Evolution of cooperation in social dilemmas under the coexistence of aspiration and imitation mechanisms

Arefin, Md. Rajib; Tanimoto, Jun

doi:10.1103/physreve.102.032120

Cited by 32 publications

(33 citation statements)

References 60 publications

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“…TR + PD: in this case, n = 1 and n = 0 capture the payoff functions of PD and TR games, respectively. Previous studies such as [39,53,76] suggest that under aspiration dynamics (with symmetric aspiration), PD ( π C < π D ) and TR ( π C > π D ) follow the bounds xasp∗<0.5 and xasp∗>0.5, respectively, where xasp∗ is the equilibrium frequency of cooperators. This can be easily verified from the linear approximation of the strategic equation in equation (2.9) under the weak selection limit ( k ≪ 1), which is given by [39,53,76] xasp∗≈12+k8false[(AD−AC)−(πD−πC)false]. Let us note that the above bounds for PD and TR are valid for weak as well as strong selection intensity [39,76].…”

Section: Resultsmentioning

confidence: 98%

“…PD inhabits both positive greed and positive fear (i.e. D g , D r > 0) as motivation for defection [39,67]. Note that if D g , D r < 0, a complete cooperation would be the eventual outcome, which corresponds to the TR game.…”

Section: Modelmentioning

confidence: 99%

“…satisfied), agents keep playing the current strategy; otherwise, consider switching to another strategy. The master equation of aspiration dynamics can be written as [36,39,52] x˙=false(1−xfalse)PDS−xPCS, where PDS and PCS illustrate the switching probability of defectors and cooperators, respectively. These probabilities can be determined by the well-known Fermi function as follows: 0.8em 0.4em1emPDS=11+exp⁡[kfalse(πD(x,n)−ADfalse)]PCS=11+exp⁡[kfalse(πC(x,n)−ACfalse)]}, where A C and A D demonstrate the aspiration level for C and D agents, respectively.…”

Section: Modelmentioning

confidence: 99%

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Imitation and aspiration dynamics bring different evolutionary outcomes in feedback-evolving games

Arefin

Tanimoto

2021

Proc. R. Soc. A.

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Feedback-evolving games characterize the interplay between the evolution of strategies and environments. Rich dynamics have been derived for such games under the premise of the replicator equation, which unveils persistent oscillations between cooperation and defection. Besides replicator dynamics, here we have employed aspiration dynamics, in which individuals, instead of comparing payoffs with opposite strategies, assess their payoffs by self-evaluation to update strategies. We start with a brief review of feedback-evolving games with replicator dynamics and then comprehensively discuss such games with aspiration dynamics. Interestingly, the tenacious cycles, as perceived in replicator dynamics, cannot be observed in aspiration dynamics. Our analysis reveals that a parameter θ —which depicts the strength of cooperation in enhancing the environment—plays a pivotal role in comprehending the dynamics. In particular, with the symmetric aspiration level, if replete and depleted states, respectively, experience Prisoner's Dilemma and Trivial games, the rich environment is achievable only when θ > 1. The case θ < 1 never allows us to reach the replete state, even with a higher cooperation level. Furthermore, if cooperators aspire less than defectors, then the enhanced state can be achieved with a relatively lower θ value compared with the opposite scenario because too much expectation from cooperation can be less beneficial.

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Section: Resultsmentioning

confidence: 98%

Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

See 1 more Smart Citation

Imitation and aspiration dynamics bring different evolutionary outcomes in feedback-evolving games

Arefin

Tanimoto

2021

Proc. R. Soc. A.

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“…However, in many nations, the government has funding constraints, space constraints, healthcare personnel and instrumentation constraints when caring for diseased people. These behavioral treatments have already demonstrated their value in studying the interaction between illnesses and human decision-making in the context of social dilemmas [24] , [25] , [26] , [27] , [28] , [29] , [30] .…”

Section: Introductionmentioning

confidence: 99%

“…Compartmental models, common tool in epidemiology and current health management systems, are widely used to investigate a pandemic or epidemic process [ 1 , 6 , 7 , 9 , 11 , 15 , 18 , 26 , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] ]. One of the most widely used epidemiological models is the SIR model [ 32 , 38 , 39 ].…”

Section: Introductionmentioning

confidence: 99%