Cooperation can emerge in prisoner’s dilemma from a multi-species predator prey replicator dynamic

Paulson, Elisabeth; Griffin, Christopher

doi:10.1016/j.mbs.2016.05.006

Cited by 11 publications

(9 citation statements)

References 16 publications

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“…According to EGT, replication dynamic means that if the payoff of one behavior is higher than the average payoff of the population, this behavior will develop [59]. That is, the growth rate of the proportion of individuals who choose this behavior in the population is greater than zero.…”

Section: The Solution Of Equilibrium Pointsmentioning

confidence: 99%

Dynamic Evolution of Safety Regulation of the Ridesharing Industry under Social Media Participation

Sun

et al. 2020

Symmetry

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The emergence of ridesharing has spread against the background of the sharing economy. There have been a lot of controversies since the emergence of ridesharing, particularly regarding regulatory issues. The safety regulation of the ridesharing industry involves many parties, including governments, platform companies, and society at large. Currently, because of the influence of information asymmetry, it increases the uncertainty of governments’ regulation effect and the difficulty of making regulation measures. Meanwhile, social media, one of the most important forces of social regulation, has not paid enough attention to playing an appropriate role in the safety regulation of the ridesharing industry. Therefore, this study constructs an evolutionary game model between governments and platform companies that concerns the safety regulations of ridesharing passengers under social media participation. The influence path of social media is explored by model solution and numerical simulation. Our results indicate that social media participation has a positive impact on this safety regulation. Specifically, social media participation could reduce governments’ regulatory costs and encourage it to strictly regulate. The exposure of social media could bring losses to platform companies involved and promote platform companies’ investments in improving passengers’ safety. This study provides a decision basis for governments to introduce social media in the safety regulation of the ridesharing industry.

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Section: The Solution Of Equilibrium Pointsmentioning

confidence: 99%

Dynamic Evolution of Safety Regulation of the Ridesharing Industry under Social Media Participation

Sun

et al. 2020

Symmetry

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“…Here (•) denotes the standard Euclidean dot product and N (i) denotes the graph-theoretic neighborhood of Player (Vertex) i. This approach is precisely the one taken in [17] when vertices are treated as species while the strategies at each vertex are treated as sub-species. Unlike [17] the exact species proportions (vertex counts) are fixed, making the analysis of Eq.…”

Section: A Derivation Of the Network Replicatormentioning

confidence: 99%

“…This approach is precisely the one taken in [17] when vertices are treated as species while the strategies at each vertex are treated as sub-species. Unlike [17] the exact species proportions (vertex counts) are fixed, making the analysis of Eq. ( 16) simpler.…”

Section: A Derivation Of the Network Replicatormentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10]) can in some cases be shown to possess a Hamiltonian structure, stemming from the dynamical description implicit in the replicator equation for the evolution of strategy choices [11][12][13]. The replicator equation is one of several differential equations proposed for evolutionary games [6,9,14] and it has also been generalized to many situations, including the coevolutionary dynamics of multiple games (different payoff matrices) [11,12,[15][16][17]. The simplest case is the bimatrix formulation [11,12], with dynamics given by: ẋi = x i (e i − x) Ay ẏi = y i (e i − y) Bx.…”

Section: Introductionmentioning

confidence: 99%

“…Here we have two interacting species, with strategy proportion vectors x(t) and y(t) and corresponding game matrices A and B (fully generalized in [17]). For the bimatrix replicator, it has been shown that all interior equilibria (corresponding to coexisting strategies or phenotypes within a species) are unstable [11].…”

Section: Introductionmentioning

confidence: 99%

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Generalized Hamiltonian Dynamics and Chaos in Evolutionary Games on Networks

Griffin¹,

Semonsen²,

Belmonte³

2020

Preprint

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We study the network replicator equation and characterize its fixed points on arbitrary graph structures for 2 × 2 symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of an independent vertex set in the graph and also show that complex behavior cannot emerge in 2 × 2 games. This links a property of the dynamical system with a combinatorial graph property. We contrast this by showing that ordinary rock-paper-scissors (RPS) exhibits chaos on the 3-cycle and that on general graphs with ≥ 3 vertices the network replicator with RPS is a generalized Hamiltonian system. This stands in stark contrast to the established fact that RPS does not exhibit chaos in the standard replicator dynamics or the bimatrix replicator dynamics, which is equivalent to the network replicator on a graph with one edge and two vertices (K 2 ).

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