Evolutionary game dynamics of death-birth process with interval payoffs on graphs

2021 ◽  
pp. 1-12
Author(s):  
Bichuan Jiang ◽  
Lan Shu
Keyword(s):  
Natural Selection ◽  
Dynamic Equation ◽  
Prisoner's Dilemma ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Fixation Probability ◽  
Weak Selection ◽  
Birth Process ◽  
Prisoner’S Dilemma Game ◽  
Game Dynamics

In this paper, we study the evolutionary game dynamics of the death-birth process with interval payoffs on graphs. First of all, we derive the interval replication dynamic equation. Secondly, we derive the fixation probability of the B-C prisoner’s dilemma game based on the death-birth process under the condition of weak selection, analyze the condition of the strategy fixed in the population, that is the condition of strategy A being dominant is analyzed. So we can judge whether natural selection is beneficial to strategy A in the game process through this condition. Finally, the feasibility of this method is verified by several examples.

THE EFFECT OF PINNING CONTROL ON EVOLUTIONARY PRISONER'S DILEMMA GAME

2010 ◽  
Vol 24 (25) ◽  
pp. 2581-2589 ◽  
Author(s):  
WEN-BO DU ◽  
HONG ZHOU ◽  
ZHEN LIU ◽  
XIAN-BIN CAO
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Pinning Control ◽  
Control Mechanisms ◽  
Control Cost ◽  
Prisoner’S Dilemma Game ◽  
Scale Free ◽  
Prisoner's Dilemma Game ◽  
Control Degree

The evolutionary game on graphs provides a natural framework to investigate the cooperation behavior existing in natural and social society. In this paper, degree-based pinning control and random pinning control are introduced into the evolutionary prisoner's dilemma game on scale-free networks, and the effects of control mechanism and control cost on the evolution are studied. Numerical simulation shows that forcing some nodes to cooperate (defect) will increase (decrease) the frequency of cooperators. Compared with random pinning control, degree-based pinning control is more efficient, and degree-based pinning control costs less than random pinning control to achieve the same goal. Numerical results also reveal that the evolutionary time series is more stable under pinning control mechanisms, especially under the degree-based pinning control.

scholarly journals Dynamic aspiration based on Win-Stay-Lose-Learn rule in spatial prisoner’s dilemma game

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0244814
Author(s):  
Zhenyu Shi ◽  
Wei Wei ◽  
Xiangnan Feng ◽  
Xing Li ◽  
Zhiming Zheng
Keyword(s):  
Achievement Motivation ◽  
Prisoner's Dilemma ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Typical Feature ◽  
Value Theory ◽  
Rule Base ◽  
Prisoner’S Dilemma Game ◽  
Prisoner's Dilemma Game ◽  
Spatial Prisoner’S Dilemma

Prisoner’s dilemma game is the most commonly used model of spatial evolutionary game which is considered as a paradigm to portray competition among selfish individuals. In recent years, Win-Stay-Lose-Learn, a strategy updating rule base on aspiration, has been proved to be an effective model to promote cooperation in spatial prisoner’s dilemma game, which leads aspiration to receive lots of attention. In this paper, according to Expected Value Theory and Achievement Motivation Theory, we propose a dynamic aspiration model based on Win-Stay-Lose-Learn rule in which individual’s aspiration is inspired by its payoff. It is found that dynamic aspiration has a significant impact on the evolution process, and different initial aspirations lead to different results, which are called Stable Coexistence under Low Aspiration, Dependent Coexistence under Moderate aspiration and Defection Explosion under High Aspiration respectively. Furthermore, a deep analysis is performed on the local structures which cause defectors’ re-expansion, the concept of END- and EXP-periods are used to justify the mechanism of network reciprocity in view of time-evolution, typical feature nodes for defectors’ re-expansion called Infectors, Infected nodes and High-risk cooperators respectively are found. Compared to fixed aspiration model, dynamic aspiration introduces a more satisfactory explanation on population evolution laws and can promote deeper comprehension for the principle of prisoner’s dilemma.

scholarly journals The evolution of payoff matrices: providing incentives to cooperate

2010 ◽  
Vol 278 (1715) ◽  
pp. 2198-2206 ◽  
Author(s):  
Erol Akçay ◽  
Joan Roughgarden
Keyword(s):  
Natural Selection ◽  
Time Scale ◽  
Prisoner's Dilemma ◽  
Genetic Model ◽  
Social Systems ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Social Situation ◽  
Payoff Matrix ◽  
Payoff Matrices

Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is stable against invasions by mutant genotypes that alter the payoffs. To answer this question, we develop a two-tiered framework with goal-oriented dynamics at the behavioural time scale and a diploid population genetic model at the evolutionary time scale. Our results are two-fold: first, we show that the prisoner's dilemma is subject to invasions by mutants that provide incentives for cooperation to their partners, and that the resulting game is a coordination game similar to the hawk–dove game. Second, we find that for a large class of mutants and symmetric games, a stable genetic polymorphism will exist in the locus determining the payoff matrix, resulting in a complex pattern of behavioural diversity in the population. Our results highlight the importance of considering the evolution of payoff matrices to understand the evolution of animal social systems.

