade and fixate in any network of rational agents, profit-maximizing over an horizon of future interactions. We find that networked rational reciprocity works better at low average connectivity and we unveil the role of network heterogeneity. Only if cooperating hubs invest in the initial cost of exploitation, the invasion of cooperation is boosted; it is otherwise hindered. Although humans might not be as rational as here assumed, our results could help the design and interpretation of new experiments in social and economic networks
... Plenty of methods have been proposed to promote it [2][3][4][5][6], and mechanism design [7][8][9]is widely applied in traditional game theories, such as the prisoner's dilemma game [4, 5, 9, 10] and public goods games [11][12][13][14][15][16][17][18][19][20], which commonly take on two forms, network games [6, 8, 9, 12, 20] and spatial games [3–5, 9, 10, 12, 15, 21]. However, the traditional game induces two challenges [22][23][24] : first, agents are subjective, not repeating actions mechanically and randomly . They have memory [8, 12, 22, 24], trust [2, 7, 8, 10, 11,[25][26][27][28], expectation [29] , altru- ism [13,16], volunteerism [19], recommendation [14], prestige and reputation [4, 6, 7, 12, 19, 23,[28][29][30] . ...
... However, the traditional game induces two challenges [22][23][24] : first, agents are subjective, not repeating actions mechanically and randomly . They have memory [8, 12, 22, 24], trust [2, 7, 8, 10, 11,[25][26][27][28], expectation [29] , altru- ism [13,16], volunteerism [19], recommendation [14], prestige and reputation [4, 6, 7, 12, 19, 23,[28][29][30] . It indicates that cooperation can be promoted based on these subjective factors; second , homogeneity should be denied, and heterogeneity is supposed to be introduced [11, 20, 25], such as group diversity [8, 23, 31], social structure [26], and network [26, 31] . ...
... Plenty of methods have been proposed to promote it [2][3][4][5][6], and mechanism design [7][8][9] is widely applied in traditional game theories, such as the prisoner's dilemma game [4,5,9,10] and public goods games [11][12][13][14][15][16][17][18][19][20], which commonly take on two forms, network games [6,8,9,12,20] and spatial games [3-5, 9, 10, 12, 15, 21]. However, the traditional game induces two challenges [22][23][24]: first, agents are subjective, not repeating actions mechanically and randomly. They have memory [8,12,22,24], trust [2,7,8,10,11,[25][26][27][28], expectation [29], altruism [13,16], volunteerism [19], recommendation [14], prestige and reputation [4,6,7,12,19,23,[28][29][30]. ...
... However, the traditional game induces two challenges [22][23][24]: first, agents are subjective, not repeating actions mechanically and randomly. They have memory [8,12,22,24], trust [2,7,8,10,11,[25][26][27][28], expectation [29], altruism [13,16], volunteerism [19], recommendation [14], prestige and reputation [4,6,7,12,19,23,[28][29][30]. It indicates that cooperation can be promoted based on these subjective factors; second, homogeneity should be denied, and heterogeneity is supposed to be introduced [11,20,25], such as group diversity [8,23,31], social structure [26], and network [26,31]. ...
It has been a long-lasting pursuit to promote cooperation, and this study aims to promote cooperation via the combination of social stratification and the spatial prisoners' dilemma game. It is previously assumed that agents share the identical payoff matrix, but the stratification or diversity exists and exerts influences in real societies. Thus, two additional classes, elites and scoundrels, derive from and coexist with the existing class, commons. Three classes have different payoff matrices. We construct a model where agents play the prisoners' dilemma game with neighbors. It indicates that stratification and temptation jointly influence cooperation. Temptation permanently reduces cooperation; elites play a positive role in promoting cooperation while scoundrels undermine it. As the temptation getting larger and larger, elites play a more and more positive and critical role while scoundrels' negative effect becomes weaker and weaker, and it is more obvious when temptation goes beyond its threshold.
... Irrational agents make choices under the influence of irrational considerations, such as emotions or feelings. They may sympathize losers with lowest payoff for the sake of values [37,38], emotion [2], altruism [11,39], commitment [39], voluntarism [30,36,40], etc. while rational agents admire and imitate winners with highest payoffs. We aim to investigate the effect of sympathy on cooperation. ...
... So far series of anti-temptation mechanisms are proposed to overcome temptation and promote cooperation, such as reputation [3,5,7,8,12,23,24], tolerance [32], punishment [21,29,32], recommendation [25], influence [28], values [37,38], emotion [2], altruism [11,39], expectation [10,34], commitment [39], and voluntarism [30,36,40]. Therefore, as the quadratic effect of sympathy on cooperation is clear, the next priority is to check whether sympathy is an effective anti-temptation mechanism or not. ...
... Public goods games (PGGs) serve as a valuable means of investigation, both in experimental settings and theoretical models, by allowing participants to equally share a public resource regardless of their individual contributions [88]. The research on public goods shows that the cooperation rate of individuals is closely related to two factors: the cooperation conditions and the punishment on free riders [89][90][91], which correspond to the descriptive norm and injunctive norm, respectively. The condition of cooperation can be the cooperative behavior of others, the reward for collaborators [92], or the punishment for uncooperative people [93]. ...
The importance of individual consumption behavior in a low-carbon economy is gradually recognized. Social norms have a significant effect on individual purchase behavior. However, the influence mechanism of social norms still needs more research. We conducted two behavioral experiments to explore the specific factors: first, the effect of descriptive norms on personal low-carbon consumption behavior through feedback information, and second, a comparison with injunctive norms, focusing on the impact of the normative focus shift brought by punishment represented by the policy implementation. The results show that social norms can effectively promote individual low-carbon consumption through feedback and high policy implementation efficiency. In particular, after effective policy implementation becomes an inherent element of injunctive norms, injunctive norms are activated and become the focus of norms, significantly improving the purchase rate of low-carbon goods.
... Such a compulsory participation assumption underlying the group selection model has been often eased in behavioral experiments [16][17][18] and evolutionary game theories [19][20][21][22][23][24][25][26][27][28][29][30]. In these studies, individual agents may opt out of prisoners' dilemma or public goods games to receive a constant payoff unrelated to the others' strategies. ...
It is puzzling how altruistic punishment of defectors can evolve in large groups of nonrelatives, since punishers should voluntarily bear individual costs of punishing to benefit those who do not pay the costs. Although two distinct mechanisms have been proposed to explain the puzzle, namely voluntary participation and group-level competition and selection, insights into their joint effects have been less clear. Here we investigated what could be combined effects of these two mechanisms on the evolution of altruistic punishment and how these effects can vary with nonparticipants’ individual payoff and group size. We modelled altruistic punishers as those who contribute to a public good and impose a fine on each defector, i.e., they are neither pure punishers nor excluders. Our simulation results show that voluntary participation has negative effects on the evolution of cooperation in small groups regardless of nonparticipants’ payoffs, while in large groups it has positive effects within only a limited range of nonparticipants’ payoff. We discuss that such asymmetric effects could be explained by evolutionary forces emerging from voluntary participation. Lastly, we suggest that insights from social science disciplines studying the exit option could enrich voluntary participation models.
