60 research outputs found
Much or More? Experiments of Rationality and Spite with School Children
Copyright © 2014 North American Journal of Pyschology.In a competitive environment the maximization of self-interest and the minimization of the other's interest can be seen as the two faces of the same coin. However, these motivations can lead to very different behaviors. In order to understand how these are expressed, we designed an experiment to measure the ability of children and teenagers to react to stimuli that induce behavior to act as a rational player (maximization of self interest) or as a spiteful player (minimization of other's interest). Each player faced the following dilemma: maximizing pay-off and incurring the risk of having a lower pay-off; or alternatively guaranteeing one’s own pay-off was not smaller than the opponent’s pay-off. A prize was attributed proportionally to the pay-off (Treatment 1) or to the player with highest pay-off (Treatment 2), which meant that the optimal behavior was different for each treatment. We performed experiments with 398 Portuguese children and teenagers and found evidence that younger children tended to be maximizers (in both variants) and that teenagers tended towards rational behavior when it was best for them and towards spiteful behavior when the latter was more advantageous
Cancer phenotype as the outcome of an evolutionary game between normal and malignant cells
There is variability in the cancer phenotype across individuals: two patients with the same tumour may experience different disease life histories, resulting from genetic variation within the tumour and from the interaction between tumour and host. Until now, phenotypic variability has precluded a clear-cut identification of the fundamental characteristics of a given tumour type.Journal ArticleResearch Support, Non-U.S. Gov'tSCOPUS: ar.jinfo:eu-repo/semantics/publishe
Stochastic differential equations for evolutionary dynamics with demographic noise and mutations
We present a general framework to describe the evolutionary dynamics of an
arbitrary number of types in finite populations based on stochastic
differential equations (SDE). For large, but finite populations this allows to
include demographic noise without requiring explicit simulations. Instead, the
population size only rescales the amplitude of the noise. Moreover, this
framework admits the inclusion of mutations between different types, provided
that mutation rates, , are not too small compared to the inverse
population size 1/N. This ensures that all types are almost always represented
in the population and that the occasional extinction of one type does not
result in an extended absence of that type. For this limits the use
of SDE's, but in this case there are well established alternative
approximations based on time scale separation. We illustrate our approach by a
Rock-Scissors-Paper game with mutations, where we demonstrate excellent
agreement with simulation based results for sufficiently large populations. In
the absence of mutations the excellent agreement extends to small population
sizes.Comment: 8 pages, 2 figures, accepted for publication in Physical Review
Mathematical description of bacterial traveling pulses
The Keller-Segel system has been widely proposed as a model for bacterial
waves driven by chemotactic processes. Current experiments on {\em E. coli}
have shown precise structure of traveling pulses. We present here an
alternative mathematical description of traveling pulses at a macroscopic
scale. This modeling task is complemented with numerical simulations in
accordance with the experimental observations. Our model is derived from an
accurate kinetic description of the mesoscopic run-and-tumble process performed
by bacteria. This model can account for recent experimental observations with
{\em E. coli}. Qualitative agreements include the asymmetry of the pulse and
transition in the collective behaviour (clustered motion versus dispersion). In
addition we can capture quantitatively the main characteristics of the pulse
such as the speed and the relative size of tails. This work opens several
experimental and theoretical perspectives. Coefficients at the macroscopic
level are derived from considerations at the cellular scale. For instance the
stiffness of the signal integration process turns out to have a strong effect
on collective motion. Furthermore the bottom-up scaling allows to perform
preliminary mathematical analysis and write efficient numerical schemes. This
model is intended as a predictive tool for the investigation of bacterial
collective motion
Reply: Evolutionary game theory: lessons and limitations, a cancer perspective
SCOPUS: le.jinfo:eu-repo/semantics/publishe
The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations
We study a class of processes that are akin to the Wright-Fisher model, with
transition probabilities weighted in terms of the frequency-dependent fitness
of the population types. By considering an approximate weak formulation of the
discrete problem, we are able to derive a corresponding continuous weak
formulation for the probability density. Therefore, we obtain a family of
partial differential equations (PDE) for the evolution of the probability
density, and which will be an approximation of the discrete process in the
joint large population, small time-steps and weak selection limit. If the
fitness functions are sufficiently regular, we can recast the weak formulation
in a more standard formulation, without any boundary conditions, but
supplemented by a number of conservation laws. The equations in this family can
be purely diffusive, purely hyperbolic or of convection-diffusion type, with
frequency dependent convection. The particular outcome will depend on the
assumed scalings. The diffusive equations are of the degenerate type; using a
duality approach, we also obtain a frequency dependent version of the Kimura
equation without any further assumptions. We also show that the convective
approximation is related to the replicator dynamics and provide some estimate
of how accurate is the convective approximation, with respect to the
convective-diffusion approximation. In particular, we show that the mode, but
not the expected value, of the probability distribution is modelled by the
replicator dynamics. Some numerical simulations that illustrate the results are
also presented
Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq equations
We establish a connection between Optimal Transport Theory and classical
Convection Theory for geophysical flows. Our starting point is the model
designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal
Transport problems. This model can be seen as a generalization of the
Darcy-Boussinesq equations, which is a degenerate version of the
Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate
different variants of the NSB equations (in particular what we call the
generalized Hydrostatic-Boussinesq equations) to various models involving
Optimal Transport (and the related Monge-Ampere equation. This includes the 2D
semi-geostrophic equations and some fully non-linear versions of the so-called
high-field limit of the Vlasov-Poisson system and of the Keller-Segel for
Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model
can be related to the magnetic relaxation model studied by Arnold and Moffatt
to obtain stationary solutions of the Euler equations with prescribed topology
Hamiltonian walks on Sierpinski and n-simplex fractals
We study Hamiltonian walks (HWs) on Sierpinski and --simplex fractals. Via
numerical analysis of exact recursion relations for the number of HWs we
calculate the connectivity constant and find the asymptotic behaviour
of the number of HWs. Depending on whether or not the polymer collapse
transition is possible on a studied lattice, different scaling relations for
the number of HWs are obtained. These relations are in general different from
the well-known form characteristic of homogeneous lattices which has thus far
been assumed to hold for fractal lattices too.Comment: 22 pages, 6 figures; final versio
Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach
Cooperation is of utmost importance to society as a whole, but is often
challenged by individual self-interests. While game theory has studied this
problem extensively, there is little work on interactions within and across
groups with different preferences or beliefs. Yet, people from different social
or cultural backgrounds often meet and interact. This can yield conflict, since
behavior that is considered cooperative by one population might be perceived as
non-cooperative from the viewpoint of another.
To understand the dynamics and outcome of the competitive interactions within
and between groups, we study game-dynamical replicator equations for multiple
populations with incompatible interests and different power (be this due to
different population sizes, material resources, social capital, or other
factors). These equations allow us to address various important questions: For
example, can cooperation in the prisoner's dilemma be promoted, when two
interacting groups have different preferences? Under what conditions can costly
punishment, or other mechanisms, foster the evolution of norms? When does
cooperation fail, leading to antagonistic behavior, conflict, or even
revolutions? And what incentives are needed to reach peaceful agreements
between groups with conflicting interests?
Our detailed quantitative analysis reveals a large variety of interesting
results, which are relevant for society, law and economics, and have
implications for the evolution of language and culture as well
Analytical Results for Individual and Group Selection of Any Intensity
The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (= fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in the limit of weak selection, where the game has a small effect on overall fitness. But this linear function makes the analysis of strong selection difficult. Here, we show that analytical results can be obtained for any intensity of selection, if fitness is defined as an exponential function of payoff. This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory
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