Related papers: A general classification of the replication dynami…
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…
Evolutionary game dynamics are often studied in the context of different population structures. Here we propose a new population structure that is inspired by simple multicellular life forms. In our model, cells reproduce but can stay…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
The well-known replicator equation in evolutionary game theory describes how population-level behaviors change over time when individuals make decisions using simple imitation learning rules. In this paper, we study evolutionary dynamics…
Selection in a time-periodic environment is modeled via the two-player replicator dynamics. For sufficiently fast environmental changes, this is reduced to a multi-player replicator dynamics in a constant environment. The two-player terms…
In this paper, we study four-strategy conservative replicator dynamics induced by constant payoff matrices. We establish necessary and sufficient conditions for permanence to occur by associating the payoff matrix with its digraph,…
To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the…
We consider ordinary differential equations on the unit simplex of $\RR^n$ that naturally occur in population games, models of learning and self reinforced random processes. Generalizing and relying on an idea introduced in \cite{DF11}, we…
Evolutionary game theory has proved to be a powerful tool to probe the self-organisation of collective behaviour by considering frequency-dependent fitness in evolutionary processes. It has shown that the stability of a strategy depends not…
We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial,…
We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed…
Replicator dynamics have been widely used in evolutionary game theory to model how strategy frequencies evolve over time in large populations. The so-called payoff matrix encodes the pairwise fitness that each strategy obtains when…
Replicator equation -- a paradigm equation in evolutionary game dynamics -- mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the…
To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite…
The paper contains the attempt to integration of the classical evolutionary game theory based on replicator dynamics and the state based approach of Houston and Mcnamara. In the new approach, individuals have different heritable strategies,…
Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can be found in stochastic game dynamical batch learning, and investigate fixation in learning…
A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire…
In social situations with which evolutionary game is concerned, individuals are considered to be heterogeneous in various aspects. In particular, they may differently perceive the same outcome of the game owing to heterogeneity in…
In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or…
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…