... On the other hand, if his/her payoff is nearly equal to the average payoff of opponent players, he/ she hardly contributes to the punishment pool. The previous study 37 reports that the avoidance of overpunishing (too much punishment on defectors with high payoff) is essential for the stable cooperation. In this study, to avoid overpunishing, the payoff of each player will be 0 when it becomes a negative value. ...
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.
... More recently, some authors have explored different ways to penalize free riders often inspired in real-life situations. In [26], the sanction that a defector has to pay is a fixed amount. Avoiding second-order free riding by introducing an entrance fee was analyzed in [15]. ...
Improving and maintaining cooperation are fundamental issues for any project to be time-persistent, and sanctioning free riders may be the most applied method to achieve it. However, the application of sanctions differs from one group (project or institution) to another. We propose an optional, public good game model where a randomly selected set of the free riders is punished. To this end, we introduce a parameter that establishes the portion of free riders sanctioned with the purpose to control the population state evolution in the game. This parameter modifies the phase portrait of the system, and we show that, when the parameter surpasses a threshold, the full cooperation equilibrium point becomes a stable global attractor. Hence, we demonstrate that the fractional approach improves cooperation while reducing the sanctioning cost.
... Elements (i)-(iii) define the EGT setup. An illustrative example is: (i) the prisoner's dilemma (PD)-the two-player-two-action game in which a cooperator (action C) provides a benefit b to the opponent at a cost c < b to herself, whereas a defector (action D) provides no benefit at no cost group [39] selection (or other forms of assortment [40,41]), and the consideration of social [42,43] and moral [44] preferences-or change the rules of the game, such as by introducing optional participation [45,46] and punishment of antisocial behaviors [47,48]. ...
Network reciprocity has been successfully put forward (since M. A. Nowak and R. May’s, 1992, influential paper) as the simplest mechanism—requiring no strategical complexity—supporting the evolution of cooperation in biological and socioeconomic systems. The mechanism is actually the network, which makes agents’ interactions localized, while network reciprocity is the property of the underlying evolutionary process to favor cooperation in sparse rather than dense networks. In theoretical models, the property holds under imitative evolutionary processes, whereas cooperation disappears in any network if imitation is replaced by the more rational best-response rule of strategy update. In social experiments, network reciprocity has been observed, although the imitative behavior did not emerge. What did emerge is a form of conditional cooperation based on direct reciprocity—the propensity to cooperate with neighbors who previously cooperated. To resolve this inconsistency, network reciprocity has been recently shown in a model that rationally confronts the two main behaviors emerging in experiments—reciprocal cooperation and unconditional defection—with rationality introduced by extending the best-response rule to a multi-step predictive horizon. However, direct reciprocity was implemented in a non-standard way, by allowing cooperative agents to temporarily cut the interaction with defecting neighbors. Here, we make this result robust to the way cooperators reciprocate, by implementing direct reciprocity with the standard tit-for-tat strategy and deriving similar results.
... Even in pool punishment, it is not easy to start costly punishment successfully, since punishing right and left in a sea of defectors imposes too much effort and cost on punishers. Several studies have proposed additional mechanisms or assumptions to overcome this emergence problem [42][43][44][45][46]. A similar problem holds for the peer punishment studied in this paper. ...
Social dilemmas are among the most puzzling issues in the biological and social sciences. Extensive theoretical efforts have been made in various realms such as economics, biology, mathematics, and even physics to figure out solution mechanisms to the dilemma in recent decades. Although punishment is thought to be a key mechanism, evolutionary game theory has revealed that the simplest form of punishment called peer punishment is useless to solve the dilemma, since peer punishment itself is costly. In the literature, more complex types of punishment, such as pool punishment or institutional punishment, have been exploited as effective mechanisms. So far, mechanisms that enable peer punishment to function as a solution to the social dilemma remain unclear. In this paper, we propose a theoretical way for peer punishment to work as a solution mechanism for the dilemma by incorporating prospect theory into evolutionary game theory. Prospect theory models human beings as agents that estimate small probabilities and loss of profit as greater than they actually are; thus, those agents feel that punishments are more frequent and harsher than they really are. We show that this kind of cognitive distortion makes players decide to cooperate to avoid being punished and that the cooperative state achieved by this mechanism is globally stable as well as evolutionarily stable in a wide range of parameter values.
... When considering the result for BA-SF, we should note one serious irony, which is that heavy sanctioning backed by jealousy [33] inevitably suppresses the total social payoff by consuming sanctions, even if the mechanism realizes an entirely cooperative society in the end. Even if all defectors are driven out of the society, the income gap stemming from degree distribution causes jealous sanctions among cooperative agents to continue. ...
Human beings have a natural tendency to feel jealous of those who have more than themselves. A previous report found that harmful behavior stemming from jealousy can actually encourage cooperation. The present study considers the efficiency of jealousy-motivated sanctions and the appropriate balance of sanctions and enforcement costs to best encourage cooperation. Through a series of numerical simulations of a spatial prisoner's dilemma game, we find that in the case of a lattice population structure, stronger sanctions and higher sanction efficiency ultimately result in more robust cooperation. In contrast, in the case of a scale-free population structure, higher sanction costs cause the cooperation level to rise.
... The most important result of their work is the highlighting of a long-run effect: social learning will lead to a cooperative society, irrespective of the number of freeriders and cooperators playing at the beginning. Dercole et al. (2013) show that the moderate punishment tends to shrink the initial conditions and foster the fixation of cooperation. ...
The aim of this paper is to better understand how cooperation mechanisms work in the context of a Q-learning model. We apply a learning reinforcement model to analyse the conditions needed to have a stable cooperative equilibrium when people take part in a common project and could take advantages of free-riding. Our results show that a stable equilibrium can be reached thank to mechanisms of punishment, but the final result strongly depends on the risk-taking individuals’ preferences. In particular, we find that the penalties will be effective only with people having high exploration rates,namely with people able to adapt their strategies and learn to cooperate. Otherwise, it is possible to have an unstable equilibrium with cooperation until individuals have a very high intrinsic motivation to cooperate, whatever the others do.
... The reason why the author includes probabilistic factor in the sanction with jealousy is to avoid overpunishing that is not necessary to fix cooperation [23]. Overpunishing means that the payoff of defectors is reduced not by a fixed penalty, but by a sanction proportional to the number of punishers. ...
The effectiveness of punishment that a player pays certain costs and punishes an uncooperative player is currently discussed in the field of the study of cooperation under non-kin relationships. The discussions of the effectiveness of punishment are based on either negative or positive point of view. Contrary to these previous discussions, this study proposes a novel model introducing an alternative notion of punishment “sanction with jealousy”. The degree of sanction is proportional to the payoff of the sanctioning player. The condition for sanction to occur reflects jealousy in that each player sanctions their neighbor players when their payoff is smaller than the payoff of their neighbor players. Utilizing this model, the author investigates whether the introduction of the sanction with jealousy improves both the number of players having the strategy of cooperation and the average payoff of all players or not. In addition, the author organizes the new findings from this investigation in comparison with these previous discussions.
