Evolutionary dynamics of individual strategies and game environments in the framework of feedback control

Abstract

A model of co-evolution between individual strategy and gaming environment is proposed here. Different from the general evolutionary game dynamics, the gaming system developed here is deeply coupled with the strategy choices and the environment state. The game state, payoff matrices and gaming environment of the system will influence each other dynamically. We firstly analyse the co-evolution between two populations with two strategies and derive the sufficient condition under which the state of strategy and environment will evolve periodically. Then we extend the model to multiple populations and strategies to study a more complicated and realistic system. In this framework, we verify whether and how the convergence will take place among groups in the multi-strategy case. Our results provide some inspirations to tackle with the cooperation dilemma and research on the self-organized evolution in multi-behaviour populations in the real-world situations.

Evolutionary Game Dynamics with Environmental Feedback in a Network with Two Communities

“… 2019 ; Liu et al. 2020 ; Shu and Fu 2022 ), the players do not interact within each community. This assumption is suitable for modeling situations in which the population of players is divided into two different roles but otherwise not in general.…”

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

“…Due to the societal and biological relevance, environmental feedback on game dynamics has attracted great attention in recent years [3,22–29]. Weitz et al .…”

“…This framework illustrates an ‘oscillatory tragedy of commons' in which the system cycles between depleted and replete environmental states with an associated fluctuation between cooperative and defective behavioural states. Subsequent works [25,29] extended this model to multiple populations as well as multiple strategies. Inspired by the work in [24], Tilman et al .…”

“…Due to the societal and biological relevance, environmental feedback on game dynamics has attracted great attention in recent years [3,[22][23][24][25][26][27][28][29]. Weitz et al [24] were among the first to propose a unified approach of feedback-evolving games within the context of pairwise interactions where the strategic composition explicitly impacts the environmental dynamics.…”

“…This framework illustrates an 'oscillatory tragedy of commons' in which the system cycles between depleted and replete environmental states with an associated fluctuation between cooperative and defective behavioural states. Subsequent works [25,29] extended this model to multiple populations as well as multiple strategies. Inspired by the work in [24], Tilman et al [3] presented a general framework of feedback-evolving games where the environmental dynamics evolve not only by the population strategy profile, but also with its own intrinsic dynamic.…”