30,566 research outputs found
Evolutionary Multiplayer Games
Evolutionary game theory has become one of the most diverse and far reaching
theories in biology. Applications of this theory range from cell dynamics to
social evolution. However, many applications make it clear that inherent
non-linearities of natural systems need to be taken into account. One way of
introducing such non-linearities into evolutionary games is by the inclusion of
multiple players. An example is of social dilemmas, where group benefits could
e.g.\ increase less than linear with the number of cooperators. Such
multiplayer games can be introduced in all the fields where evolutionary game
theory is already well established. However, the inclusion of non-linearities
can help to advance the analysis of systems which are known to be complex, e.g.
in the case of non-Mendelian inheritance. We review the diachronic theory and
applications of multiplayer evolutionary games and present the current state of
the field. Our aim is a summary of the theoretical results from well-mixed
populations in infinite as well as finite populations. We also discuss examples
from three fields where the theory has been successfully applied, ecology,
social sciences and population genetics. In closing, we probe certain future
directions which can be explored using the complexity of multiplayer games
while preserving the promise of simplicity of evolutionary games.Comment: 14 pages, 2 figures, review pape
Evolutionary Games with Affine Fitness Functions: Applications to Cancer
We analyze the dynamics of evolutionary games in which fitness is defined as
an affine function of the expected payoff and a constant contribution. The
resulting inhomogeneous replicator equation has an homogeneous equivalent with
modified payoffs. The affine terms also influence the stochastic dynamics of a
two-strategy Moran model of a finite population. We then apply the affine
fitness function in a model for tumor-normal cell interactions to determine
which are the most successful tumor strategies. In order to analyze the
dynamics of concurrent strategies within a tumor population, we extend the
model to a three-strategy game involving distinct tumor cell types as well as
normal cells. In this model, interaction with normal cells, in combination with
an increased constant fitness, is the most effective way of establishing a
population of tumor cells in normal tissue.Comment: The final publication is available at http://www.springerlink.com,
http://dx.doi.org/10.1007/s13235-011-0029-
Fixation and escape times in stochastic game learning
Evolutionary dynamics in finite populations is known to fixate eventually in
the absence of mutation. We here show that a similar phenomenon can be found in
stochastic game dynamical batch learning, and investigate fixation in learning
processes in a simple 2x2 game, for two-player games with cyclic interaction,
and in the context of the best-shot network game. The analogues of finite
populations in evolution are here finite batches of observations between
strategy updates. We study when and how such fixation can occur, and present
results on the average time-to-fixation from numerical simulations. Simple
cases are also amenable to analytical approaches and we provide estimates of
the behaviour of so-called escape times as a function of the batch size. The
differences and similarities with escape and fixation in evolutionary dynamics
are discussed.Comment: 19 pages, 9 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 dynamics, intrinsic noise and cycles of co-operation
We use analytical techniques based on an expansion in the inverse system size
to study the stochastic evolutionary dynamics of finite populations of players
interacting in a repeated prisoner's dilemma game. We show that a mechanism of
amplification of demographic noise can give rise to coherent oscillations in
parameter regimes where deterministic descriptions converge to fixed points
with complex eigenvalues. These quasi-cycles between co-operation and defection
have previously been observed in computer simulations; here we provide a
systematic and comprehensive analytical characterization of their properties.
We are able to predict their power spectra as a function of the mutation rate
and other model parameters, and to compare the relative magnitude of the cycles
induced by different types of underlying microscopic dynamics. We also extend
our analysis to the iterated prisoner's dilemma game with a win-stay lose-shift
strategy, appropriate in situations where players are subject to errors of the
trembling-hand type.Comment: 14 pages, 12 figures, accepted for publication by Phys. Rev.
Multigame Effect in Finite Populations Induces Strategy Linkage Between Two Games
Evolutionary game dynamics with two 2-strategy games in a finite population
has been investigated in this study. Traditionally, frequency-dependent
evolutionary dynamics are modeled by deterministic replicator dynamics under
the assumption that the population size is infinite. However, in reality,
population sizes are finite. Recently, stochastic processes in finite
populations have been introduced into evolutionary games in order to study
finite size effects in evolutionary game dynamics. However, most of these
studies focus on populations playing only single games. In this study, we
investigate a finite population with two games and show that a finite
population playing two games tends to evolve toward a specific direction to
form particular linkages between the strategies of the two games
Evolutionary prisoner's dilemma game with dynamic preferential selection
We study a modified prisoner's dilemma game taking place on two-dimensional
disordered square lattices. The players are pure strategists and can either
cooperate or defect with their immediate neighbors. In the generations each
player update its strategy by following one of the neighboring strategies with
a probability dependent on the payoff difference. The neighbor selection obeys
a dynamic preferential rule, i.e., the more frequently a neighbor's strategy
was adopted by the focal player in the previous rounds, the larger probability
it will be chosen to refer to in the subsequent rounds. It is found that
cooperation is substantially promoted due to this simple selection mechanism.
Corresponding analysis is provided by the investigations of the distribution of
players' impact weights, persistence, and as well as correlation function.Comment: 7 pages, 5 figure
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