... In the public goods game that is classified as the group interaction, the previous study 34 reports that the avoidance of overpunishing is essential for the stable cooperation. Overpunishing means that the decrease of payoff of punished defectors is not constant, but variable depending on the number of punishers. ...
There are two types of costly punishment, i.e. peer-punishment and pool-punishment. While peer-punishment applies direct face to face punishment, pool-punishment is based on multi-point, collective interaction among group members. Regarding those two types of costly punishment, peer-punishment is especially considered to have the flaws that it lowers the average payoff of all players as well as pool-punishment does, and facilitates antisocial behaviour like retaliation of a defector on a cooperator. Here, this study proposes the new peer-punishment that punishment to an opponent player works at high probability when an opponent one is uncooperative, and the difference of payoff between a player and an opponent one becomes large in order to prevent such antisocial behaviour. It is natural to think that players of high payoff do not expect to punish others of lower payoff because they do not have any complaints regarding their economic wealth. The author shows that the introduction of the proposed peer-punishment increases both the number of cooperative players and the average payoff of all players in various types of topology of connections between players.
... More recently, Dercole et al. (2013) analyzed how milder punishment reduces the proportion of initial conditions leading to the fixation of cooperation. The authors' conclusion is that over-punishment is not needed, and equilibria characterized by cooperation can be obtained with a gentle punishing scheme. ...
An evolutionary game model is devised to analyze whether cooperation can evolve in a context where individuals are willing to cooperate only from the second period. Results of the analysis suggest that giving all players a second chance can be a better strategy for a final stable, attractive equilibrium with cooperation. JEL Codes: C70, C72, D62, D83.
... Plenty of methods have been proposed to promote cooperation [1][2][3][4][5][6], and mechanism design [7][8][9]is widely applied in traditional game theory, such as N-person prisoner's dilemma (NPD) games [4,5,9,10], which regularly takes on two forms, spatial games [3][4][5][10][11][12][13][14][15][16][17][18][19]and network games [6,8,9,20] whose one recent progress is the interdependent network game [21][22][23][24]. However, traditional evolutionary game, such as traditional spatial reciprocity [25][26][27][28][29][30][31], induces some challenges [32][33][34], one of which denies homogeneity and introduces heterogeneity [11,20,25] into settings of models. They believe that complete homogeneity does not exist in the real world. ...
Cooperation is vital for the human society and this study focuses on how to promote cooperation. In our stratification model, there exist three classes: two minorities are elites who are prone to cooperate and scoundrels who are born to defect; one majority is the class of common people. Agents of these three classes interact with each other on a square lattice. Commons’ cooperation and its factors are investigated. Contradicting our common sense, it indicates that elites play a negative role while scoundrels play a positive one in promoting commons’ cooperation. Besides, effects of good and bad neighbors vary with temptation. When the temptation is smaller the positive effect is able to overcome the negative effect, but the later prevails when the temptation is larger. It concludes that common people are more prone to cooperate in harsh environment with bad neighbors, and a better environment with good neighbors merely leads to laziness and free riding of commons.
... Reflecting this, it is often explicitly assumed that pool punishment becomes active if at least a threshold number of players, more than one, contribute to it [28][29][30] . This means that in such large populations it is not easy to successfully start up costly punishment 31,32 , even with considering punishment of second-order free riders 33 (Fig. 1a,b). ...
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 previous studies (Wolff, 2012;Helbing et al., 2010a) have stressed that the random mutation can create some extent of strategy-mixing, and the introduction of mutation enable us to yield the deterministic replicator dynamics in the limit of frequent sampling in the absence of mutations in a large population (Dercole et al., 2013). Moreover, in the presence of the mutation, even though altruistic punishers and selfish punishers evolving from random mutation frequencies cannot stabilize full cooperation (Wolff, 2012), they could have more chances to touch the firstorder free riders (D) and second-order free riders (C) (Helbing et al., 2010a) to suppress them. ...
... Leaving everything else unchanged, one may speculate that such diminishing taxes are able to raise the fraction of pool punishers in the population, and that they suppress tax evasion. It is relatively simple to incorporate diminishing taxes into our model (for peer punishment systems in infinitely large populations , this has been done by Dercole et al., 2013). Only the Wu et al., 2012) which is only valid for weak selection in our case (as it presumes that populations do not settle at mixed states). ...
In many species, mutual cooperation is stabilized by forms of policing and peer punishment: if cheaters are punished, there is a strong selective pressure to cooperate. Most human societies have complemented, and sometimes even replaced, such peer punishment mechanisms with pool punishment, where punishment is outsourced to central institutions such as the police. Even before free-riding occurs, such institutions require investments, which could serve as costly signals. Here, we show with a game theoretical model that this signaling effect in turn can be crucial for the evolution of punishment institutions: In the absence of such signals, pool punishment is only stable with second-order punishment and can only evolve when individuals have the freedom not to take part in any interaction. With such signals, individuals can opportunistically adjust their behavior, which promotes the evolution of stable pool punishment even in situations where no one can stand aside. Thus, the human propensity to react opportunistically to credible punishment threats is often sufficient to establish stable punishment institutions and to maintain high levels of cooperation.
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.
Since M. A. Nowak & R. May’s (1992) influential paper, limiting each agent’s interactions to a few neighbors in a network of contacts has been proposed as the simplest mechanism to support the evolution of cooperation in biological and socio-economic systems. The network allows cooperative agents to self-assort into clusters, within which they reciprocate cooperation. This (induced) network reciprocity has been observed in several theoreticalmodels and shown to predict the fixation of cooperation under a simple rule: the benefit produced by an act of cooperation must outweigh the cost of cooperating with all neighbors. However, the experimental evidence among humans is controversial: though the rule seems to be confirmed, the underlying modeling assumptions are not. Specifically, models assume that agents update their strategies by imitating better performing neighbors, even though imitation lacks rationality when interactions are far from all-to-all. Indeed, imitation did not emerge in experiments. What did emerge is that humans are conditioned by their own mood and that, when in a cooperative mood, they reciprocate cooperation. To help resolve the controversy, we design a model in which we rationally confront the two main behaviors emerging from experiments—reciprocal cooperation and unconditional defection—in a networked prisoner’s dilemma. Rationality is introduced by means of a predictive rule for strategy update and is bounded by the assumed model society. We show that both reciprocity and a multi-step predictive horizon are necessary to stabilize cooperation, and sufficient for its fixation, provided the game benefit-to-cost ratio is larger than a measure of network connectivity. We hence rediscover the rule of network reciprocity, underpinned however by a different evolutionary mechanism.
