Discrete replicator dynamics view evolution as a coordination game played among genes. While previous models of discrete replicator dynamics do not consider environments that respond to the mixed strategy that a population plays, our model incorporates a feedbackbased payoff matrix, which depends on the frequency distribution of alleles. In this model, we construct an environment that is compos...

A deterministic learning model applied to a game with multiple equilibria produces distinct basins of attraction for those equilibria. In symmetric two-by-two games, basins of attraction are invariant to a wide range of learning rules including best response dynamics, replicator dynamics, and fictitious play. In this paper, we construct a class of three-by-three symmetric games for which the ov...

Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is modeled by a continuous time Markov chain in a finite atom space. We establish conditions for this dynamic to have an analogous characterization of the long-run b...

We discuss a simple version of the Minority Game (MG) in which agents hold only one strategy each, but in which their capitals evolve dynamically according to their success and in which the total trading volume varies in time accordingly. This feature is known to be crucial for MGs to reproduce stylised facts of real market data. The stationary states and phase diagram of the model can be compu...

1 Abstract In this paper is presented the new modelling framework combining the repli-cator dynamics (which is the standard model of the frequency dependent selection) with the Leslie Matrix model of the age-structured population. Firstly the continuous version of the discrete Leslie Matrix model is derived. It is shown that Euler–Lotka equation is satisfied when new model reaches the steady st...

In this study we present an extension of the dynamics of diffusion in multiplex graphs, which makes the equations compatible with the replicator equation with mutations. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to account for nonlinear terms when working with fractions of individuals. We also derive the...

Evolutionary game theory combines game theory and dynamical systems and is customarily adopted to describe evolutionary dynamics in multi–agent systems. In particular, it has been proven to be a successful tool to describe multi–agent learning dynamics. To the best of our knowledge, we provide in this paper the first replicator dynamics applicable to the sequence form of an extensive–form game,...