scholarly journals Evolutionary dynamics of cooperation in a population with probabilistic corrupt enforcers and violators

2019 ◽  
Vol 29 (11) ◽  
pp. 2127-2149 ◽  
Author(s):  
Linjie Liu ◽  
Xiaojie Chen ◽  
Attila Szolnoki
Keyword(s):  
Mathematical Analysis ◽  
Evolutionary Dynamics ◽  
Necessary Conditions ◽  
Evolution Of Cooperation ◽  
Altruistic Behavior ◽  
Heteroclinic Cycle ◽  
Public Goods Game ◽  
The Public ◽  
Key Driver ◽  
Open Question

Pro-social punishment is a key driver of harmonious and stable society. However, this institution is vulnerable to corruption since law-violators can avoid sanctioning by paying bribes to corrupt law-enforcers. Consequently, to understand how altruistic behavior survives in a corrupt environment is an open question. To reveal potential explanations here, we introduce corrupt enforcers and violators into the public goods game with pool punishment, and assume that punishers, as corrupt enforcers, may select defectors probabilistically to take a bribe from, and meanwhile defectors, as corrupt violators, may select punishers stochastically to be corrupted. By means of mathematical analysis, we aim to study the necessary conditions for the evolution of cooperation in such corrupt environment. We find that cooperation can be maintained in the population in two distinct ways. First, cooperators, defectors, and punishers can coexist by all keeping a steady fraction of the population. Second, these three strategies can form a cyclic dominance that resembles a rock-scissors-paper cycle or a heteroclinic cycle. We theoretically identify conditions when the competing strategies coexist in a stationary way or they dominate each other in a cyclic way. These predictions are confirmed numerically.

Evolutionary Dynamics of Cooperation in a Corrupt Society with Anti-Corruption Control

2021 ◽  
Vol 31 (03) ◽  
pp. 2150039
Author(s):  
Linjie Liu ◽  
Xiaojie Chen
Keyword(s):  
System Dynamics ◽  
Public Goods ◽  
Social Exclusion ◽  
Evolutionary Dynamics ◽  
Parameter Range ◽  
Heteroclinic Cycle ◽  
Public Goods Game ◽  
The Public ◽  
Emergence Of Cooperation

The importance of cooperation is self-evident to humans, yet the existence of corruption where law violators can avoid being punished by paying bribes to corrupt law enforcers may threaten the maintenance of cooperation. Although powerful monitoring has been used to resolve such matters, existing studies show that the effects of such measures are either transient or uncertain. Thus how to efficiently control the occurrence of corruption for the emergence of cooperation remains a challenge. Here, we introduce social exclusion into the public goods game, and respectively propose three measures to control corruption, namely, the exclusion of corrupt punishers, the exclusion of corrupt defectors, and the exclusion of both corrupt punishers and corrupt defectors. Our results show that the system dynamics driven by these three measures can exhibit many interesting dynamical outcomes including the dominance of defectors, rock-scissors-paper cycle, heteroclinic cycle, or interior attractor. We further demonstrate that excluding corrupt punishers can improve the situation of corruption more efficiently than excluding corrupt defectors. In addition, excluding both corrupt defectors and corrupt punishers can more effectively promote the emergence of cooperation for a broad parameter range.

scholarly journals Cooperation evolves by the payoff-difference-based probabilistic reward

2021 ◽  
Vol 94 (11) ◽  
Author(s):  
Tetsushi Ohdaira
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
The Other ◽  
Evolution Of Cooperation ◽  
Public Goods Game ◽  
Prisoner’S Dilemma Game ◽  
The Public ◽  
Prisoner's Dilemma Game ◽  
The Difference ◽  
Spatial Prisoner’S Dilemma

Abstract In the previous studies, the author proposes the payoff-difference-based probabilistic peer-punishment that the probability of punishing a defector increases as the difference of payoff between a player and a defector increases and shows that the proposed peer-punishment effectively increases the number of cooperators and the average payoff of all players. On the other hand, reward as well as punishment is considered to be a mechanism promoting cooperation, and many studies have discussed the effect of reward in the public goods game, a multiplayer version of the prisoner’s dilemma game. Based on the discussion of those existing studies, this study introduces the payoff-difference-based probabilistic reward that the probability of rewarding a cooperator increases as the difference of payoff between a player and a cooperator increases. The author utilizes the framework of the spatial prisoner’s dilemma game of the previous study and shows that the reward of this study realizes the evolution of cooperation except some cases. Graphic abstract

scholarly journals Evolution of prosocial punishment in unstructured and structured populations and in the presence of antisocial punishment

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0254860
Author(s):  
Mohammad Salahshour
Keyword(s):  
Large Body ◽  
Theoretical Models ◽  
Free Rider ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Public Goods Game ◽  
The Public ◽  
Free Rider Problem ◽  
Altruistic Punishment ◽  
Public Resource

A large body of empirical evidence suggests that altruistic punishment abounds in human societies. Based on such evidence, it is suggested that punishment serves an important role in promoting cooperation in humans and possibly other species. However, as punishment is costly, its evolution is subject to the same problem that it tries to address. To suppress this so-called second-order free-rider problem, known theoretical models on the evolution of punishment resort to one of the few established mechanisms for the evolution of cooperation. This leaves the question of whether altruistic punishment can evolve and give rise to the evolution of cooperation in the absence of such auxiliary cooperation-favoring mechanisms unaddressed. Here, by considering a population of individuals who play a public goods game, followed by a public punishing game, introduced here, we show that altruistic punishment indeed evolves and promotes cooperation in the absence of a cooperation-favoring mechanism. In our model, the punishment pool is considered a public resource whose resources are used for punishment. We show that the evolution of a punishing institution is facilitated when resources in the punishment pool, instead of being wasted, are used to reward punishers when there is nobody to punish. Besides, we show that higher returns to the public resource or punishment pool facilitate the evolution of prosocial instead of antisocial punishment. We also show that an optimal cost of investment in the punishment pool facilitates the evolution of prosocial punishment. Finally, our analysis shows that being close to a physical phase transition facilitates the evolution of altruistic punishment.

scholarly journals Evolutionary dynamics with game transitions

2019 ◽  
Vol 116 (51) ◽  
pp. 25398-25404 ◽  
Author(s):  
Qi Su ◽  
Alex McAvoy ◽  
Long Wang ◽  
Martin A. Nowak
Keyword(s):  
Strong Influence ◽  
Evolutionary Dynamics ◽  
Simple Game ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Altruistic Behavior ◽  
Weak Selection ◽  
Time Step ◽  
Mutual Cooperation ◽  
Connected Populations

The environment has a strong influence on a population’s evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals’ behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceedsk−k′, where k is the average number of neighbors of an individual andk′captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.

scholarly journals Evolutionary dynamics of group interactions on structured populations: a review

2013 ◽  
Vol 10 (80) ◽  
pp. 20120997 ◽  
Author(s):  
Matjaž Perc ◽  
Jesús Gómez-Gardeñes ◽  
Attila Szolnoki ◽  
Luis M. Floría ◽  
Yamir Moreno
Keyword(s):  
Statistical Physics ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Structured Populations ◽  
Public Goods Game ◽  
Group Interactions ◽  
The Public ◽  
Living Organisms ◽  
Class Representative

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.

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