341 research outputs found
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
An evolutionary game model for behavioral gambit of loyalists: Global awareness and risk-aversion
We study the phase diagram of a minority game where three classes of agents
are present. Two types of agents play a risk-loving game that we model by the
standard Snowdrift Game. The behaviour of the third type of agents is coded by
{\em indifference} w.r.t. the game at all: their dynamics is designed to
account for risk-aversion as an innovative behavioral gambit. From this point
of view, the choice of this solitary strategy is enhanced when innovation
starts, while is depressed when it becomes the majority option. This implies
that the payoff matrix of the game becomes dependent on the global awareness of
the agents measured by the relevance of the population of the indifferent
players. The resulting dynamics is non-trivial with different kinds of phase
transition depending on a few model parameters. The phase diagram is studied on
regular as well as complex networks
If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation
Spatial reciprocity is a well known tour de force of cooperation promotion. A
thorough understanding of the effects of different population densities is
therefore crucial. Here we study the evolution of cooperation in social
dilemmas on different interaction graphs with a certain fraction of vacant
nodes. We find that sparsity may favor the resolution of social dilemmas,
especially if the population density is close to the percolation threshold of
the underlying graph. Regardless of the type of the governing social dilemma as
well as particularities of the interaction graph, we show that under pairwise
imitation the percolation threshold is a universal indicator of how dense the
occupancy ought to be for cooperation to be optimally promoted. We also
demonstrate that myopic updating, due to the lack of efficient spread of
information via imitation, renders the reported mechanism dysfunctional, which
in turn further strengthens its foundations.Comment: 6 two-column pages, 5 figures; accepted for publication in Scientific
Reports [related work available at http://arxiv.org/abs/1205.0541
Aspiration Dynamics of Multi-player Games in Finite Populations
Studying strategy update rules in the framework of evolutionary game theory,
one can differentiate between imitation processes and aspiration-driven
dynamics. In the former case, individuals imitate the strategy of a more
successful peer. In the latter case, individuals adjust their strategies based
on a comparison of their payoffs from the evolutionary game to a value they
aspire, called the level of aspiration. Unlike imitation processes of pairwise
comparison, aspiration-driven updates do not require additional information
about the strategic environment and can thus be interpreted as being more
spontaneous. Recent work has mainly focused on understanding how aspiration
dynamics alter the evolutionary outcome in structured populations. However, the
baseline case for understanding strategy selection is the well-mixed population
case, which is still lacking sufficient understanding. We explore how
aspiration-driven strategy-update dynamics under imperfect rationality
influence the average abundance of a strategy in multi-player evolutionary
games with two strategies. We analytically derive a condition under which a
strategy is more abundant than the other in the weak selection limiting case.
This approach has a long standing history in evolutionary game and is mostly
applied for its mathematical approachability. Hence, we also explore strong
selection numerically, which shows that our weak selection condition is a
robust predictor of the average abundance of a strategy. The condition turns
out to differ from that of a wide class of imitation dynamics, as long as the
game is not dyadic. Therefore a strategy favored under imitation dynamics can
be disfavored under aspiration dynamics. This does not require any population
structure thus highlights the intrinsic difference between imitation and
aspiration dynamics
A generalized public goods game with coupling of individual ability and project benefit
Facing a heavy task, any single person can only make a limited contribution
and team cooperation is needed. As one enjoys the benefit of the public goods,
the potential benefits of the project are not always maximized and may be
partly wasted. By incorporating individual ability and project benefit into the
original public goods game, we study the coupling effect of the four
parameters, the upper limit of individual contribution, the upper limit of
individual benefit, the needed project cost and the upper limit of project
benefit on the evolution of cooperation. Coevolving with the individual-level
group size preferences, an increase in the upper limit of individual benefit
promotes cooperation while an increase in the upper limit of individual
contribution inhibits cooperation. The coupling of the upper limit of
individual contribution and the needed project cost determines the critical
point of the upper limit of project benefit, where the equilibrium frequency of
cooperators reaches its highest level. Above the critical point, an increase in
the upper limit of project benefit inhibits cooperation. The evolution of
cooperation is closely related to the preferred group-size distribution. A
functional relation between the frequency of cooperators and the dominant group
size is found
Coveting thy neighbors fitness as a means to resolve social dilemmas
In spatial evolutionary games the fitness of each individual is traditionally
determined by the payoffs it obtains upon playing the game with its neighbors.