This chapter presents the fundamental concept of evolutionary game theory. Originally, game theory referred to a mathematical framework for the human decision-making process, containing various variants—whether a game is zero-sum (constant-sum), meaning that if one player wins the other must lose, or non-zero-sum (non-constant-sum); whether a game is symmetric, with both a focal player and an opponent sharing a common payoff structure, or asymmetric; whether a game is 2-player or multi-player; whether a game has two strategies or multiple—and so forth. In any case, classical game theory primarily concerns determining game equilibrium, or a game solution, which can be understood as a steady-state solution or a static solution in the field of conventional science and engineering. On the other hand, evolutionary game theory is rather concerned with the time-evolution of a system. This theory, as well as profound observation of the dynamical process, may allow us to solve some scientific questions—e.g., why cooperation is commonly observed in many animal species, including human beings.
The puzzle of altruistic behaviours among multi-agent systems poses a dilemma, which has been an overlapping topic that covers many subjects. The public goods game can be regarded as a paradigm for modelling and exploring it. In the traditional definition of public goods game, the equally divided benefit among all participants leads to the dominance of defection. Much effort has been made to explain the evolution of cooperation, including the model in which the payoff ceilings for defectors are introduced. Further, we study a three-strategy evolutionary public goods game by providing the role of being loners. The payoff ceilings will take effect when the number of cooperators exceeds some threshold. Analysis results by following the replicator dynamics indicate that lower values of the payoff ceilings can better promote levels of public cooperation. Importantly, a remarkable cyclic route has been found: when receiving relative lower benefits, loners act as catalysts, helping the population to escape from mutual defection to cooperation. And, the stable equilibrium points from cooperation to isolation can be realised by improving the fixed payoffs of loners. Finally, broader ceilings also for cooperators provide us more hints about how to suppress the spreading of defectors under certain conditions.
Traditional replication dynamic model and the corresponding concept of evolutionary stable strategy (ESS) only takes into account whether the system can return to the equilibrium after being subjected to a small disturbance. In the real world, due to continuous noise, the ESS of the system may not be stochastically stable. In this paper, a model of voluntary public goods game with punishment is studied in a stochastic situation. Unlike the existing model, we describe the evolutionary process of strategies in the population as a generalized quasi-birth-and-death process. And we investigate the stochastic stable equilibrium (SSE) instead. By numerical experiments, we get all possible SSEs of the system for any combination of parameters, and investigate the influence of parameters on the probabilities of the system to select different equilibriums. It is found that in the stochastic situation, the introduction of the punishment and non-participation strategies can change the evolutionary dynamics of the system and equilibrium of the game. There is a large range of parameters that the system selects the cooperative states as its SSE with a high probability. This result provides us an insight and control method for the evolution of cooperation in the public goods game in stochastic situations.
Biogas, which plays an important role in energy production and environmental protection, is developing at a large-scale in China to accommodate the modernization and fast pace that the Chinese agricultural sector has experienced over the last decade due to the rapid development of large-scale farms and stockbreeding in recent years. This study introduced life cycle assessment (LCA) into emergy evaluation to analyze each production step of a large-scale biogas project in China and to compare the economic and ecological performance of the biogas production system (BPS) and biogas plus electricity production system (BEPS) of a project. Our findings indicated that the energy return rate of biogas production system was lower than that of traditional energy production system currently. Emergy efficiency of the large-scale biogas project was 77.9–95.6% higher than that of the small-scale biogas project. The emission mitigation intensity was also 125.7–172.7 times higher for the large-scale plant than for the small-scale plant. The sustainability of the large-scale biogas project was 1.16–11.87 times higher than that of other renewable energy production systems, but 66.0–74.4% lower than that of the small-scale biogas project due to an insufficient amount of raw material inputs and the higher cost of equipment investment in anaerobic fermentation and electricity generation steps. Moreover, the economic and ecological performance of BEPS was worse than that of BPS. We suggested that the sustainability of the large-scale biogas project would be improved by measures: first, providing a suitable quantity and ratio of raw materials; second, reducing the equipment investment of fermentation and the generator; third, using the electricity from the biogas system.
Significance
Humans usually punish free riders but refuse to sanction those who cooperate but do not punish. However, such second-order punishment is essential to maintain cooperation. The central authorities established in modern societies punish both free riders and tax evaders. This is a paradox: would individuals who do not engage in second-order punishment strive for an authority that does? We address this puzzle with a mathematical model and an economic experiment. When individuals can choose between authorities by migrating between different communities, we find a costly bias against second-order punishment. When subjects use a majority vote instead, they vote for an authority with second-order punishment. These findings also suggest that other pressing social dilemmas could be solved by democratic voting.
MATCONT is a graphical MATLAB software package for the interactive numerical study of dynamical systems. It allows one to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles, and fold bifurcation points of limit cycles. All curves are computed by the same function that implements a prediction-correction continuation algorithm based on the Moore-Penrose matrix pseudo-inverse. The continuation of bifurcation points of equilibria and limit cycles is based on bordering methods and minimally extended systems. Hence no additional unknowns such as singular vectors and eigenvectors are used and no artificial sparsity in the systems is created. The sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard Matlab sparse matrix methods. The MATLAB environment makes the standard MATLAB Ordinary Differential Equations (ODE) Suite interactively available and provides computational and visualization tools; it also eliminates the compilation stage and so makes installation straightforward. Compared to other packages such as AUTO and CONTENT, adding a new type of curves is easy in the MATLAB environment. We illustrate this by a detailed description of the limit point curve type.
Minigames capturing the essence of Public Goods experiments show that even in the absence of rationality assumptions, both
punishment and reward will fail to bring about prosocial behavior. This result holds in particular for the well-known Ultimatum
Game, which emerges as a special case. But reputation can induce fairness and cooperation in populations adapting through
learning or imitation. Indeed, the inclusion of reputation effects in the corresponding dynamical models leads to the evolution
of economically productive behavior, with agents contributing to the public good and either punishing those who do not or
rewarding those who do. Reward and punishment correspond to two types of bifurcation with intriguing complementarity. The
analysis suggests that reputation is essential for fostering social behavior among selfish agents, and that it is considerably
more effective with punishment than with reward.
