Related papers: Oscillatory equilibrium in asymmetric evolutionary…
We study the evolutionary robustness of strategies in infinitely repeated prisoners' dilemma games in which players make mistakes with a small probability and are patient. The evolutionary process we consider is given by the replicator…
Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to…
With the growing number of discovered exoplanets, the Gaia concept finds its second wind. The Gaia concept defines that the biosphere of an inhabited planet regulates a planetary climate through feedback loops such that the planet remains…
A system made up of N interacting species is considered. Self-reaction terms are assumed of the logistic type. Pairwise interactions take place among species according to different modalities, thus yielding a complex asymmetric disordered…
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…
We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…
Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We…
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,…
Mating preferences of many biological species are not constant but season-dependent. Within the framework of evolutionary game theory this can be modeled with two finite opposite-sex populations playing against each other following the…
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…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
Here, we address the essential question of whether, in the context of evolving populations, ecosystems attain properties that enable persistence of the ecosystem itself. We use a simple ecosystem model describing resource, producer, and…
In this paper, we discover that the class of random polynomials arising from the equilibrium analysis of random asymmetric evolutionary games is \textit{exactly} the Kostlan-Shub-Smale system of random polynomials, revealing an intriguing…
Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two…
In this paper, we examine the long-run behavior of regularized, no-regret learning in finite games. A well-known result in the field states that the empirical frequencies of no-regret play converge to the game's set of coarse correlated…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
How coperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model…
We consider a model of cultural evolution for a strategy selection in a population of individuals who interact in a game theoretic framework. The evolution combines individual learning of the environment (population strategy profile),…
In this paper, we focus on studying the passivity properties of different versions of replicator dynamics (RD). RD is an important class of evolutionary dynamics in evolutionary game theory. Evolutionary dynamics describe how the population…