Correction to ‘Scaling the phase-planes of social dilemma strengths shows game-class changes in the five rules governing the evolution of cooperation’

Despite the accumulation of research on indirect reciprocity over the past 30 years and the publication of over 100,000 related papers, there are still many issues to be addressed. Here, we look back on the research that has been done on indirect reciprocity and identify the issues that have been resolved and the ones that remain to be resolved. This manuscript introduces indirect reciprocity in the context of the evolution of cooperation, basic models of social dilemma situations, the path taken in the elaboration of mathematical analysis using evolutionary game theory, the discovery of image scoring norms, and the breakthroughs brought about by the analysis of the evolutionary instability of the norms. Moreover, it presents key results obtained by refining the assessment function, resolving the punishment dilemma, and presenting a complete solution to the social dilemma problem. Finally, it discusses the application of indirect reciprocity in various disciplines.

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Stochasticity, Selection, and the Evolution of Cooperation in a Two-Level Moran Model of the Snowdrift Game

Complexity ◽

10.1155/2018/9836150 ◽

2018 ◽

Vol 2018 ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

Brian McLoone ◽

Wai-Tong Louis Fan ◽

Adam Pham ◽

Rory Smead ◽

Laurence Loewe

Keyword(s):

Stochastic Dynamics ◽

Cooperative Behavior ◽

Social Dilemma ◽

Threshold Effect ◽

Payoff Matrix ◽

Multilevel Selection ◽

Evolution Of Cooperation ◽

Interior Equilibrium ◽

Moran Model ◽

Snowdrift Game

The Snowdrift Game, also known as the Hawk-Dove Game, is a social dilemma in which an individual can participate (cooperate) or not (defect) in producing a public good. It is relevant to a number of collective action problems in biology. In a population of individuals playing this game, traditional evolutionary models, in which the dynamics are continuous and deterministic, predict a stable, interior equilibrium frequency of cooperators. Here, we examine how finite population size and multilevel selection affect the evolution of cooperation in this game using a two-level Moran process, which involves discrete, stochastic dynamics. Our analysis has two main results. First, we find that multilevel selection in this model can yield significantly higher levels of cooperation than one finds in traditional models. Second, we identify a threshold effect for the payoff matrix in the Snowdrift Game, such that below (above) a determinate cost-to-benefit ratio, cooperation will almost surely fix (go extinct) in the population. This second result calls into question the explanatory reach of traditional continuous models and suggests a possible alternative explanation for high levels of cooperative behavior in nature.

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Peer pressure induced punishment resolves social dilemma on interdependent networks

Scientific Reports ◽

10.1038/s41598-021-95303-0 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Kaipeng Hu ◽

Yewei Tao ◽

Yongjuan Ma ◽

Lei Shi

Keyword(s):

Random Network ◽

Social Dilemma ◽

Small World ◽

Peer Pressure ◽

Evolution Of Cooperation ◽

Interdependent Networks ◽

Interdependent Network ◽

Psychological Harm ◽

Will Force ◽

The Impact

AbstractDespite the fruitful evidence to support the emergence of cooperation, irrational decisions are still an essential part of promoting cooperation. Among the many factors that affect human rational decision-making, peer pressure is unique to social organisms and directly affects individual cooperative behaviors in the process of social interaction. This kind of pressure psychologically forces individuals to behave consistently with their partners, and partners with inconsistent behaviors may suffer psychological blows. As feedback, this psychological harm may in turn affect individual cooperative decisions. There is evidence that when peer pressure exists, partnerships can reduce free-riding in enterprise. Based on interdependent networks, this paper studies the impact of peer pressure on cooperation dynamics when the strategies of corresponding partners from different layers of the networks are inconsistent. We assume that when individuals are under peer pressure, their payoffs will be compromised. The simulation results show that the punishment effect will force the expulsion of partners with different strategies, which will further reduce the proportion of partners with inconsistent strategies in the system. However, in most cases, only moderate fines are most conductive to the evolution of cooperation, and the punishment mechanisms can effectively promote the interdependent network reciprocity. The results on the small world and random network prove the robustness of the result. In addition, under this mechanism, the greater the payoff dependence between partners, the better the effect of interdependent network reciprocity.