Both laboratory and field data suggest that people punish noncooperators
even in one-shot interactions. Although such ‘‘altruistic
punishment’’ may explain the high levels of cooperation in human
societies, it creates an evolutionary puzzle: existing models suggest
that altruistic cooperation among nonrelatives is evolutionarily
stable only in small groups. Thus, applying such models to the
evolution of altruistic punishment leads to the prediction that
people will not incur costs to punish others to provide benefits to
large groups of nonrelatives. However, here we show that an
important asymmetry between altruistic cooperation and altruistic
punishment allows altruistic punishment to evolve in populations
engaged in one-time, anonymous interactions. This process allows
both altruistic punishment and altruistic cooperation to be maintained
even when groups are large and other parameter values
approximate conditions that characterize cultural evolution in
the small-scale societies in which humans lived for most of our
prehistory. PNAS vol. 100, pgs. 3531-3535
Self-interest frequently causes individuals engaged in joint enterprises to choose actions that are counterproductive. Free-riders can invade a society of cooperators, causing a tragedy of the commons. Such social dilemmas can be overcome by positive or negative incentives. Even though an incentive-providing institution may protect a cooperative society from invasion by free-riders, it cannot always convert a society of free-riders to cooperation. In the latter case, both norms, cooperation and defection, are stable: To avoid a collapse to full defection, cooperators must be sufficiently numerous initially. A society of free-riders is then caught in a social trap, and the institution is unable to provide an escape, except at a high, possibly prohibitive cost. Here, we analyze the interplay of (a) incentives provided by institutions and (b) the effects of voluntary participation. We show that this combination fundamentally improves the efficiency of incentives. In particular, optional participation allows institutions punishing free-riders to overcome the social dilemma at a much lower cost, and to promote a globally stable regime of cooperation. This removes the social trap and implies that whenever a society of cooperators cannot be invaded by free-riders, it will necessarily become established in the long run, through social learning, irrespective of the initial number of cooperators. We also demonstrate that punishing provides a "lighter touch" than rewarding, guaranteeing full cooperation at considerably lower cost.
We consider generic parameterized autonomous ODEs of the form dx/dt ≡ ẋ = f(x, α), where x ∈ ℝn is the vector of state variables, α ∈ ℝm represents parameters, and f(x, α) ∈ ℝn. There are several interactive software packages for analysis of dynamical systems defined by ODEs. The most widely used are AUTO86/97[1], CONTENT[2] and XPPAUT.The Matlab software package MATCONT provides an interactive environment for the continuation and normal form analysis of dynamical systems. This analysis is complementary to the simulation of the systems which is also included in the package and can be used in their identification, control, and optimization. MATCONT is designed to exploit the power of Matlab. It is developed in parallel with the continuation toolbox CL_MATCONT, a package of Matlab routines that can be used from the command line.We consider the following model of an autonomous electronic circuit where x, y and z are state variables and β,γ,ν,r,a3,b3 are parameters: [see pdf for formula]We compute a branch of equilibria with free parameter ν stating from the trivial solution x = 0.00125, y = -0.001, z = 0.00052502 at β = 0.5, γ = -0.6, r = -0.6, a3 = 0.32858, b3 = 0.93358, ν = -0.9, ε = 0.001. We start a curve of periodic orbits from a Hopf point on this curve choosing ν as the free parameter. We detect a torus bifurcation point at ν = -0.59575. We continue the torus bifurcation in two parameters ν, ε and find that it shrinks to a single point for decreasing values of ν (Figure 2).
MUCH attention has been given to the Prisoners' Dilemma as a metaphor
for the problems surrounding the evolution of coopera-tive
behaviour1-6. This work has dealt with the relative merits of
various strategies (such as tit-for-tat) when players who recognize each
other meet repeatedly, and more recently with ensembles of strategies
and with the effects of occasional errors. Here we neglect all
strategical niceties or memories of past encounters, considering only
two simple kinds of players: those who always cooperate and those who
always defect. We explore the consequences of placing these players in a
two-dimensional spatial array: in each round, every individual 'plays
the game' with the immediate neighbours; after this, each site is
occupied either by its original owner or by one of the neighbours,
depending on who scores the highest total in that round; and so to the
next round of the game. This simple, and purely deterministic, spatial
version of the Prisoners' Dilemma, with no memories among players and no
strategical elaboration, can generate chaotically changing spatial
patterns, in which cooperators and defectors both persist indefinitely
(in fluctuating proportions about predictable long-term averages). If
the starting configurations are sufficiently symmetrical, these
ever-changing sequences of spatial patterns-dynamic fractals-can be
extraordinarily beautiful, and have interesting mathematical properties.
There are potential implications for the dynamics of a wide variety of
spatially extended systems in physics and biology.
In social dilemma situations, each individual always receives a higher payoff for defecting than for cooperating, but all are better off if all cooperate than if all defect. Often, however, people in social dilemmas attend more to the group's payoffs than to their own, either automatically or to behave “appropriately.” But whereas social identity elicits cooperative behaviour in dilemmas, it is generally only for the benefit of an “in-group.” Dilemmas between groups (requiring self-sacrificial behaviour within) are often the most extreme. Consequently, the framing and manipulation of group identity is critical to cooperation rate as demonstrated by careful laboratory experimentation. Dans les situations de dilemme social, il est plus rentable pour chaque individu de démissionner que de coopérer, mais tous s'en trouvent mieux si tous coopèrent que s'ils démissionnent. Cependant, les personnes aux prises avec des dilemmes sociaux considèrent davantage les retombées pour le groupe que pour elles-mêmes, de façon automatique ou pour se comporter de façon correcte. Bien que l'identification sociale favorise le comportement coopératif en situation de dilemme, cela ne vaut que pour le groupe d'appartenance. Les dilemmes entre groupes (qui requièrent le sacrifice de soi à l'intérieur du groupe) sont souvent les plus extrêmes. Des expériences en laboratoire montrent que l'encadrement et la manipulation de l'identification au groupe affectent fortement le taux de coopération.
The evolution and maintenance of cooperation in human and animal societies challenge various disciplines ranging from evolutionary biology to anthropology, social sciences, and economics. In social interactions, cooperators increase the welfare of the group at some cost to themselves whereas defectors attempt to free ride and neither provide benefits nor incur costs. The problem of cooperation becomes even more pronounced when increasing the number of interacting individuals. Punishment and voluntary participation have been identified as possible factors to support cooperation and prevent cheating. Typically, punishment behavior is unable to gain a foothold in a population, while volunteering alone can efficiently prevent deadlocks in states of mutual defection but is unable to stabilize cooperation. The combined effects of the two mechanisms have surprisingly different consequences in finite and infinite populations. Here we provide a detailed comparison of the two scenarios and demonstrate that driven by the inherent stochasticity of finite populations, the possibility to abstain from social interactions plays a pivotal role, which paves the way for the establishment of cooperation and punishment.
Theoretical and empirical research highlights the role of punishment in promoting collaborative efforts. However, both the emergence and the stability of costly punishment are problematic issues. It is not clear how punishers can invade a society of defectors by social learning or natural selection, or how second-order free-riders (who contribute to the joint effort but not to the sanctions) can be prevented from drifting into a coercion-based regime and subverting cooperation. Here we compare the prevailing model of peer-punishment with pool-punishment, which consists in committing resources, before the collaborative effort, to prepare sanctions against free-riders. Pool-punishment facilitates the sanctioning of second-order free-riders, because these are exposed even if everyone contributes to the common good. In the absence of such second-order punishment, peer-punishers do better than pool-punishers; but with second-order punishment, the situation is reversed. Efficiency is traded for stability. Neither other-regarding tendencies or preferences for reciprocity and equity, nor group selection or prescriptions from higher authorities, are necessary for the emergence and stability of rudimentary forms of sanctioning institutions regulating common pool resources and enforcing collaborative efforts.