Since defection yields the highest individual benefits, the outlook for
cooperators is gloomy. While network reciprocity promotes collaborative
efforts, chances of averting the impending social decline are slim if the
temptation to defect is strong. It is therefore of interest to identify viable
mechanisms that provide additional support for the evolution of cooperation.
Inspired by the fact that the environment may be just as important as
inheritance for individual development, we introduce a simple switch that
allows a player to either keep its original payoff or use the average payoff of
all its neighbors. Depending on which payoff is higher, the influence of either
option can be tuned by means of a single parameter. We show that, in general,
taking into account the environment promotes cooperation. Yet coveting the
fitness of one's neighbors too strongly is not optimal. In fact, cooperation
thrives best only if the influence of payoffs obtained in the traditional way
is equal to that of the average payoff of the neighborhood. We present results
for the prisoner's dilemma and the snowdrift game, for different levels of
uncertainty governing the strategy adoption process, and for different
neighborhood sizes. Our approach outlines a viable route to increased levels of
cooperative behavior in structured populations, but one that requires a
thoughtful implementation.Comment: 10 two-column pages, 5 figures; accepted for publication in Journal
of Theoretical Biolog
Coevolution of teaching activity promotes cooperation
Evolutionary games are studied where the teaching activity of players can
evolve in time. Initially all players following either the cooperative or
defecting strategy are distributed on a square lattice. The rate of strategy
adoption is determined by the payoff difference and a teaching activity
characterizing the donor's capability to enforce its strategy on the opponent.
Each successful strategy adoption process is accompanied with an increase in
the donor's teaching activity. By applying an optimum value of the increment
this simple mechanism spontaneously creates relevant inhomogeneities in the
teaching activities that support the maintenance of cooperation for both the
prisoner's dilemma and the snowdrift game.Comment: 10 pages, 4 figures; accepted for publication in New Journal of
Physic
Optimal interdependence between networks for the evolution of cooperation
Recent research has identified interactions between networks as crucial for the outcome of evolutionary
games taking place on them. While the consensus is that interdependence does promote cooperation by
means of organizational complexity and enhanced reciprocity that is out of reach on isolated networks, we
here address the question just how much interdependence there should be. Intuitively, one might assume
the more the better. However, we show that in fact only an intermediate density of sufficiently strong
interactions between networks warrants an optimal resolution of social dilemmas. This is due to an intricate
interplay between the heterogeneity that causes an asymmetric strategy flow because of the additional links
between the networks, and the independent formation of cooperative patterns on each individual network.
Presented results are robust to variations of the strategy updating rule, the topology of interdependent
networks, and the governing social dilemma, thus suggesting a high degree of universality
Threshold games and cooperation on multiplayer graphs
Objective: The study investigates the effect on cooperation in multiplayer
games, when the population from which all individuals are drawn is structured -
i.e. when a given individual is only competing with a small subset of the
entire population.
Method: To optimize the focus on multiplayer effects, a class of games were
chosen for which the payoff depends nonlinearly on the number of cooperators -
this ensures that the game cannot be represented as a sum of pair-wise
interactions, and increases the likelihood of observing behaviour different
from that seen in two-player games. The chosen class of games are named
"threshold games", and are defined by a threshold, , which describes the
minimal number of cooperators in a given match required for all the
participants to receive a benefit. The model was studied primarily through
numerical simulations of large populations of individuals, each with
interaction neighbourhoods described by various classes of networks.
Results: When comparing the level of cooperation in a structured population
to the mean-field model, we find that most types of structure lead to a
decrease in cooperation. This is both interesting and novel, simply due to the
generality and breadth of relevance of the model - it is likely that any model
with similar payoff structure exhibits related behaviour.
More importantly, we find that the details of the behaviour depends to a
large extent on the size of the immediate neighbourhoods of the individuals, as
dictated by the network structure. In effect, the players behave as if they are
part of a much smaller, fully mixed, population, which we suggest an expression
for.Comment: in PLOS ONE, 4th Feb 201
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