Punishment, especially selfish punishment, has recently been identified as a potent promoter in sustaining or even enhancing the cooperation among unrelated individuals. However, without other key mechanisms, the first-order social dilemma and second-order social dilemma are still two enduring conundrums in biology and the social sciences even with the presence of punishment. In the present study, we investigate a spatial evolutionary four-strategy prisoner's dilemma game model with avoiding mechanism, where the four strategies are cooperation, defection, altruistic and selfish punishment. By introducing the low level of random mutation of strategies, we demonstrate that the presence of selfish punishment with avoiding mechanism can alleviate the two kinds of social dilemmas for various parametrizations. In addition, we propose an extended pair approximation method, whose solutions can essentially estimate the dynamical behaviors and final evolutionary frequencies of the four strategies. At last, considering the analogy between our model and the classical Lotka-Volterra system, we introduce interaction webs based on the spatial replicator dynamics and the transformed payoff matrix to qualitatively characterize the emergent co-exist strategy phases, and its validity are supported by extensive simulations.
Previous studies suggest that punishment is a useful way to promote cooperation in the well-mixed public goods game, whereas it still lacks specific evidence that punishment maintains cooperation in spatial prisoner's dilemma game as well. To address this issue, we introduce a mechanism of recorded punishment, involved with memory and punishment, into spatial prisoner's dilemma game. We find that increasing punishment rate or memory length promotes the evolution of cooperation monotonously. Interestingly, compared with traditional version, recorded punishment will facilitate cooperation better…
The mitigation of the effects of climate change on humankind is one of the most pressing and important collective governance problems nowadays$^{1-4}$. To explore different solutions and scenarios, previous works have framed this problem into a Public Goods Game (PGG), where a dilemma between short-term interests and long-term sustainability arises$^{5-9}$. In such a context, subjects are placed in groups and play a PGG with the aim of avoiding dangerous climate change impact. Here we report on a lab experiment designed to explore two important ingredients: costly punishment to free-riders and…
Empirical studies have shown that individuals' behaviors are largely influenced by social conformity, including punishment. However, a coevolutionary theoretical framework that takes into account effects of conformity on individuals' punishment behaviors has not been put forward yet. Herein we propose a coevolutionary game model to extend the theory of cooperation with conformity in spatial public goods game by considering pool punishment, as well as two converse feedback modes of conformity that strongly affect cooperators' punishment behaviors. We focus on how different parameters and spatia…
Punishment and partner switching are two well-studied mechanisms that support the evolution of cooperation. Observation of human behaviour suggests that the extent to which punishment is adopted depends on the usage of alternative mechanisms, including partner switching. In this study, we investigate the combined effect of punishment and partner switching in evolutionary prisoner's dilemma games conducted on a network. In the model, agents are located on the network and participate in the prisoner's dilemma games with punishment. In addition, they can opportunistically switch interaction partn…
Identifying mechanisms able to sustain costly cooperation among self-interested agents is a central problem across social and biological sciences. One possible solution is peer punishment: when agents have an opportunity to sanction defectors, classical behavioral experiments suggest that cooperation can take root. Overlooked from standard experimental designs, however, is the fact that real-world human punishment -- the administration of justice -- is intrinsically noisy. Here we show that stochastic punishment falls short of sustaining cooperation in the repeated public good game. As punishm…
Prosocial punishment has been proved to be a powerful mean to promote cooperation. Recent studies have found that social exclusion, which indeed can be regarded as a kind of punishment, can also support cooperation. However, if prosocial punishment and exclusion are both present, it is still unclear which strategy is more advantageous to curb free-riders. Here we first study the direct competition between different types of punishment and exclusion. We find that pool (peer) exclusion can always outperform pool (peer) punishment both in the optional and in the compulsory public goods game, no m…
Cooperation is central to the success of human societies as it is crucial for overcoming some of the most pressing social challenges of our time. Yet how human cooperation is achieved and may persist is still a main puzzle in the social and biological sciences. Recently, scholars have recognized the importance of social norms as solutions to major local and large-scale collective action problems, from the management of water resources to the reduction of smoking in public places to the change in fertility practices. Yet a well-founded model of the effect of social norms on human cooperation is…
Monitoring and reporting incorrect acts are pervasive for maintaining human cooperation, but in theory it is unclear how they influence each other. To explore their possible interactions we consider spatially structured population where individuals face the collective-risk social dilemma. In our minimal model cooperator players report defection according to the loss of their interests. In parallel we assume a monitoring institution that monitors all group member and identifies wrong behavior with a certain probability. In response to these feedbacks a sanctioning institution develops punishmen…
Is it rational for selfish individuals to cooperate? The conventional answer based on analysis of games such as the Prisoners Dilemma (PD) is that it is not, even though mutual cooperation results in a better outcome for all. This incompatibility between individual rationality and collective benefit lies at the heart of questions about the evolution of cooperation, as illustrated by PD and similar games. Here, we argue that this apparent incompatibility is due to an inconsistency in the standard Nash framework for analyzing non-cooperative games and propose a new paradigm, that of the co-actio…
In daily life, subjects often face a social dilemma in two stages. In Stage 1, they recognize the social dilemma structure of the decision problem at hand (a tension between personal interest and collective interest); in Stage 2, they have to choose between gathering additional information to learn the exact payoffs corresponding to each of the two options or making a choice without looking at the payoffs. While previous theoretical research suggests that the mere act of considering one's strategic options in a social dilemma will be met with distrust, no experimental study has tested this hyp…
