275 research outputs found
Mobility and asymmetry effects in one-dimensional rock-paper-scissors games
As the behavior of a system composed of cyclically competing species is
strongly influenced by the presence of fluctuations, it is of interest to study
cyclic dominance in low dimensions where these effects are the most prominent.
We here discuss rock-paper-scissors games on a one-dimensional lattice where
the interaction rates and the mobility can be species dependent. Allowing only
single site occupation, we realize mobility by exchanging individuals of
different species. When the interaction and swapping rates are symmetric, a
strongly enhanced swapping rate yields an increased mixing of the species,
leading to a mean-field like coexistence even in one-dimensional systems. This
coexistence is transient when the rates are asymmetric, and eventually only one
species will survive. Interestingly, in our spatial games the dominating
species can differ from the species that would dominate in the corresponding
nonspatial model. We identify different regimes in the parameter space and
construct the corresponding dynamical phase diagram.Comment: 6 pages, 5 figures, to appear in Physical Review
Stability and Diversity in Collective Adaptation
We derive a class of macroscopic differential equations that describe
collective adaptation, starting from a discrete-time stochastic microscopic
model. The behavior of each agent is a dynamic balance between adaptation that
locally achieves the best action and memory loss that leads to randomized
behavior. We show that, although individual agents interact with their
environment and other agents in a purely self-interested way, macroscopic
behavior can be interpreted as game dynamics. Application to several familiar,
explicit game interactions shows that the adaptation dynamics exhibits a
diversity of collective behaviors. The simplicity of the assumptions underlying
the macroscopic equations suggests that these behaviors should be expected
broadly in collective adaptation. We also analyze the adaptation dynamics from
an information-theoretic viewpoint and discuss self-organization induced by
information flux between agents, giving a novel view of collective adaptation.Comment: 22 pages, 23 figures; updated references, corrected typos, changed
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Multiple Steady States, Limit Cycles and Chaotic Attractors in Evolutionary Games with Logit Dynamics
This paper investigates, by means of simple, three and four strategy games, the occurrence of periodic and chaotic behaviour in a smooth version of the Best Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cycles, do occur under the Logit Dynamics, even for three strategy games. Moreover, we show that the Logit Dynamics displays another bifurcation which cannot to occur under the Replicator Dynamics: the fold catastrophe. Finally, we find, in a four strategy game, a period-doubling route to chaotic dynamics under a 'weighted' version of the Logit Dynamics.
Oscillatory dynamics in evolutionary games are suppressed by heterogeneous adaptation rates of players
Game dynamics in which three or more strategies are cyclically competitive,
as represented by the rock-scissors-paper game, have attracted practical and
theoretical interests. In evolutionary dynamics, cyclic competition results in
oscillatory dynamics of densities of individual strategists. In finite-size
populations, it is known that oscillations blow up until all but one strategies
are eradicated if without mutation. In the present paper, we formalize
replicator dynamics with players that have different adaptation rates. We show
analytically and numerically that the heterogeneous adaptation rate suppresses
the oscillation amplitude. In social dilemma games with cyclically competing
strategies and homogeneous adaptation rates, altruistic strategies are often
relatively weak and cannot survive in finite-size populations. In such
situations, heterogeneous adaptation rates save coexistence of different
strategies and hence promote altruism. When one strategy dominates the others
without cyclic competition, fast adaptors earn more than slow adaptors. When
not, mixture of fast and slow adaptors stabilizes population dynamics, and slow
adaptation does not imply inefficiency for a player.Comment: 4 figure
Coevolutionary dynamics of a variant of the cyclic Lotka-Volterra model with three-agent interactions
We study a variant of the cyclic Lotka-Volterra model with three-agent
interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors
game, the model describes an ideal ecosystem in which cyclic competition among
three species develops through cooperative predation. Its rate equations in a
well-mixed environment display a degenerate Hopf bifurcation, occurring as
reactions involving two predators plus one prey have the same rate as reactions
involving two preys plus one predator. We estimate the magnitude of the
stochastic noise at the bifurcation point, where finite size effects turn
neutrally stable orbits into erratically diverging trajectories. In particular,
we compare analytic predictions for the extinction probability, derived in the
Fokker-Planck approximation, with numerical simulations based on the Gillespie
stochastic algorithm. We then extend the analysis of the phase portrait to
heterogeneous rates. In a well-mixed environment, we observe a continuum of
degenerate Hopf bifurcations, generalizing the above one. Neutral stability
ensues from a complex equilibrium between different reactions. Remarkably, on a
two-dimensional lattice, all bifurcations disappear as a consequence of the
spatial locality of the interactions. In the second part of the paper, we
investigate the effects of mobility in a lattice metapopulation model with
patches hosting several agents. We find that strategies propagate along the
arms of rotating spirals, as they usually do in models of cyclic dominance. We
observe propagation instabilities in the regime of large wavelengths. We also
examine three-agent interactions inducing nonlinear diffusion.Comment: 22 pages, 13 figures. v2: version accepted for publication in EPJ
Resurgence of oscillation in coupled oscillators under delayed cyclic interaction
This paper investigates the emergence of amplitude death and revival of
oscillations from the suppression states in a system of coupled dynamical units
interacting through delayed cyclic mode. In order to resurrect the oscillation
from amplitude death state, we introduce asymmetry and feedback parameter in
the cyclic coupling forms as a result of which the death region shrinks due to
higher asymmetry and lower feedback parameter values for coupled oscillatory
systems. Some analytical conditions are derived for amplitude death and revival
of oscillations in two coupled limit cycle oscillators and corresponding
numerical simulations confirm the obtained theoretical results. We also report
that the death state and revival of oscillations from quenched state are
possible in the network of identical coupled oscillators. The proposed
mechanism has also been examined using chaotic Lorenz oscillator.Comment: 16 pages, 13 figure
Dynamics of a linearly-perturbed May-Leonard competition model
The May--Leonard model was introduced to examine the behavior of three
competing populations where rich dynamics, such as limit cycles and nonperiodic
cyclic solutions, arise. In this work, we perturb the system by adding the
capability of global mutations, allowing one species to evolve to the other two
in a linear manner. We find that for small mutation rates the perturbed system
not only retains some of the dynamics seen in the classical model, such as the
three-species equal-population equilibrium bifurcating to a limit cycle, but
also exhibits new behavior. For instance, we capture curves of fold
bifurcations where pairs of equilibria emerge and then coalesce. As a result,
we uncover parameter regimes with new types of stable fixed points that are
distinct from the single- and dual-population equilibria characteristic of the
original model. In short, a linear perturbation proves to be not at all
trivial, with the modified system exhibiting new behavior captured even with
small mutation rates.Comment: 29 pages, 12 figure
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
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