Chaos in game dynamics

Skyrms, Brian

doi:10.1007/bf00171693

Cited by 33 publications

(20 citation statements)

References 56 publications

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“…Other research has highlighted the importance of the dynamics of learning (Rayner et al ., ) in reproducing particular statistical features observed in empirical data, and Skyrms (); Hommes and Sorger () and Sato et al . () demonstrated the existence of chaotic attractors in strategy dynamics in several theoretical settings, including an expectations framework.…”

Section: Resultssupporting

confidence: 53%

A Simulation Analysis of Herding and Unifractal Scaling Behaviour

Phelps

2013

Intell. Sys. Acc. Fin. Mgmt.

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We model the financial market using a class of agent-based models in which agents' expectations are driven by heuristic forecasting rules (in contrast to the rational expectations models used in traditional theories of financial markets). We show that within this framework, we can reproduce unifractal scaling with respect to three well-known power-laws relating: (i) moments of the absolute price-change to the time-scale over which they are measured; (ii) magnitude of returns with respect to their probability; (iii) the autocorrelation of absolute returns with respect to lag. In contrast to previous studies, we systematically analyse all three power-laws simultaneously using the same underlying model by making observations at different time-scales. We show that the first two scaling laws are remarkably robust to the time-scale over which observations are made, irrespective of the model configuration.However, in contrast to previous studies, we show that herding may explain why long-memory is observed at all frequencies. *

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Section: Resultssupporting

confidence: 53%

A Simulation Analysis of Herding and Unifractal Scaling Behaviour

Phelps

2013

Intell. Sys. Acc. Fin. Mgmt.

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“…The Poincaré-Bendixson theorem [19] establishes that chaos can only arise in a continuous dynamical system (specified by differential equations) if it has three or more dimensions. Accordingly, Skyrms [20] showed that chaos does not exist for three types (also referred to as strategies) and gave examples of chaotic dynamics on strange attractors with four strategies. Further examples were provided in [21,22].…”

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confidence: 99%

Chaos and Unpredictability in Evolutionary Dynamics in Discrete Time

2011

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A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from those of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace the usual fixed-point population solutions. We observe the familiar period-doubling and chaotic-band-splitting attractor cascades of unimodal maps but in some cases more elaborate variations appear due to bimodality. Also unphysical stationary solutions can have unusual physical implications, such as the uncertainty of the final population caused by sensitivity to initial conditions and fractality of attractor preimage manifolds.

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“…For example, chaos in the iterated version of the PD game has been reported among 10 different strategies under frequency-dependent selection in discrete time [8]. On the other hand, chaos in lowdimensional continuous dynamics is a more challenging * hang-hyun.jo@apctp.org † wsjung@postech.ac.kr ‡ seungki@pknu.ac.kr issue, considering that chaos is impossible when the dimensionality of the strategy space is less than three [9].…”

Section: Introductionmentioning

confidence: 99%

Chaos and unpredictability in evolution of cooperation in continuous time

You

Kwon

et al. 2017

Phys. Rev. E

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Cooperators benefit others with paying costs. Evolution of cooperation crucially depends on the cost-benefit ratio of cooperation, denoted as c. In this work, we investigate the infinitely repeated prisoner's dilemma for various values of c with four of the representative memory-one strategies, i.e., unconditional cooperation, unconditional defection, tit-for-tat, and win-stay-lose-shift. We consider replicator dynamics which deterministically describes how the fraction of each strategy evolves over time in an infinite-sized well-mixed population in the presence of implementation error and mutation among the four strategies. Our finding is that this three-dimensional continuous-time dynamics exhibits chaos through a bifurcation sequence similar to that of a logistic map as c varies. If mutation occurs with rate μ≪1, the position of the bifurcation sequence on the c axis is numerically found to scale as μ^{0.1}, and such sensitivity to μ suggests that mutation may have nonperturbative effects on evolutionary paths. It demonstrates how the microscopic randomness of the mutation process can be amplified to macroscopic unpredictability by evolutionary dynamics.

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Chaos in game dynamics

Cited by 33 publications

References 56 publications

A Simulation Analysis of Herding and Unifractal Scaling Behaviour

A Simulation Analysis of Herding and Unifractal Scaling Behaviour

Chaos and Unpredictability in Evolutionary Dynamics in Discrete Time

Chaos and unpredictability in evolution of cooperation in continuous time

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