Evolutionary dynamics of the delayed replicator-mutator equation: Limit cycle and cooperation

Mittal, S.; Mukhopadhyay, Archan; Chakraborty, Sagar

doi:10.1103/physreve.101.042410

Cited by 26 publications

(11 citation statements)

References 60 publications

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“…Mutation is one of the omnipresent phenomena in biology and eco-evolutionary dynamics. The evolutionary dynamics of multigame are relatively ignored in most of the earlier studies on mutation [114][115][116][117][118]. Our results may reveal exciting findings on the inclusion of mutations.…”

Section: Discussionmentioning

confidence: 73%

Complex evolutionary dynamics due to punishment and free space in ecological multigames

et al. 2021

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The concurrence of ecological and evolutionary processes often arises as an integral part of various biological and social systems. We here study eco-evolutionary dynamics by adopting two paradigmatic metaphors of social dilemmas with contrasting outcomes. We use the Prisoner’s Dilemma and Snowdrift games as the backbone of the proposed mathematical model. Since cooperation is a costly proposition in the face of the Darwinian theory of evolution, we go beyond the traditional framework by introducing punishment as an additional strategy. Punishers bare an additional cost from their own resources to try and discourage or prohibit free-riding from selfish defectors. Our model also incorporates the ecological signature of free space, which has an altruistic-like impact because it allows others to replicate and potentially thrive. We show that the consideration of these factors has broad implications for better understanding the emergent complex evolutionary dynamics. In particular, we report the simultaneous presence of different subpopulations through the spontaneous emergence of cyclic dominance, and we determine various stationary points using traditional game-theoretic concepts and stability analysis.

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Section: Discussionmentioning

confidence: 73%

Complex evolutionary dynamics due to punishment and free space in ecological multigames

et al. 2021

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“…Essentially this means that the form of U 0 could deviate from the prisoner's dilemma. In general, depending on how the preference of the players change as degradation of the shared resource takes place, U 0 could be the payoff matrix for any of the four classes of games [51][52][53][54][55]. The games are classified into four types based on the correspondence of the Nash equilibria with cooperation and defection: (i) in the harmony game, the Nash equilibrium is mutual cooperation; (ii) in the anti-coordination game, there exists a unique mixed symmetric Nash equilibrium in which the players play a mixed strategy randomized over the pure strategies; (iii) in the prisoner's dilemma, the mutual defection is the unique Nash equilibrium; and (iv) in the coordination game, there are two symmetric pure Nash equilibria [(cooperate, cooperate) and (defect, defect)] and one mixed symmetric Nash equilibrium like the one in the anti-coordination games.…”

Section: Resultsmentioning

confidence: 99%

“…Since we want to analyse the dependence of TOC on the strategic interactions modelled by all possible types of U 0 , it is convenient to present the results on a plane spanned by ∆ 0 RT = 0 and ∆ 0 SP = 0. Thus the ∆ 0 RT −∆ 0 SP plane is divided into four quadrants identified by the four aforementioned different types of games, each having a distinct structure of the corresponding payoff matrix [51][52][53][54][55], viz., that of the harmony game, the anti-coordination game, the prisoner's dilemma, and the coordination game.…”

Section: B Relevant Partition Of the Parameter Spacementioning

confidence: 99%

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

Bairagya,

Mondal,

Chowdhury

et al. 2021

Preprint

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The tragedy of the commons (TOC) is an unfortunate situation where a shared resource is exhausted due to uncontrolled exploitation by the selfish individuals of a population. Recently, the paradigmatic replicator equation has been used in conjunction with a phenomenological equation for the state of the shared resource to gain insight into the influence of the games on the TOC. The replicator equation, by construction, models a fixed infinite population undergoing microevolution. Thus, it is unable to capture any effect of the population growth and the carrying capacity of the population although the TOC is expected to be dependent on the size of the population. Therefore, in this paper, we present a mathematical framework that incorporates the density dependent payoffs and the logistic growth of the population in the eco-evolutionary dynamics modelling the game-resource feedback. We discover a bistability in the dynamics: a finite carrying capacity can either avert or cause the TOC depending on the initial states of the resource and the initial fraction of cooperators. In fact, depending on the type of strategic game-theoretic interaction, a finite carrying capacity can either avert or cause the TOC when it is exactly the opposite for the corresponding case with infinite carrying capacity.

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“…In this setting, one should be able to explore collective phenomena like synchronization onto an attractor. Furthermore, one could also ponder upon how bounded rationality [114][115][116], mutation [117] and delay [118], and hypergames [119] in a deme would modify the results of this paper.…”

Section: Discussionmentioning

confidence: 99%

Amplitude death in coupled replicator map lattice: averting migration dilemma

Sadhukhan,

Chattopadhyay,

Chakraborty

2021

Preprint

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Populations composed of a collection of subpopulations (demes) with random migration between them are quite common occurrences. The emergence and sustenance of cooperation in such a population is a highly researched topic in the evolutionary game theory. If the individuals in every deme are considered to be either cooperators or defectors, the migration dilemma can be envisaged: The cooperators would not want to migrate to a defector-rich deme as they fear of facing exploitation; but without migration, cooperation can not be established throughout the network of demes. With a view to studying the aforementioned scenario, in this paper, we set up a theoretical model consisting of a coupled map lattice of replicator maps based on two-player-two-strategy games. The replicator map considered is capable of showing a variety of evolutionary outcomes, like convergent (fixed point) outcomes and nonconvergent (periodic and chaotic) outcomes. Furthermore, this coupled network of the replicator maps undergoes the phenomenon of amplitude death leading to nonoscillatory stable synchronized states. We specifically explore the effect of (i) the nature of coupling that models migration between the maps, (ii) the heterogenous demes (in the sense that not all the demes have same game being played by the individuals), (iii) the degree of the network, and (iv) the cost associated with the migration. In the course of investigation, we are intrigued by the effectiveness of the random migration in sustaining a uniform cooperator fraction across a population irrespective of the details of the replicator dynamics and the interaction among the demes.

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Evolutionary dynamics of the delayed replicator-mutator equation: Limit cycle and cooperation

Cited by 26 publications

References 60 publications

Complex evolutionary dynamics due to punishment and free space in ecological multigames

Complex evolutionary dynamics due to punishment and free space in ecological multigames

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

Amplitude death in coupled replicator map lattice: averting migration dilemma

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