EFFECTS OF LEARNING ACTIVITY ON COOPERATION IN EVOLUTIONARY PRISONER'S DILEMMA GAME

2008 ◽  
Vol 19 (09) ◽  
pp. 1377-1387 ◽  
Author(s):  
XIAOJIE CHEN ◽  
FENG FU ◽  
LONG WANG
Keyword(s):  
Prisoner's Dilemma ◽  
Cooperative Behavior ◽  
Social Systems ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Individual Learning ◽  
Intermediate Level ◽  
Learning Activity ◽  
Prisoner’S Dilemma Game ◽  
Prisoner's Dilemma Game

We study the evolutionary Prisoner's Dilemma game under individual learning activity mechanism on small-world and scale-free networks, respectively. Each player updates its strategy with quenched learning rate which characterizes the strength of individual learning activity during the evolutionary process. Simulation results show that the mechanism of learning activity presents nontrivial phenomena on both the two networks: optimal intermediate levels of learning activity can promote or sustain cooperation. Specifically, there exists an interesting resonance-like manner in the evolutionary game when the intermediate level of learning activity promotes cooperation, and there exists a plateau for cooperation in the favorable moderate region of learning activity when the intermediate level of learning activity sustains cooperation. Moreover, these interesting phenomena are not sensitive to the two networks with other topological parameters. Our work can be helpful in reflecting the effects of individual learning mechanism on cooperative behavior in social systems.

scholarly journals Degree of Satisfaction-based Adaptive Interaction in Spatial Prisoner's Dilemma

2021 ◽  
Author(s):  
Jiaqi Li ◽  
Jianwu Dang ◽  
Jianlei Zhang ◽  
Zengqiang Chen ◽  
Matthias Dehmer
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
The Other ◽  
Square Lattice ◽  
Game Dynamics ◽  
Degree Of Satisfaction ◽  
Cooperative Dynamics ◽  
Adaptive Interaction ◽  
Spatial Prisoner’S Dilemma

Abstract To study why the altruistic cooperation behavior can emerge and maintain among egoistical individuals, researchers across several disciplines have made great contributions for the solutions of this fascinating problem. Ordinarily, the spatial structure is a most-often used framework to investigate the cooperative dynamics of evolutionary game. However, very few researchers take into account the reaction of evolutionary game dynamics to interactive intensity between individuals. On account of this, we propose a computational model of automatic adjustment the interactive intensity based on individual’s degree of satisfaction to study the iterated prisoner’s dilemma game in a two-dimensional square lattice. In this model, selfish individual considers whether the benefits obtained from the other party satisfies its own requirements to determine the intensity of interaction from it to the other party. More specifically, the interactive intensity from an individual x to its some neighbor y is driven by the relations between x obtained current benefit from y (denoted by Px→y) and x’s satisfaction payoff (denoted by Sp). If Px→y > Sp, x will increase the intensity of interaction from itself to y; On the contrary, if Px→y < Sp, x will weaken the intensity of interaction; Other scenario remain the same. Simulation results show that the proposed mechanism can effectively promote the emergence and maintain of cooperation in population, and the satisfying coefficient α (0 < α < 1) plays an essential role on cooperation. Interestingly, we found that there are some optimal values α can lead to the best promotion of cooperation. But individual’s overclaim (α > 1) is not conducive to the effective promotion of cooperation between selfish individuals even for some very small temptation to defect. Our results may contribute to the understanding of cooperative dynamics by considering the reaction of evolutionary game dynamics to network.

Facial Likability and Smiling Enhance Cooperation, but Have No Direct Effect on Moralistic Punishment

2016 ◽  
Vol 63 (5) ◽  
pp. 263-277 ◽  
Author(s):  
Laura Mieth ◽  
Raoul Bell ◽  
Axel Buchner
Keyword(s):  
Conditional Probability ◽  
Direct Effect ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Prisoner’S Dilemma Game ◽  
Costly Punishment ◽  
Prisoner's Dilemma Game ◽  
Moralistic Punishment

Abstract. The present study serves to test how positive and negative appearance-based expectations affect cooperation and punishment. Participants played a prisoner’s dilemma game with partners who either cooperated or defected. Then they were given a costly punishment option: They could spend money to decrease the payoffs of their partners. Aggregated over trials, participants spent more money for punishing the defection of likable-looking and smiling partners compared to punishing the defection of unlikable-looking and nonsmiling partners, but only because participants were more likely to cooperate with likable-looking and smiling partners, which provided the participants with more opportunities for moralistic punishment. When expressed as a conditional probability, moralistic punishment did not differ as a function of the partners’ facial likability. Smiling had no effect on the probability of moralistic punishment, but punishment was milder for smiling in comparison to nonsmiling partners.

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