Cheng Haihui, Meng Xinzhu
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China.
Biosystems. 2023 Jan;223:104801. doi: 10.1016/j.biosystems.2022.104801. Epub 2022 Nov 11.
Replicator dynamics is widely used in evolutionary game theory, however, most previous studies on replicator dynamics focus on single games and ignore multiple social dilemmas encountered by individuals in a population. This paper uses replicator dynamics to construct a multigame system with environmental space and delay based on three social dilemmas. For the non-delayed and delayed multigame systems, rich dynamics for stability, bistability, transcritical bifurcation, Hopf bifurcation, and the direction, stability and periodic variation of periodic solutions are comprehensively investigated. Accordingly, we use numerical simulations to assist in exploring the effects of multigame, environmental space, and time delay on strategic dynamics. The results show that large proportions of snowdrift game and stag hunt game are conducive to the prosperity of cooperators, and defectors are easy to survive when the proportion of prisoner's dilemma is large. The cooperator gains the advantage of benefit distribution from environmental space, or the defector gets less benefit distribution as punishment, which will make pure cooperation the dominant strategy. Furthermore, environmental space can allow cooperation and defection to coexist oscillatingly. Interestingly, large delays reverse the coexistence of cooperation and defection to a situation dominated by the purely cooperative strategy.
复制者动态在进化博弈论中被广泛应用，然而，以往大多数关于复制者动态的研究都集中在单一博弈上，而忽略了群体中个体所面临的多种社会困境。本文基于三种社会困境，运用复制者动态构建了一个具有环境空间和延迟的多博弈系统。对于无延迟和有延迟的多博弈系统，全面研究了稳定性、双稳态、跨临界分岔、霍普夫分岔的丰富动态，以及周期解的方向、稳定性和周期变化。相应地，我们使用数值模拟来辅助探索多博弈、环境空间和时间延迟对策略动态的影响。结果表明，较大比例的雪堆博弈和猎鹿博弈有利于合作者的繁荣，当囚徒困境的比例较大时，背叛者容易生存。合作者从环境空间中获得利益分配优势，或者背叛者因受到惩罚而获得较少的利益分配，这将使纯合作成为主导策略。此外，环境空间可以允许合作与背叛以振荡的方式共存。有趣的是，大延迟将合作与背叛的共存逆转到由纯合作策略主导的局面。
