891 research outputs found
Co-evolution of strategy and structure in complex networks with dynamical linking
Here we introduce a model in which individuals differ in the rate at which
they seek new interactions with others, making rational decisions modeled as
general symmetric two-player games. Once a link between two individuals has
formed, the productivity of this link is evaluated. Links can be broken off at
different rates. We provide analytic results for the limiting cases where
linking dynamics is much faster than evolutionary dynamics and vice-versa, and
show how the individual capacity of forming new links or severing inconvenient
ones maps into the problem of strategy evolution in a well-mixed population
under a different game. For intermediate ranges, we investigate numerically the
detailed interplay determined by these two time-scales and show that the scope
of validity of the analytical results extends to a much wider ratio of time
scales than expected
Similarity based cooperation and spatial segregation
We analyze a cooperative game, where the cooperative act is not based on the
previous behaviour of the co-player, but on the similarity between the players.
This system has been studied in a mean-field description recently [A. Traulsen
and H. G. Schuster, Phys. Rev. E 68, 046129 (2003)]. Here, the spatial
extension to a two-dimensional lattice is studied, where each player interacts
with eight players in a Moore neighborhood. The system shows a strong
segregation independent on parameters. The introduction of a local conversion
mechanism towards tolerance allows for four-state cycles and the emergence of
spiral waves in the spatial game. In the case of asymmetric costs of
cooperation a rich variety of complex behavior is observed depending on both
cooperation costs. Finally, we study the stabilization of a cooperative fixed
point of a forecast rule in the symmetric game, which corresponds to
cooperation across segregation borders. This fixed point becomes unstable for
high cooperation costs, but can be stabilized by a linear feedback mechanism.Comment: 7 pages, 9 figure
Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)
In the context of smooth interval maps, we study an inducing scheme approach
to prove existence and uniqueness of equilibrium states for potentials
with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used
by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of
Perron-Frobenius operators. We demonstrate that this `bounded range' condition
on the potential is important even if the potential is H\"older continuous. We
also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues
and operator norms. Added extra references and corrected some typo
Stochasticity and evolutionary stability
In stochastic dynamical systems, different concepts of stability can be
obtained in different limits. A particularly interesting example is
evolutionary game theory, which is traditionally based on infinite populations,
where strict Nash equilibria correspond to stable fixed points that are always
evolutionarily stable. However, in finite populations stochastic effects can
drive the system away from strict Nash equilibria, which gives rise to a new
concept for evolutionary stability. The conventional and the new stability
concepts may apparently contradict each other leading to conflicting
predictions in large yet finite populations. We show that the two concepts can
be derived from the frequency dependent Moran process in different limits. Our
results help to determine the appropriate stability concept in large finite
populations. The general validity of our findings is demonstrated showing that
the same results are valid employing vastly different co-evolutionary
processes
Replicators in Fine-grained Environment: Adaptation and Polymorphism
Selection in a time-periodic environment is modeled via the two-player
replicator dynamics. For sufficiently fast environmental changes, this is
reduced to a multi-player replicator dynamics in a constant environment. The
two-player terms correspond to the time-averaged payoffs, while the three and
four-player terms arise from the adaptation of the morphs to their varying
environment. Such multi-player (adaptive) terms can induce a stable
polymorphism. The establishment of the polymorphism in partnership games
[genetic selection] is accompanied by decreasing mean fitness of the
population.Comment: 4 pages, 2 figure
Stochastic gain in population dynamics
We introduce an extension of the usual replicator dynamics to adaptive
learning rates. We show that a population with a dynamic learning rate can gain
an increased average payoff in transient phases and can also exploit external
noise, leading the system away from the Nash equilibrium, in a reasonance-like
fashion. The payoff versus noise curve resembles the signal to noise ratio
curve in stochastic resonance. Seen in this broad context, we introduce another
mechanism that exploits fluctuations in order to improve properties of the
system. Such a mechanism could be of particular interest in economic systems.Comment: accepted for publication in Phys. Rev. Let
Hawks and Doves on Small-World Networks
We explore the Hawk-Dove game on networks with topologies ranging from
regular lattices to random graphs with small-world networks in between. This is
done by means of computer simulations using several update rules for the
population evolutionary dynamics. We find the overall result that cooperation
is sometimes inhibited and sometimes enhanced in those network structures, with
respect to the mixing population case. The differences are due to different
update rules and depend on the gain-to-cost ratio. We analyse and qualitatively
explain this behavior by using local topological arguments.Comment: 12 pages, 8 figure
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Ecological theatre and the evolutionary game: how environmental and demographic factors determine payoffs in evolutionary games
In the standard approach to evolutionary games and replicator dynamics, differences in fitness can be interpreted as an excess from the mean Malthusian growth rate in the population. In the underlying reasoning, related to an analysis of "costs" and "benefits", there is a silent assumption that fitness can be described in some type of units. However, in most cases these units of measure are not explicitly specified. Then the question arises: are these theories testable? How can we measure "benefit" or "cost"? A natural language, useful for describing and justifying comparisons of strategic "cost" versus "benefits", is the terminology of demography, because the basic events that shape the outcome of natural selection are births and deaths. In this paper, we present the consequences of an explicit analysis of births and deaths in an evolutionary game theoretic framework. We will investigate different types of mortality pressures, their combinations and the possibility of trade-offs between mortality and fertility. We will show that within this new approach it is possible to model how strictly ecological factors such as density dependence and additive background fitness, which seem neutral in classical theory, can affect the outcomes of the game. We consider the example of the Hawk-Dove game, and show that when reformulated in terms of our new approach new details and new biological predictions are produced
Nongaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process
The appropriate description of fluctuations within the framework of
evolutionary game theory is a fundamental unsolved problem in the case of
finite populations. The Moran process recently introduced into this context
[Nowak et al., Nature (London) 428, 646 (2004)] defines a promising standard
model of evolutionary game theory in finite populations for which analytical
results are accessible. In this paper, we derive the stationary distribution of
the Moran process population dynamics for arbitrary games for the
finite size case. We show that a nonvanishing background fitness can be
transformed to the vanishing case by rescaling the payoff matrix. In contrast
to the common approach to mimic finite-size fluctuations by Gaussian
distributed noise, the finite size fluctuations can deviate significantly from
a Gaussian distribution.Comment: 4 pages (2 figs). Published in Physical Review E (Rapid
Communications
Coexistence and Survival in Conservative Lotka-Volterra Networks
Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network's interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time
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