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We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths…
We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three…
Evolutionary game dynamics with two 2-strategy games in a finite population has been investigated in this study. Traditionally, frequency-dependent evolutionary dynamics are modeled by deterministic replicator dynamics under the assumption…
In this paper, we formulate a finite population variation of the Fisher-KPP equation using the fact that the reaction term can be generated from the replicator dynamic using a two-player two-strategy skew-symmetric game. We use prior…
Finite and infinite population models are frequently used in population dynamics. However, their interrelationship is rarely discussed. In this work, we examine the limits of large populations of the Moran process (a finite-population…
Evolutionary game dynamics in finite populations is typically subject to noise, inducing effects which are not present in deterministic systems, including fixation and extinction. In the first part of this paper we investigate the…
Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time…
This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…
A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
Many models of population dynamics are formulated as deterministic iterated maps although real populations are stochastic. This is justifiable in the limit of large population sizes, as the stochastic fluctuations are negligible then.…
We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two…
Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…
We study the influence of stochastic effects due to finite population size in the evolutionary dynamics of populations interacting in the multi-person Prisoner's Dilemma game. This paper is an extension of the investigation presented in a…
People tend to align their use of language to the linguistic behaviour of their own ingroup and to simultaneously diverge from the language use of outgroups. This paper proposes to model this phenomenon of sociolinguistic identity…
The tragedy of the commons (TOC) is an unfortunate situation where a shared resource is exhausted due to uncontrolled exploitation by the selfish individuals of a population. Recently, the paradigmatic replicator equation has been used in…
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…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…