401,511 research outputs found
Evolutionary Game Dynamics for Two Interacting Populations under Environmental Feedback
We study the evolutionary dynamics of games under environmental feedback
using replicator equations for two interacting populations. One key feature is
to consider jointly the co-evolution of the dynamic payoff matrices and the
state of the environment: the payoff matrix varies with the changing
environment and at the same time, the state of the environment is affected
indirectly by the changing payoff matrix through the evolving population
profiles. For such co-evolutionary dynamics, we investigate whether convergence
will take place, and if so, how. In particular, we identify the scenarios where
oscillation offers the best predictions of long-run behavior by using
reversible system theory. The obtained results are useful to describe the
evolution of multi-community societies in which individuals' payoffs and
societal feedback interact.Comment: 7 pages, submitted to a conferenc
Comparing reactive and memory-one strategies of direct reciprocity
Direct reciprocity is a mechanism for the evolution of cooperation based on
repeated interactions. When individuals meet repeatedly, they can use
conditional strategies to enforce cooperative outcomes that would not be
feasible in one-shot social dilemmas. Direct reciprocity requires that
individuals keep track of their past interactions and find the right response.
However, there are natural bounds on strategic complexity: Humans find it
difficult to remember past interactions accurately, especially over long
timespans. Given these limitations, it is natural to ask how complex strategies
need to be for cooperation to evolve. Here, we study stochastic evolutionary
game dynamics in finite populations to systematically compare the evolutionary
performance of reactive strategies, which only respond to the co-player's
previous move, and memory-one strategies, which take into account the own and
the co-player's previous move. In both cases, we compare deterministic strategy
and stochastic strategy spaces. For reactive strategies and small costs, we
find that stochasticity benefits cooperation, because it allows for
generous-tit-for-tat. For memory one strategies and small costs, we find that
stochasticity does not increase the propensity for cooperation, because the
deterministic rule of win-stay, lose-shift works best. For memory one
strategies and large costs, however, stochasticity can augment cooperation.Comment: 18 pages, 7 figure
Promotion of cooperation induced by the interplay between structure and game dynamics
We consider the coupled dynamics of the adaption of network structure and the
evolution of strategies played by individuals occupying the network vertices.
We propose a computational model in which each agent plays a -round
Prisoner's Dilemma game with its immediate neighbors, after that, based upon
self-interest, partial individuals may punish their defective neighbors by
dismissing the social tie to the one who defects the most times, meanwhile seek
for a new partner at random from the neighbors of the punished agent. It is
found that the promotion of cooperation is attributed to the entangled
evolution of individual strategy and network structure. Moreover, we show that
the emerging social networks exhibit high heterogeneity and disassortative
mixing pattern. For a given average connectivity of the population and the
number of rounds, there is a critical value for the fraction of individuals
adapting their social interactions, above which cooperators wipe out defectors.
Besides, the effects of the average degree, the number of rounds, and the
intensity of selection are investigated by extensive numerical simulations. Our
results to some extent reflect the underlying mechanism promoting cooperation.Comment: 13 pages, 6 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 of cooperation on interdependent networks with Prisoner's Dilemma and Snowdrift Game
The world in which we are living is a huge network of networks and should be
described by interdependent networks. The interdependence between networks
significantly affects the evolutionary dynamics of cooperation on them.
Meanwhile, due to the diversity and complexity of social and biological
systems, players on different networks may not interact with each other by the
same way, which should be described by multiple models in evolutionary game
theory, such as the Prisoner's Dilemma and Snowdrift Game. We therefore study
the evolutionary dynamics of cooperation on two interdependent networks playing
different games respectively. We clearly evidence that, with the increment of
network interdependence, the evolution of cooperation is dramatically promoted
on the network playing Prisoner's Dilemma. The cooperation level of the network
playing Snowdrift Game reduces correspondingly, although it is almost
invisible. In particular, there exists an optimal intermediate region of
network interdependence maximizing the growth rate of the evolution of
cooperation on the network playing Prisoner's Dilemma. Remarkably, players
contacting with other network have advantage in the evolution of cooperation
than the others on the same network.Comment: 6 pages, 6 figure
Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations
Finite-size fluctuations in coevolutionary dynamics arise in models of
biological as well as of social and economic systems. This brief tutorial
review surveys a systematic approach starting from a stochastic process
discrete both in time and state. The limit of an infinite
population can be considered explicitly, generally leading to a replicator-type
equation in zero order, and to a Fokker-Planck-type equation in first order in
. Consequences and relations to some previous approaches are
outlined.Comment: Banach Center publications, in pres
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