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The concept of evolutionarily stability and its relation with the fixed points of the replicator equation are important aspects of evolutionary game dynamics. In the light of the fact that oscillating state of a population and individuals…
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…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
We use the indirect evolutionary approach to study evolutionarily stable preferences against multiple mutations in single- and multi-population matching settings, respectively. Players choose strategies to maximize their subjective…
Evolutionarily stable strategy (ESS) is the defining concept of evolutionary game theory. It has a fairly unanimously accepted definition for the case of symmetric games which are played in a homogeneous population where all individuals are…
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…
Animal behavior and evolution can often be described by game-theoretic models. Although in many situations, the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only…
Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a…
We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical…
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…
Discrete-time replicator map is a prototype of evolutionary selection game dynamical models that have been very successful across disciplines in rendering insights into the attainment of the equilibrium outcomes, like the Nash equilibrium…
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…
The analysis of equilibrium points in random games has been of great interest in evolutionary game theory, with important implications for understanding of complexity in a dynamical system, such as its behavioural, cultural or biological…
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…
Applying the concepts and formalisms from Evolutionary Game Theory to the data regime, the fundamental paradigms of Evolutionary Data Theory are introduced. Interpreting data in matrix form as evolutionary entities, input data is mapped to…
Evolutionary game theory has been a successful tool to combine classical game theory with learning-dynamical descriptions in multiagent systems. Provided some symmetric structures of interacting players, many studies have been focused on…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
Recently, the eco-evolutionary game theory which describes the coupled dynamics of strategies and environment have attracted great attention. At the same time, most of the current work is focused on the classic two-player two-strategy game.…
Evolutionary game theory classically investigates which behavioral patterns are evolutionarily successful in a single game. More recently, a number of contributions have studied the evolution of preferences instead: which subjective…
The best-response dynamics is an example of an evolutionary game where players update their strategy in order to maximize their payoff. The main objective of this paper is to study a stochastic spatial version of this game based on the…