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Evolutionary game dynamics describes not only frequency dependent genetical evolution, but also cultural evolution in humans. In this context, successful strategies spread by imitation. It has been shown that the details of strategy update…
Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties and…
Chemical equilibrium is fully characterized by thermodynamics, while the rates of chemical reactions can be calculated for ideal solutions by using mass-action equations. The evaluation of the rates of reactions in a non-ideal system is…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some…
Recently, an evolutionary game dynamics model taking into account the environmental feedback has been proposed to describe the co-evolution of strategic actions of a population of individuals and the state of the surrounding environment;…
Given a large population of players, each player has three possible choices between option 1 or 2 or no option. The two options are equally favorable and the population has to reach consensus on one of the two options quickly and in a…
We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse…
Response theory provides a pathway for understanding the sensitivity of a system and for predicting how its statistical properties change when a perturbation is applied. In the case of complex and multiscale systems, to achieve enhanced…
We discuss a model for evolutionary game dynamics in a growing, network-structured population. In our model, new players can either make connections to random preexisting players or preferentially attach to those that have been successful…
The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many…
The statistical picture of the solution space for a binary perceptron is studied. The binary perceptron learns a random classification of input random patterns by a set of binary synaptic weights. The learning of this network is difficult…
As mathematical model for the evolutionary equations of species the masterequation is choiced. Two formulations will be demonstrated to include the changes of parameters into the masterequation - that is, on the one hand, the formation of a…
Here we will use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games on $Z^d$, $d\ge 3$ when the interaction kernel is finite range, symmetric, and has covariance matrix $\sigma^2I$. The…
In population games, a large population of players, modeled as a continuum, is divided into subpopulations, and the fitness or payoff of each subpopulation depends on the overall population composition. Evolutionary dynamics describe how…
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
Many real-world systems exhibit ``noisy'' evolution in time; interpreting their finitely-sampled behavior as arising from continuous-time processes (in the It\^o or Stratonovich sense) has led to significant success in modeling and analysis…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…