8,921 research outputs found
Evolutionary dynamics on any population structure
Evolution occurs in populations of reproducing individuals. The structure of
a biological population affects which traits evolve. Understanding evolutionary
game dynamics in structured populations is difficult. Precise results have been
absent for a long time, but have recently emerged for special structures where
all individuals have the same number of neighbors. But the problem of
determining which trait is favored by selection in the natural case where the
number of neighbors can vary, has remained open. For arbitrary selection
intensity, the problem is in a computational complexity class which suggests
there is no efficient algorithm. Whether there exists a simple solution for
weak selection was unanswered. Here we provide, surprisingly, a general formula
for weak selection that applies to any graph or social network. Our method uses
coalescent theory and relies on calculating the meeting times of random walks.
We can now evaluate large numbers of diverse and heterogeneous population
structures for their propensity to favor cooperation. We can also study how
small changes in population structure---graph surgery---affect evolutionary
outcomes. We find that cooperation flourishes most in societies that are based
on strong pairwise ties.Comment: 68 pages, 10 figure
Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
Evolutionary game dynamics is one of the most fruitful frameworks for
studying evolution in different disciplines, from Biology to Economics. Within
this context, the approach of choice for many researchers is the so-called
replicator equation, that describes mathematically the idea that those
individuals performing better have more offspring and thus their frequency in
the population grows. While very many interesting results have been obtained
with this equation in the three decades elapsed since it was first proposed, it
is important to realize the limits of its applicability. One particularly
relevant issue in this respect is that of non-mean-field effects, that may
arise from temporal fluctuations or from spatial correlations, both neglected
in the replicator equation. This review discusses these temporal and spatial
effects focusing on the non-trivial modifications they induce when compared to
the outcome of replicator dynamics. Alongside this question, the hypothesis of
linearity and its relation to the choice of the rule for strategy update is
also analyzed. The discussion is presented in terms of the emergence of
cooperation, as one of the current key problems in Biology and in other
disciplines.Comment: Review, 48 pages, 26 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
Asymmetric evolutionary games
Evolutionary game theory is a powerful framework for studying evolution in
populations of interacting individuals. A common assumption in evolutionary
game theory is that interactions are symmetric, which means that the players
are distinguished by only their strategies. In nature, however, the microscopic
interactions between players are nearly always asymmetric due to environmental
effects, differing baseline characteristics, and other possible sources of
heterogeneity. To model these phenomena, we introduce into evolutionary game
theory two broad classes of asymmetric interactions: ecological and genotypic.
Ecological asymmetry results from variation in the environments of the players,
while genotypic asymmetry is a consequence of the players having differing
baseline genotypes. We develop a theory of these forms of asymmetry for games
in structured populations and use the classical social dilemmas, the Prisoner's
Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric
games reveal essential differences between models of genetic evolution based on
reproduction and models of cultural evolution based on imitation that are not
apparent in symmetric games.Comment: accepted for publication in PLOS Comp. Bio
Cooperation with both synergistic and local interactions can be worse than each alone
Cooperation is ubiquitous ranging from multicellular organisms to human
societies. Population structures indicating individuals' limited interaction
ranges are crucial to understand this issue. But it is still at large to what
extend multiple interactions involving nonlinearity in payoff play a role on
cooperation in structured populations. Here we show a rule, which determines
the emergence and stabilization of cooperation, under multiple discounted,
linear, and synergistic interactions. The rule is validated by simulations in
homogenous and heterogenous structured populations. We find that the more
neighbors there are the harder for cooperation to evolve for multiple
interactions with linearity and discounting. For synergistic scenario, however,
distinct from its pairwise counterpart, moderate number of neighbors can be the
worst, indicating that synergistic interactions work with strangers but not
with neighbors. Our results suggest that the combination of different factors
which promotes cooperation alone can be worse than that with every single
factor.Comment: 32 pages, 4 figure
Coevolutionary games - a mini review
Prevalence of cooperation within groups of selfish individuals is puzzling in
that it contradicts with the basic premise of natural selection. Favoring
players with higher fitness, the latter is key for understanding the challenges
faced by cooperators when competing with defectors. Evolutionary game theory
provides a competent theoretical framework for addressing the subtleties of
cooperation in such situations, which are known as social dilemmas. Recent
advances point towards the fact that the evolution of strategies alone may be
insufficient to fully exploit the benefits offered by cooperative behavior.
Indeed, while spatial structure and heterogeneity, for example, have been
recognized as potent promoters of cooperation, coevolutionary rules can extend
the potentials of such entities further, and even more importantly, lead to the
understanding of their emergence. The introduction of coevolutionary rules to
evolutionary games implies, that besides the evolution of strategies, another
property may simultaneously be subject to evolution as well. Coevolutionary
rules may affect the interaction network, the reproduction capability of
players, their reputation, mobility or age. Here we review recent works on
evolutionary games incorporating coevolutionary rules, as well as give a
didactic description of potential pitfalls and misconceptions associated with
the subject. In addition, we briefly outline directions for future research
that we feel are promising, thereby particularly focusing on dynamical effects
of coevolutionary rules on the evolution of cooperation, which are still widely
open to research and thus hold promise of exciting new discoveries.Comment: 24 two-column pages, 10 figures; accepted for publication in
BioSystem
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