Aspiration promotes cooperation in the prisoner's dilemma game with the imitation rule

Liu, Xuesong; He, Mingfeng; Kang, Yibin; Pan, Qiuhui

doi:10.1103/physreve.94.012124

Cited by 58 publications

(26 citation statements)

References 47 publications

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“…Moreover, Xu et al [34] demonstrated that average abundance function reaches the highest value when both interaction coefficient and aspiration level are at appropriate level. Xuesong Liu [35] affirmed that the combination of aspiration rule and imitation rule is conducive to the increasing of average abundance function. Chen et al [36] corroborated that the suboptimal selection based on aspiration level is beneficial for average abundance function.…”

Section: The Comparison Between Aspiration Rule and Imitation Rulementioning

confidence: 93%

The characteristics of average abundance function with mutation of multi-player threshold public goods evolutionary game model under redistribution mechanism

Xia

2021

BMC Ecol Evo

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Background In recent years, the average abundance function has attracted much attention as it reflects the degree of cooperation in the population. Then it is significant to analyse how average abundance functions can be increased to promote the proliferation of cooperative behaviour. However, further theoretical analysis for average abundance function with mutation under redistribution mechanism is still lacking. Furthermore, the theoretical basis for the corresponding numerical simulation is not sufficiently understood. Results We have deduced the approximate expressions of average abundance function with mutation under redistribution mechanism on the basis of different levels of selection intensity $$\omega$$ ω (sufficiently small and large enough). In addition, we have analysed the influence of the size of group d, multiplication factor r, cost c, aspiration level $$\alpha$$ α on average abundance function from both quantitative and qualitative aspects. Conclusions (1) The approximate expression will become the linear equation related to selection intensity when $$\omega$$ ω is sufficiently small. (2) On one hand, approximation expression when $$\omega$$ ω is large enough is not available when r is small and m is large. On the other hand, this approximation expression will become more reliable when $$\omega$$ ω is larger. (3) On the basis of the expected payoff function $$\pi \left( \centerdot \right)$$ π ⋅ and function $$h(i,\omega )$$ h ( i , ω ) , the corresponding results for the effects of parameters (d,r,c,$$\alpha$$ α ) on average abundance function $$X_{A}(\omega )$$ X A ( ω ) have been explained.

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Section: The Comparison Between Aspiration Rule and Imitation Rulementioning

confidence: 93%

The characteristics of average abundance function with mutation of multi-player threshold public goods evolutionary game model under redistribution mechanism

Xia

2021

BMC Ecol Evo

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“…In the complex battlefield environment, the information acquisition is incomplete, asymmetric, which requires the swarm to achieve selfmanagement and self-coordination, and this requirement just coincides with the aspiration-driven dynamics. Moreover, the existing results show that, in both prisoner's dilemma game and public goods game, the dynamic mechanism driven by aspiration can improve the average abundance value and promote cooperation more than the traditional imitation dynamics [43,44].…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Cooperative Evolution Mechanism of Unmanned Swarm within the Framework of Public Goods Game

et al. 2021

Mathematical Problems in Engineering

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One of the key advantages of unmanned swarm operation is its autonomous cooperation. When the communication is interrupted or the centralized control manner is lost, the cooperative operation can still be carried out orderly. This work proposed a cooperative evolution mechanism within the framework of multiplayer public goods game to solve the problem of autonomous collaboration of unmanned swarm in case of failure of centralized control. It starts with the requirement analysis of autonomous cooperation in unmanned swarm, and then, the evolutionary game model of multiplayer public goods based on aspiration-driven dynamics is established. On this basis, the average abundance function is constructed by theoretical derivation, and furthermore, the influence of cost, multiplication factor, and aspiration level on the average abundance is simulated. Finally, the evolutionary mechanism of parameter adjustment in swarm cooperation is revealed via case study, and deliberate proposals are suggested to provide a meaningful exploration in the actual control of unmanned swarm cooperation.

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“…Therefore, the inclusion of heterogeneous updating is much needed to reflect a more realistic scenario. In fact, some of the previous studies [39,40] have already explored the presence of heterogenous updating in classical social dilemma games, such as dyadic games. In those cases, the existence of aspiration-led updating in addition to the imitation rule has seemed to ensure the survival of cooperation, even in a defective milieu (such as the Prisoner's Dilemma; PD) [37,38].…”

Section: Introductionmentioning

confidence: 99%

Vaccinating behaviour guided by imitation and aspiration

2020

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Vaccinating decisions can be influenced by imitation as well as self-evaluation or aspiration. This work analyses vaccinating behaviours by coupling both imitation and aspiration update rules, adopting an existing set-up of the mean-field vaccination game. We incorporate the imitation mechanism with several variants of the aspiration protocol, encompassing constant and adaptive aspirations. Equations of the combined dynamics have been derived by grouping the population according to (i) vaccinating strategies and (ii) healthy and infected status within each strategy. If aspiration levels are fixed but differentiated by vaccinating strategies, then vaccinators aspiring less than non-vaccinators are found to ameliorate the vaccination coverage, thereby yielding a less infectious state. The adaptive aspirations maintain a positive correlation with the vaccine efficacy while keeping the opposite relation with vaccination cost. When vaccinating strategies, aspirations and update rules are allowed to evolve synchronously, then either the imitation or aspiration process takes over the entire population. If aspiration rules prevail, then vaccinees and non-vaccinees coexist equally (according to (i)) or vaccine uptake follows a non-monotonic trend with the efficacy (according to (ii)). The imitative rule performs better when vaccination is less expensive or cheap, while aspiration updating safeguards the tenacity of vaccinees despite vaccination being expensive.

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Aspiration promotes cooperation in the prisoner's dilemma game with the imitation rule

Cited by 58 publications

References 47 publications

The characteristics of average abundance function with mutation of multi-player threshold public goods evolutionary game model under redistribution mechanism

The characteristics of average abundance function with mutation of multi-player threshold public goods evolutionary game model under redistribution mechanism

Cooperative Evolution Mechanism of Unmanned Swarm within the Framework of Public Goods Game

Vaccinating behaviour guided by imitation and aspiration

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