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Evolution of Cooperation in Social Dilemma

Artificial Life VII ◽

10.7551/mitpress/1432.003.0026 ◽

2000 ◽

Keyword(s):

Social Dilemma ◽

Evolution Of Cooperation

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Evolutionary Cooperation in Networked Public Goods Game with Dependency Groups

Complexity ◽

10.1155/2019/8670802 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8

Author(s):

Xuzhen Zhu ◽

Xin Su ◽

Jinming Ma ◽

Hui Tian ◽

RunRan Liu

Keyword(s):

Public Goods ◽

Enhancement Factor ◽

Transition Probabilities ◽

Social Dilemma ◽

Small World ◽

Evolution Of Cooperation ◽

Square Lattice ◽

Public Goods Game ◽

Conducting Research ◽

Group Density

Either in microlevel organizations or macrolevel societies, the individuals acquire benefits or payoffs by forming interdependency groups linked by common interests. Conducting research on the effects of interdependency groups on the evolution of cooperation could have a better understanding of the social dilemma problem. In this paper, we studied a spatial public goods game with nonlocal interdependency groups where each of participants is located in a two-dimensional square lattice or Watts–Strogatz small-world network with payoffs obtaining from the interactions with nearest neighbors. In terms of the enhancement factor, the effects of group density on the evolutionary cooperation can be quite different. For a low enhancement factor, the cooperation level is a nonmonotonic function with the varying density of interdependency groups in the system, which means a proper density of interdependency groups can best promote the cooperative level. For a moderate enhancement factor, a higher density of interdependency groups can always correspond to a higher cooperative level. However, if the enhancement factor is too high, a high density of interdependency groups can impede the evolutionary cooperation. We give the explanations for the different roles of group density of interdependency by using the transition probabilities of C players into D players as well as the reverse. Our findings are very helpful for the understanding of emergence cooperation as well as the cooperation regulation in the selfish individuals.

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Evolution of Cooperation with Peer Punishment under Prospect Theory

Games ◽

10.3390/g10010011 ◽

2019 ◽

Vol 10 (1) ◽

pp. 11 ◽

Cited By ~ 4

Author(s):

Satoshi Uchida ◽

Hitoshi Yamamoto ◽

Isamu Okada ◽

Tatsuya Sasaki

Keyword(s):

Game Theory ◽

Prospect Theory ◽

Evolutionary Game Theory ◽

Evolutionary Game ◽

Social Dilemma ◽

Cognitive Distortion ◽

Evolution Of Cooperation ◽

Human Beings ◽

Wide Range ◽

Parameter Values

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.

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Effects of defensive cooperation strategy on the evolution of cooperation in social dilemma

Applied Mathematics and Computation ◽

10.1016/j.amc.2021.126047 ◽

2021 ◽

Vol 399 ◽

pp. 126047

Author(s):

Liyan Gao ◽

Qiuhui Pan ◽

Mingfeng He

Keyword(s):

Social Dilemma ◽

Evolution Of Cooperation ◽

Cooperation Strategy

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Scaling the phase-planes of social dilemma strengths shows game-class changes in the five rules governing the evolution of cooperation

Royal Society Open Science ◽

10.1098/rsos.181085 ◽

2018 ◽

Vol 5 (10) ◽

pp. 181085 ◽

Cited By ~ 61

Author(s):

Hiromu Ito ◽

Jun Tanimoto

Keyword(s):

Game Theory ◽

Phase Plane ◽

Social Dilemma ◽

Evolution Of Cooperation ◽

Cooperative Behaviour ◽

Universal Scaling ◽

Different Types ◽

Scaling Parameters ◽

Animal Societies

Game theory has been extensively applied to help explain how cooperative behaviour is promoted in human and animal societies. How do humans and animals establish reciprocity when confronting a social dilemma? In 2006, Nowak theoretically proved that numerous mechanisms and models for evolving cooperative behaviour reported over the last few decades can be distilled into five reciprocity mechanisms (rules). Additionally, universal scaling parameters were proposed to measure two different types of dilemmas, namely, the gamble-intending dilemma (GID) and risk-averting dilemma (RAD). In this work, by drawing a RAD–GID phase-plane diagram for pair-wise games, we prove that these five rules have four different dilemma resolution (relaxation) mechanisms. These diagrams also demonstrate whether and when game-class change (resolution of a dilemma) occurs, thus implying how defectors can be eliminated.

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