Because mutually beneficial cooperation may unravel unless most members of a group contribute, people often gang up on free-riders,
punishing them when this is cost-effective in sustaining cooperation. In contrast, current models of the evolution of cooperation
assume that punishment is uncoordinated and unconditional. These models have difficulty explaining the evolutionary emergence
of punishment because rare unconditional punishers bear substantial costs and hence are eliminated. Moreover, in human behavioral
experiments in which punishment is uncoordinated, the sum of costs to punishers and their targets often exceeds the benefits
of the increased cooperation that results from the punishment of free-riders. As a result, cooperation sustained by punishment
may actually reduce the average payoffs of group members in comparison with groups in which punishment of free-riders is not
an option. Here, we present a model of coordinated punishment that is calibrated for ancestral human conditions and captures
a further aspect of reality missing from both models and experiments: The total cost of punishing a free-rider declines as
the number of punishers increases. We show that punishment can proliferate when rare, and when it does, it enhances group-average
payoffs.
Cooperation in joint enterprises poses a social dilemma. How can altruistic behavior be sustained if selfish alternatives provide a higher payoff? This social dilemma can be overcome by the threat of sanctions. But a sanctioning system is itself a public good and poses a second-order social dilemma. In this paper, we show by means of deterministic and stochastic evolutionary game theory that imitation-driven evolution can lead to the emergence of cooperation based on punishment, provided the participation in the joint enterprise is not compulsory. This surprising result—cooperation can be enforced if participation is voluntary—holds even in the case of ‘strong altruism’, when the benefits of a player’s contribution are reaped by the other participants only.
Altruistic punishment has been shown to invade when rare if individuals are allowed to opt out of cooperative ventures. Individuals that opt out do not contribute to the common enterprise or derive benefits from it. This result is potentially significant because it offers an explanation for the origin of large-scale cooperation in one-shot interactions among unrelated individuals. Here, we show that this result is not a general consequence of optional participation in cooperative activities, but depends on special assumptions about cooperative pay-offs. We extend the pay-off structure of optional participation models to consider the effects of economies and diseconomies of scale in public-goods production, rival and non-rival consumption of goods, and different orderings of the pay-offs of freeriding and opting out. This more general model highlights the kinds of pay-offs for which optional participation favours cooperation, and those in which it does not.
The Prisoner's Dilemma is the leading metaphor for the evolution of cooperative behaviour in populations of selfish agents, especially since the well-known computer tournaments of Axelrod and their application to biological communities. In Axelrod's simulations, the simple strategy tit-for-tat did outstandingly well and subsequently became the major paradigm for reciprocal altruism. Here we present extended evolutionary simulations of heterogeneous ensembles of probabilistic strategies including mutation and selection, and report the unexpected success of another protagonist: Pavlov. This strategy is as simple as tit-for-tat and embodies the fundamental behavioural mechanism win-stay, lose-shift, which seems to be a widespread rule. Pavlov's success is based on two important advantages over tit-for-tat: it can correct occasional mistakes and exploit unconditional cooperators. This second feature prevents Pavlov populations from being undermined by unconditional cooperators, which in turn invite defectors. Pavlov seems to be more robust than tit-for-tat, suggesting that cooperative behaviour in natural situations may often be based on win-stay, lose-shift.
Darwinian evolution has to provide an explanation for cooperative behaviour. Theories of cooperation are based on kin selection (dependent on genetic relatedness), group selection and reciprocal altruism. The idea of reciprocal altruism usually involves direct reciprocity: repeated encounters between the same individuals allow for the return of an altruistic act by the recipient. Here we present a new theoretical framework, which is based on indirect reciprocity and does not require the same two individuals ever to meet again. Individual selection can nevertheless favour cooperative strategies directed towards recipients that have helped others in the past. Cooperation pays because it confers the image of a valuable community member to the cooperating individual. We present computer simulations and analytic models that specify the conditions required for evolutionary stability of indirect reciprocity. We show that the probability of knowing the 'image' of the recipient must exceed the cost-to-benefit ratio of the altruistic act. We propose that the emergence of indirect reciprocity was a decisive step for the evolution of human societies.
Human cooperation is an evolutionary puzzle. Unlike other creatures, people frequently cooperate with genetically unrelated strangers, often in large groups, with people they will never meet again, and when reputation gains are small or absent. These patterns of cooperation cannot be explained by the nepotistic motives associated with the evolutionary theory of kin selection and the selfish motives associated with signalling theory or the theory of reciprocal altruism. Here we show experimentally that the altruistic punishment of defectors is a key motive for the explanation of cooperation. Altruistic punishment means that individuals punish, although the punishment is costly for them and yields no material gain. We show that cooperation flourishes if altruistic punishment is possible, and breaks down if it is ruled out. The evidence indicates that negative emotions towards defectors are the proximate mechanism behind altruistic punishment. These results suggest that future study of the evolution of human cooperation should include a strong focus on explaining altruistic punishment.
The evolution of cooperation among nonrelated individuals is one of the fundamental problems in biology and social sciences.
Reciprocal altruism fails to provide a solution if interactions are not repeated often enough or groups are too large. Punishment
and reward can be very effective but require that defectors can be traced and identified. Here we present a simple but effective
mechanism operating under full anonymity. Optional participation can foil exploiters and overcome the social dilemma. In voluntary
public goods interactions, cooperators and defectors will coexist. We show that this result holds under very diverse assumptions
on population structure and adaptation mechanisms, leading usually not to an equilibrium but to an unending cycle of adjustments
(a Red Queen type of evolution). Thus, voluntary participation offers an escape hatch out of some social traps. Cooperation
can subsist in sizable groups even if interactions are not repeated, defectors remain anonymous, players have no memory, and
assortment is purely random.
Collective efforts are a trademark of both insect and human societies. They are achieved through relatedness in the former and unknown mechanisms in the latter. The problem of achieving cooperation among non-kin has been described as the 'tragedy of the commons', prophesying the inescapable collapse of many human enterprises. In public goods experiments, initial cooperation usually drops quickly to almost zero. It can be maintained by the opportunity to punish defectors or the need to maintain good reputation. Both schemes require that defectors are identified. Theorists propose that a simple but effective mechanism operates under full anonymity. With optional participation in the public goods game, 'loners' (players who do not join the group), defectors and cooperators will coexist through rock-paper-scissors dynamics. Here we show experimentally that volunteering generates these dynamics in public goods games and that manipulating initial conditions can produce each predicted direction. If, by manipulating displayed decisions, it is pretended that defectors have the highest frequency, loners soon become most frequent, as do cooperators after loners and defectors after cooperators. On average, cooperation is perpetuated at a substantial level.
