Game-environment feedback dynamics in growing population: Effect of finite carrying capacity

Bairagya, Joy Das; Mondal, Samrat Sohel; Chowdhury, Debashish; Chakraborty, Sagar

doi:10.1103/physreve.104.044407

Cited by 17 publications

(16 citation statements)

References 86 publications

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“…For future convenience we first introduce four parameters [60,[64][65][66] that can be intuitively interpreted as four distinct types of incentives for changes in the strategies:…”

Section: Resultsmentioning

confidence: 99%

“…We believe that the mathematical framework explored in this paper opens up the possibility of further exciting research themes in the game-resource feedback dynamics. For example, one could construct a model that takes the effect of changing population size [66] into account. Specifically, one could consider a renewable resource with intrinsic growth dynamics and study the effect of a finite growing population on the mechanism of reward and punishment.…”

Section: Discussionmentioning

confidence: 99%

“…Consequently, there is a potential change in the interactions pattern amongst the individuals. This concept is mathematized by the form of the total payoff matrix U(n) as given below [60,[64][65][66]…”

Section: Reinforcement By Shared Resource's Feedbackmentioning

confidence: 99%

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Reward versus punishment: averting the tragedy of the commons in eco-evolutionary dynamics

2022

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We consider an unstructured population of individuals who are randomly matched in an underlying population game in which the payoﬀs depend on the evolving state of the common resource exploited by the population. There are many known mechanisms for averting the overexploitation (tragedy) of the (common) resource. Probably one of the most common mechanism is reinforcing cooperation through rewards and punishments. Additionally, the depleting resource can also provide feedback that reinforces cooperation. Thus, it is an interesting question that how reward and punishment comparatively fare in averting the tragedy of the common in the game-resource feedback evolutionary dynamics. Our main ﬁnding is that, while averting the tragedy of the common completely, rewarding cooperators cannot get rid of all the defectors, unlike what happens when defectors are punished; and as a consequence, in the completely replete resource state, the outcome of the population game can be socially optimal in the presence of the punishment but not so in the presence of the reward.

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“…For future convenience we first introduce four parameters [60,[64][65][66] that can be intuitively interpreted as four distinct types of incentives for changes in the strategies:…”

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Reward versus punishment: averting the tragedy of the commons in eco-evolutionary dynamics

2022

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“…In the light of the existing literature on microscopic stochastic birth-death process [34][35][36] leading to replicator equation in the mean field limit and that on the microscopic process leading similarly to deterministic population dynamics equation (e.g., logistic equation [37]), in this paper we are motivated to derive the macroscopic model of the game-environment feedback dynamics starting from a microscopic multidimensional birth-death process that incorporates the feedback between the evolutionary system and an ecological self-renewing resource. Furthermore, this endeavour automatically facilitates the study of finite sized population with a finite carrying capacity which is known to have quite non-trivial counter-intuitive effects [38]. In passing, we remark that there do exist extensive investigations using stochastic models [39][40][41][42][43] that, however, do not include an explicit equation for resource's dynamics and capture the environmental changes mostly through rather ad-hoc time-dependent carrying capacity.…”

Section: Introductionmentioning

confidence: 99%

Eco-evolutionary games for harvesting self-renewing common resource: Effect of growing harvester population

Bairagya¹,

Mondal²,

Chowdhury³

et al. 2022

Preprint

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The tragedy of the commons (TOC) is a ubiquitous social dilemma witnessed in interactions between a population of living entities and shared resources available to them: The individuals in the population tend to selfishly overexploit a common resource as it is arguably the rational choice, or in case of non-human beings, it may be an evolutionarily uninvadable action. How to avert the TOC is a significant problem related to the conservation of resources. It is not hard to envisage situations where the resource could be self-renewing and the size of the population may be dependent on the state of the resource through the fractions of the population employing different exploitation rates. If the self-renewal rate of the resource lies between the maximum and the minimum exploitation rates, it is not a priori obvious under what conditions the TOC can be averted. In this paper, we address this question analytically and numerically using the setup of an evolutionary game theoretical replicator equation that models the Darwinian tenet of natural selection. Through the replicator equation, while we investigate how a population of replicators exploit the shared resource, the latter's dynamical feedback on the former is also not ignored. We also present a transparent bottom-up derivation of the game-resource feedback model to facilitate future studies on the stochastic effects on the findings presented herein.

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“…However, much of the current work is focused on the classic two-player two-strategy game [43][44][45][46][47][48][49][50]. There are few studies on environmental feedback dynamics with three or more strategies.…”

Section: Introductionmentioning

confidence: 99%

Game-environment feedback dynamics for voluntary prisoner's dilemma games

Li¹,

Liu²,

Wu³

et al. 2021

Preprint

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Recently, the eco-evolutionary game theory which describes the coupled dynamics of strategies and environment have attracted great attention. At the same time, most of the current work is focused on the classic two-player two-strategy game. In this work, we study multi-strategy eco-evolutionary game theory which is an extension of the framework. For simplicity, we'll focus on the voluntary participation Prisoner's dilemma game. For the general class of payoff-dependent feedback dynamics, we show the conditions for the existence and stability of internal equilibrium by using the replicator dynamics, respectively. Where internal equilibrium points, such as, two-strategy coexistence states, three-strategy coexistence states, persistent oscillation states and interior saddle points. These states are determined by the relative feedback strength and payoff matrix, and are independent of the relative feedback speed and initial state. In particular, the three-strategy coexistence provides a new mechanism for maintaining biodiversity in biology, ecology, and sociology. Besides, we find that this three-strategy model return to the persistent oscillation state of the two-strategy model when there is no defective strategy at the initial moment.

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Game-environment feedback dynamics in growing population: Effect of finite carrying capacity

Cited by 17 publications

References 86 publications

Reward versus punishment: averting the tragedy of the commons in eco-evolutionary dynamics

Reward versus punishment: averting the tragedy of the commons in eco-evolutionary dynamics

Eco-evolutionary games for harvesting self-renewing common resource: Effect of growing harvester population

Game-environment feedback dynamics for voluntary prisoner's dilemma games

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