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

Md Rajib Arefin, Jun Tanimoto

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Article number20210240
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2251
Publication statusPublished - Jul 28 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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