Some of the most fundamental questions concerning our evolutionary origins, our social relations, and the organization of society are centred around issues of altruism and selfishness. Experimental evidence indicates that human altruism is a powerful force and is unique in the animal world. However, there is much individual heterogeneity and the interaction between altruists and selfish individuals is vital to human cooperation. Depending on the environment, a minority of altruists can force a majority of selfish individuals to cooperate or, conversely, a few egoists can induce a large number of altruists to defect. Current gene-based evolutionary theories cannot explain important patterns of human altruism, pointing towards the importance of both theories of cultural evolution as well as gene-culture co-evolution.
The evolution of cooperation within sizable groups of nonrelated humans offers many challenges for our understanding. Current research has highlighted two factors boosting cooperation in public goods interactions, namely, costly punishment of defectors and the option to abstain from the joint enterprise. A recent modeling approach has suggested that the autarkic option acts as a catalyzer for the ultimate fixation of altruistic punishment. We present an alternative, more microeconomically based model that yields a bistable outcome instead. Evolutionary dynamics can lead either to a Nash equilibrium of punishing and nonpunishing cooperators or to an oscillating state without punishers.
Cooperation is needed for evolution to construct new levels of organization. Genomes, cells, multicellular organisms, social insects, and human society are all based on cooperation. Cooperation means that selfish replicators forgo some of their reproductive potential to help one another. But natural selection implies competition and therefore opposes cooperation unless a specific mechanism is at work. Here I discuss five mechanisms for the evolution of cooperation: kin selection, direct reciprocity, indirect reciprocity, network reciprocity, and group selection. For each mechanism, a simple rule is derived that specifies whether natural selection can lead to cooperation.
A class of models of biological population and communities with a singular equilibrium at the origin is analyzed; it is shown that these models can possess a dynamical regime of deterministic extinction, which is crucially important from the biological standpoint. This regime corresponds to the presence of a family of homoclinics to the origin, so-called elliptic sector. The complete analysis of possible topological structures in a neighborhood of the origin, as well as asymptotics to orbits tending to this point, is given. An algorithmic approach to analyze system behavior with parameter changes is presented. The developed methods and algorithm are applied to existing mathematical models of biological systems. In particular, we analyze a model of anticancer treatment with oncolytic viruses, a parasite-host interaction model, and a model of Chagas' disease.
In human societies, cooperative behavior in joint enterprises is often enforced through institutions that impose sanctions
on defectors. Many experiments on so-called public goods games have shown that in the absence of such institutions, individuals
are willing to punish defectors, even at a cost to themselves. Theoretical models confirm that social norms prescribing the
punishment of uncooperative behavior are stable—once established, they prevent dissident minorities from spreading. But how
can such costly punishing behavior gain a foothold in the population? A surprisingly simple model shows that if individuals
have the option to stand aside and abstain from the joint endeavor, this paves the way for the emergence and establishment
of cooperative behavior based on the punishment of defectors. Paradoxically, the freedom to withdraw from the common enterprise
leads to enforcement of social norms. Joint enterprises that are compulsory rather than voluntary are less likely to lead
to cooperation.
Several evolutionary models in distinct biological fields—population genetics, population ecology, early biochemical evolution and sociobiology—lead independently to the same class of replicator dynamics.
In this paper, we present a cultural evolutionary model in which norms for cooperation and punishment are acquired via two cognitive mechanisms: (1) payoff-biased transmission—a tendency to copy the most successful individual; and (2) conformist transmission—a tendency to copy the most frequent behavior in the population. We first show that if a finite number of punishment stages is permitted (e.g. two stages of punishment occur if some individuals punish people who fail to punish non-cooperators), then an arbitrarily small amount of conformist transmission will stabilize cooperative behavior by stabilizing punishment at some n -th stage. We then explain how, once cooperation is stabilized in one group, it may spread through a multi-group population via cultural group selection. Finally, once cooperation is prevalent, we show how prosocial genes favoring cooperation and punishment may invade in the wake of cultural group selection.
Existing models suggest that reciprocity is unlikely to evolve in large groups as a result of natural selection. In these models, reciprocators punish noncooperation by with-holding future cooperation, and thus also penalize other cooperators in the group. Here, we analyze a model in which the response is some form of punishment that is directed solely at noncooperators. We refer to such alternative forms of punishment as retribution. We show that cooperation enforced by retribution can lead to the evolution of cooperation in two qualitatively different ways. (1) If benefits of cooperation to an individual are greater than the costs to a single individual of coercing the other n − 1 individuals to cooperate, then strategies which cooperate and punish noncooperators, strategies which cooperate only if punished, and, sometimes, strategies which cooperate but do not punish will coexist in the long run. (2) If the costs of being punished are large enough, moralistic strategies which cooperate, punish noncooperators, and punish those who do not punish noncooperators can be evolutionarily stable. We also show, however, that moralistic strategies can cause any individually costly behavior to be evolutionarily stable, whether or not it creates a group benefit.
Recently, several authors have investigated the evolution of reciprocal altruism using the repeated prisoner's dilemma game. These models suggest that natural selection is likely to favor behavioral strategies leading to reciprocal cooperation when pairs of individuals interact repeatedly in potentially cooperative situations. Using the repeated n-person prisoner's dilemma game, we consider whether reciprocal altruism is also likely to evolve when social interactions involve more individuals. We show that the conditions that allow the evolution of reciprocal cooperation become extremely restrictive as group size increases.
How did human cooperation evolve? Recent evidence shows that many people are willing to engage in altruistic punishment, voluntarily paying a cost to punish noncooperators. Although this behavior helps to explain how cooperation can persist, it creates an important puzzle. If altruistic punishment provides benefits to nonpunishers and is costly to punishers, then how could it evolve? Drawing on recent insights from voluntary public goods games, I present a simple evolutionary model in which altruistic punishers can enter and will always come to dominate a population of contributors, defectors, and nonparticipants. The model suggests that the cycle of strategies in voluntary public goods games does not persist in the presence of punishment strategies. It also suggests that punishment can only enforce payoff-improving strategies, contrary to a widely cited "folk theorem" result that suggests that punishment can allow the evolution of any strategy.
Cooperation, where one individual incurs a cost to help another, is a fundamental building block of the natural world and human society. It has been suggested that costly punishment can promote the evolution of cooperation, with the threat of punishment deterring free-riders. Recent experiments, however, have revealed the existence of 'antisocial' punishment, where non-cooperators punish cooperators. While various theoretical models find that punishment can promote the evolution of cooperation, these models a priori exclude the possibility of antisocial punishment. Here we extend the standard theory of optional public goods games to include the full set of punishment strategies. We find that punishment no longer increases cooperation, and that selection favours substantial levels of antisocial punishment for a wide range of parameters. Furthermore, we conduct behavioural experiments, showing results consistent with our model predictions. As opposed to an altruistic act that promotes cooperation, punishment is mostly a self-interested tool for protecting oneself against potential competitors.