Entanglement: Balancing Punishment and Compensation, Repeated Dilemma Game-Theoretic Analysis of Maximum Compensation Problem for Bypass and Least Cost Paths in Fact-Checking, Case of Fake News with Weak Wallace's Law
Prisoner's Dilemma is a game theory model used to describe altruistic behavior seen in various populations. This theoretical game is important in understanding why a seemingly selfish strategy does persist and spread throughout a population that is mixing homogeneously at random. For a population with structure determined by social interactions, Prisoner's Dilemma brings to light certain requirements for the altruistic strategy to become established. Monte Carlo simulations of Prisoner's Dilemma are carried out using both simulated social networks and a dataset of a real social network. In bot…
Although cooperation is central to the organisation of many social systems, relatively little is known about cooperation in situations of collective emergency. When groups of people flee from a danger such as a burning building or a terrorist attack, the collective benefit of cooperation is important, but the cost of helping is high and the temptation to defect is strong. To explore the degree of cooperation in emergencies, we develop a new social game, the help-or-escape social dilemma. Under time and monetary pressure, players decide how much risk they are willing to take in order to help ot…
The network reciprocity is an important dynamic rule fostering the emergence of cooperation among selfish individuals. This was reported firstly in the seminal work of Nowak and May, where individuals were arranged on the regular lattice network, and played the prisoner's dilemma game (PDG). In the standard PDG, one often assumes that the players have perfect rationality. However, in reality, we human are far from rational agents, as we often make mistakes, and behave irrationally. Accordingly, in this work, we introduce the element of noise into the measurement of fitness, which is determined…
The promise of punishment and reward in promoting public cooperation is debatable. While punishment is traditionally considered more successful than reward, the fact that the cost of punishment frequently fails to offset gains from enhanced cooperation has lead some to reconsider reward as the main catalyst behind collaborative efforts. Here we elaborate on the "stick versus carrot" dilemma by studying the evolution of cooperation in the spatial public goods game, where besides the traditional cooperators and defectors, rewarding cooperators supplement the array of possible strategies. The lat…
According to Thomas Hobbes' Leviathan [1651; 2008 (Touchstone, New York), English Ed], "the life of man [is] solitary, poor, nasty, brutish, and short," and it would need powerful social institutions to establish social order. In reality, however, social cooperation can also arise spontaneously, based on local interactions rather than centralized control. The self-organization of cooperative behavior is particularly puzzling for social dilemmas related to sharing natural resources or creating common goods. Such situations are often described by the prisoner's dilemma. Here, we report the sudde…
Here we study the effects of adopting different strategies against different opponent instead of adopting the same strategy against all of them in the prisoner dilemma structured in well-mixed populations. We consider an evolutionary process in which strategies that provide reproductive success are imitated and players replace one of their worst interactions by the new one. We set individuals in a well-mixed population so that network reciprocity effect is excluded and we analyze both synchronous and asynchronous updates. As a consequence of the replacement rule, we show that mutual cooperatio…
The Prisoner's Dilemma game has a long history stretching across the social, biological, and physical sciences. In 2012, Press and Dyson developed a method for analyzing the mapping of the 8-dimensional strategy profile onto the 2-dimensional payoff space in an infinitely iterated Prisoner's Dilemma game, based on Markov chain analysis and memory-one strategies. We generalize this approach and introduce the concept of strategy parameter to show that linear relations among player payoffs are a ubiquitous feature of the infinitely iterated Prisoner's Dilemma game. Our extended analysis is applie…
The functioning of animal as well as human societies fundamentally relies on cooperation. Yet, defection is often favorable for the selfish individual, and social dilemmas arise. Selection by individuals' fitness, usually the basic driving force of evolution, quickly eliminates cooperators. However, evolution is also governed by fluctuations that can be of greater importance than fitness differences, and can render evolution effectively neutral. Here, we investigate the effects of selection versus fluctuations in social dilemmas. By studying the mean extinction times of cooperators and defecto…
We study the evolution of cooperation in structured populations within popular models of social dilemmas, whereby simple coevolutionary rules are introduced that may enhance players abilities to enforce their strategy on the opponent. Coevolution thus here refers to an evolutionary process affecting the teaching activity of players that accompanies the evolution of their strategies. Particularly, we increase the teaching activity of a player after it has successfully reproduced, yet we do so depending on the disseminated strategy. We separately consider coevolution affecting either only the co…
Cooperative behavior in real social dilemmas is often perceived as a phenomenon emerging from norms and punishment. To overcome this paradigm, we highlight the interplay between the influence of social networks on individuals, and the activation of spontaneous self-regulating mechanisms, which may lead them to behave cooperatively, while interacting with others and taking conflicting decisions over time. By extending Evolutionary game theory over networks, we prove that cooperation partially or fully emerges whether self-regulating mechanisms are sufficiently stronger than social pressure. Int…
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the spreading and disappearance of strategies. In this paper, it is shown that success-driven motion can trigger such local agglomeration and may, therefore, be used to supplement other mechanisms supporting cooperation, like reputation or punishment. Success-driven motion is formulated here as a function of the game-theoretical payoffs. It can change the outcome an…
In the collective-risk social dilemma, players lose their personal endowments if contributions to the common pool are too small. This fact alone, however, does not always deter selfish individuals from defecting. The temptations to free-ride on the prosocial efforts of others are strong because we are hardwired to maximize our own fitness regardless of the consequences this might have for the public good. Here we show that the addition of risky assets to the personal endowments, both of which are lost if the collective target is not reached, can contribute to solving the collective-risk social…
