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, $\mu$, 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 $\mu N\ll1$ 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 $n$--simplex fractals. Via numerical analysis of exact recursion relations for the number of HWs we calculate the connectivity constant $\omega$ 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