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"Technology is not the answer to the population problem. Rather, what is needed is 'mutual coercion mutually agreed upon'--everyone voluntarily giving up the freedom to breed without limit. If we all have an equal right to many 'commons' provided by nature and by the activities of modern governments, then by breeding freely we behave as do herders sharing a common pasture. Each herder acts rationally by adding yet one more beast to his/her herd, because each gains all the profit from that addition, while bearing only a fraction of its costs in overgrazing, which are shared by all the users. The logic of the system compels all herders to increase their herds without limit, with the 'tragic,' i.e. 'inevitable,' 'inescapable' result: ruin the commons. Appealing to individual conscience to exercise restraint in the use of social-welfare or natural commons is likewise self-defeating: the conscientious will restrict use (reproduction), the heedless will continue using (reproducing), and gradually but inevitably the selfish will out-compete the responsible. Temperance can be best accomplished through administrative law, and a 'great challenge...is to invent the corrective feedbacks..to keep custodians honest.'"
Glossary
Definition of the Subject
Introduction
Continuation and Discretization of Solutions
Normal Forms and the Center Manifold
Continuation and Detection of Bifurcations
Branch Switching
Connecting Orbits
Software Environments
Future Directions
Bibliography
Punishing defectors is an important means of stabilizing cooperation. When levels of cooperation and punishment are continuous, individuals must employ suitable social standards for defining defectors and for determining punishment levels. Here we investigate the evolution of a social reaction norm, or psychological response function, for determining the punishment level meted out by individuals in dependence on the cooperation level exhibited by their neighbors in a lattice-structured population. We find that (1) cooperation and punishment can undergo runaway selection, with evolution towards enhanced cooperation and an ever more demanding punishment reaction norm mutually reinforcing each other; (2) this mechanism works best when punishment is strict, so that ambiguities in defining defectors are small; (3) when the strictness of punishment can adapt jointly with the threshold and severity of punishment, evolution favors the strict-and-severe punishment of individuals who offer slightly less than average cooperation levels; (4) strict-and-severe punishment naturally evolves and leads to much enhanced cooperation when cooperation without punishment would be weak and neither cooperation nor punishment are too costly; and (5) such evolutionary dynamics enable the bootstrapping of cooperation and punishment, through which defectors who never punish gradually and steadily evolve into cooperators who punish those they define as defectors.
In biology altruistic behaviour of selfish individuals often can be modelled by the iterated Prisoner's Dilemma game (PD). If the opponents are caught repeatedly in this dilemma reciprocity may lead to cooperative strategies adopted by the individuals. In this article we present results from numerical simulations of the infinitely iterated stochastic alternating PD. First we investigate influences of the memory size on strategies in the alternating two player PD. We show that Firm but Fair is a strong strategy hardly affected by memory size and different values of the temptation to defect. Second we discuss successful strategies in the alternating N player N step memory PD. In this situation we focus on the stability of cooperative strategies and compare the results to experiments of predator inspection by sticklebacks carried out by Milinski and co-workers.Copyright 1998 Academic Press Limited
Cooperation is fundamental to many biological systems. A common metaphor for studying the evolution of cooperation is the Prisoner's Dilemma, a game with two strategies: cooperate or defect. However, cooperation is rare all or nothing, and its evolution probably involves the gradual extension of initially modest degrees of assistance. The inability of the Prisoner's Dilemma to capture this basic aspect limits its use for understanding the evolutionary origins of cooperation. Here we consider a framework for cooperation based on the concept of investment: an act which is costly, but which benefits other individuals, where the cost and benefit depend on the level of investment made. In the resulting Continuous Prisoner's Dilemma the essential problem of cooperation remains: in the absence of any additional structure non-zero levels of investment cannot evolve. However, if investments are considered in a spatially structured context, selfish individuals who make arbitrarily low investments can be invaded by higher-investing mutants. This results in the mean level of investment evolving to significant levels, where it is maintained indefinitely. This approach provides a natural solution to the fundamental problem of how cooperation gradually increases from a non-cooperative state.
The "tragedy of the commons," that is, the selfish exploitation of resources in the public domain, is a reason for many of our everyday social conflicts. However, humans are often more helpful to others than evolutionary theory would predict, unless indirect reciprocity takes place and is based on image scoring (which reflects the way an individual is viewed by a group), as recently shown by game theorists. We tested this idea under conditions that control for confounding factors. Donations were more frequent to receivers who had been generous to others in earlier interactions. This shows that image scoring promotes cooperative behavior in situations where direct reciprocity is unlikely.
The problem of sustaining a public resource that everybody is free to overuse-the 'tragedy of the commons'-emerges in many social dilemmas, such as our inability to sustain the global climate. Public goods experiments, which are used to study this type of problem, usually confirm that the collective benefit will not be produced. Because individuals and countries often participate in several social games simultaneously, the interaction of these games may provide a sophisticated way by which to maintain the public resource. Indirect reciprocity, 'give and you shall receive', is built on reputation and can sustain a high level of cooperation, as shown by game theorists. Here we show, through alternating rounds of public goods and indirect reciprocity games, that the need to maintain reputation for indirect reciprocity maintains contributions to the public good at an unexpectedly high level. But if rounds of indirect reciprocation are not expected, then contributions to the public good drop quickly to zero. Alternating the games leads to higher profits for all players. As reputation may be a currency that is valid in many social games, our approach could be used to test social dilemmas for their solubility.
The public goods game represents a straightforward generalization of the prisoner's dilemma to an arbitrary number of players. Since the dominant strategy is to defect, both classical and evolutionary game theory predict the asocial outcome that no player contributes to the public goods. In contrast to the compulsory public goods game, optional participation provides a natural way to avoid deadlocks in the state of mutual defection. The three resulting strategies--collaboration or defection in the public goods game, as well as not joining at all--are studied by means of a replicator dynamics, which can be completely analysed in spite of the fact that the payoff terms are nonlinear. If cooperation is valuable enough, the dynamics exhibits a rock-scissors-paper type of cycling between the three strategies, leading to sizeable average levels of cooperation in the population. Thus, voluntary participation makes cooperation feasible. But for each strategy, the average payoff value remains equal to the earnings of those not participating in the public goods game.
Many people voluntarily incur costs to punish violations of social norms. Evolutionary models and empirical evidence indicate that such altruistic punishment has been a decisive force in the evolution of human cooperation. We used H2 15O positron emission tomography to examine the neural basis for altruistic punishment of defectors in an economic exchange. Subjects could punish defection either symbolically or effectively. Symbolic punishment did not reduce the defector's economic payoff, whereas effective punishment did reduce the payoff. We scanned the subjects' brains while they learned about the defector's abuse of trust and determined the punishment. Effective punishment, as compared with symbolic punishment, activated the dorsal striatum, which has been implicated in the processing of rewards that accrue as a result of goal-directed actions. Moreover, subjects with stronger activations in the dorsal striatum were willing to incur greater costs in order to punish. Our findings support the hypothesis that people derive satisfaction from punishing norm violations and that the activation in the dorsal striatum reflects the anticipated satisfaction from punishing defectors.