Related papers: Nonlinear Dynamics of the Rock-Paper-Scissors Game…
We model evolution according to an asymmetric game as occurring in multiple finite populations, one for each role in the game, and study the effect of subjecting individuals to stochastic strategy mutations. We show that, when these…
We study evolutionary multi-player games in finite populations, subject to fluctuating environments. The population undergoes a birth-death process with absorbing states, and the environment follows a Markovian process, resulting in a…
Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The…
Cooperators benefit others with paying costs. Evolution of cooperation crucially depends on the cost-benefit ratio of cooperation, denoted as $c$. In this work, we investigate the infinitely repeated prisoner's dilemma for various values of…
We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their…
This paper is concerned with the death-birth updating process. This model is an example of a spatial game in which players located on the~$d$-dimensional integer lattice are characterized by one of two possible strategies and update their…
Antipredator behaviour is a self-preservation strategy present in many biological systems, where individuals join the effort in a collective reaction to avoid being caught by an approaching predator. We study a nonhierarchical tritrophic…
Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns…
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.…
A simple model of cyclically competing species on a directed graph with quenched disorder is proposed as an extension of the rock-paper-scissors model. By assuming that the effects of loops in a directed random graph can be ignored in the…
In an iterated non-cooperative game, if all the players act to maximize their individual accumulated payoff, the system as a whole usually converges to a Nash equilibrium that poorly benefits any player. Here we show that such an…
In this paper, we study analytically the statistics of the number of equilibria in pairwise social dilemma evolutionary games with mutation where a game's payoff entries are random variables. Using the replicator-mutator equations, we…
Recent developments of eco-evolutionary models have shown that evolving feedbacks between behavioral strategies and the environment of game interactions, leading to changes in the underlying payoff matrix, can impact the underlying…
We consider two-player combinatorial games in which the graph of positions is random and perhaps infinite, focusing on directed Galton-Watson trees. As the offspring distribution is varied, a game can undergo a phase transition, in which…
We are interested in the convergence of the value of n-stage games as n goes to infinity and the existence of the uniform value in stochastic games with a general set of states and finite sets of actions where the transition is commutative.…
We study a class of algebras we regard as generalized Rock-Paper-Scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by hypertournament algebras, count these algebras, study…
We provide a classification of symmetric three-player games with two strategies and investigate evolutionary and asymptotic stability (in the replicator dynamics) of their Nash equilibria. We discuss similarities and differences between…
We study agents on a network playing an iterated Prisoner's dilemma against their neighbors. The resulting spatially extended co-evolutionary game exhibits stationary states which are Nash equilibria. After perturbation of these equilibria,…
The predominant paradigm in evolutionary game theory and more generally online learning in games is based on a clear distinction between a population of dynamic agents that interact given a fixed, static game. In this paper, we move away…
We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the…