2,416 research outputs found
Time averages, recurrence and transience in the stochastic replicator dynamics
We investigate the long-run behavior of a stochastic replicator process,
which describes game dynamics for a symmetric two-player game under aggregate
shocks. We establish an averaging principle that relates time averages of the
process and Nash equilibria of a suitably modified game. Furthermore, a
sufficient condition for transience is given in terms of mixed equilibria and
definiteness of the payoff matrix. We also present necessary and sufficient
conditions for stochastic stability of pure equilibria.Comment: Published in at http://dx.doi.org/10.1214/08-AAP577 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Mobility and asymmetry effects in one-dimensional rock-paper-scissors games
As the behavior of a system composed of cyclically competing species is
strongly influenced by the presence of fluctuations, it is of interest to study
cyclic dominance in low dimensions where these effects are the most prominent.
We here discuss rock-paper-scissors games on a one-dimensional lattice where
the interaction rates and the mobility can be species dependent. Allowing only
single site occupation, we realize mobility by exchanging individuals of
different species. When the interaction and swapping rates are symmetric, a
strongly enhanced swapping rate yields an increased mixing of the species,
leading to a mean-field like coexistence even in one-dimensional systems. This
coexistence is transient when the rates are asymmetric, and eventually only one
species will survive. Interestingly, in our spatial games the dominating
species can differ from the species that would dominate in the corresponding
nonspatial model. We identify different regimes in the parameter space and
construct the corresponding dynamical phase diagram.Comment: 6 pages, 5 figures, to appear in Physical Review
Enhancement of cooperation in highly clustered scale-free networks
We study the effect of clustering on the organization of cooperation, by
analyzing the evolutionary dynamics of the Prisoner's Dilemma on scale-free
networks with a tunable value of clustering. We find that a high value of the
clustering coefficient produces an overall enhancement of cooperation in the
network, even for a very high temptation to defect. On the other hand, high
clustering homogeneizes the process of invasion of degree classes by defectors,
decreasing the chances of survival of low densities of cooperator strategists
in the network.Comment: 4 pages, 3 figure
Panama "Barro Blancho" case report
The case study report presents the results of the Barro Blanco case study by combining and elaborating on information and data collected during a pre-study report and data and insights gathered during field research. It analyzes the case study according to international human rights standards and applicable institutional safeguards. It also investigates to which extent public owners/shareholders of development banks can be heal responsible for the implementation of climate projects
The Dynamics of Asymmetric Games
A game dynamical analysis of a simple asymmetric game (two roles with two alternatives each) shows that an interesting class of "semi-stable" heteroclinic cycles leading to a highly unpredictable behavior can occur in a robust way. Biological examples related to conflicts over ownership and parental investment are analyzed
Resonance bifurcations from robust homoclinic cycles
We present two calculations for a class of robust homoclinic cycles with
symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic
stability given by Krupa and Melbourne are not optimal.
Firstly, we compute optimal conditions for asymptotic stability using
transition matrix techniques which make explicit use of the geometry of the
group action.
Secondly, through an explicit computation of the global parts of the Poincare
map near the cycle we show that, generically, the resonance bifurcations from
the cycles are supercritical: a unique branch of asymptotically stable period
orbits emerges from the resonance bifurcation and exists for coefficient values
where the cycle has lost stability. This calculation is the first to explicitly
compute the criticality of a resonance bifurcation, and answers a conjecture of
Field and Swift in a particular limiting case. Moreover, we are able to obtain
an asymptotically-correct analytic expression for the period of the bifurcating
orbit, with no adjustable parameters, which has not proved possible previously.
We show that the asymptotic analysis compares very favourably with numerical
results.Comment: 24 pages, 3 figures, submitted to Nonlinearit
Aspiring to the fittest and promotion of cooperation in the prisoner's dilemma game
Strategy changes are an essential part of evolutionary games. Here we
introduce a simple rule that, depending on the value of a single parameter ,
influences the selection of players that are considered as potential sources of
the new strategy. For positive players with high payoffs will be considered
more likely, while for negative the opposite holds. Setting equal to
zero returns the frequently adopted random selection of the opponent. We find
that increasing the probability of adopting the strategy from the fittest
player within reach, i.e. setting positive, promotes the evolution of
cooperation. The robustness of this observation is tested against different
levels of uncertainty in the strategy adoption process and for different
interaction network. Since the evolution to widespread defection is tightly
associated with cooperators having a lower fitness than defectors, the fact
that positive values of facilitate cooperation is quite surprising. We show
that the results can be explained by means of a negative feedback effect that
increases the vulnerability of defectors although initially increasing their
survivability. Moreover, we demonstrate that the introduction of
effectively alters the interaction network and thus also the impact of
uncertainty by strategy adoptions on the evolution of cooperation.Comment: 7 two-column pages, 5 figures; accepted for publication in Physical
Review
Restricted connections among distinguished players support cooperation
We study the evolution of cooperation within the spatial prisoner's dilemma
game on a square lattice where a fraction of players can spread their
strategy more easily than the rest due to a predetermined larger teaching
capability. In addition, players characterized with the larger teaching
capability are allowed to temporarily link with distant opponents of the same
kind with probability , thus introducing shortcut connections among the
distinguished. We show that these additional temporary connections are able to
sustain cooperation throughout the whole range of the temptation to defect.
Remarkably, we observe that as the temptation to defect increases the optimal
decreases, and moreover, only minute values of warrant the best
promotion of cooperation. Our study thus indicates that influential individuals
must be few and sparsely connected in order for cooperation to thrive in a
defection prone environment.Comment: 6 two-column pages, 6 figures; accepted for publication in Physical
Review
Selection of dynamical rules in spatial Prisoner's Dilemma games
We study co-evolutionary Prisoner's Dilemma games where each player can
imitate both the strategy and imitation rule from a randomly chosen neighbor
with a probability dependent on the payoff difference when the player's income
is collected from games with the neighbors. The players, located on the sites
of a two-dimensional lattice, follow unconditional cooperation or defection and
use individual strategy adoption rule described by a parameter. If the system
is started from a random initial state then the present co-evolutionary rule
drives the system towards a state where only one evolutionary rule remains
alive even in the coexistence of cooperative and defective behaviors. The final
rule is related to the optimum providing the highest level of cooperation and
affected by the topology of the connectivity structure.Comment: 5 two-column pages, 3 figure
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