Related papers: The replicator equation in stochastic spatial evol…
Fudenberg and Harris' stochastic version of the classical replicator dynamics is considered. The behavior of this diffusion process in the presence of an evolutionarily stable strategy is investigated. Moreover, extinction of dominated…
We study adaptive dynamics in games where players abandon the population at a given rate, and are replaced by naive players characterized by a prior distribution over the admitted strategies. We demonstrate how such process leads…
The probability that the frequency of a particular trait will eventually become unity, the so-called fixation probability, is a central issue in the study of population evolution. Its computation, once we are given a stochastic finite…
In this work we propose a kinetic formulation for evolutionary game theory for zero sum games when the agents use mixed strategies. We start with a simple adaptive rule, where after an encounter each agent increases the probability of play…
Game theory deals with strategic interactions among players and evolutionary game dynamics tracks the fate of the players' populations under selection. In this paper, we consider the replicator equation for two-player-two-strategy games…
We adapt a fitness function from evolutionary game theory as a mechanism for aggregation and dispersal in a partial differential equation (PDE) model of two interacting populations, described by density functions $u$ and $v$. We consider a…
We propose a simple model of network co-evolution in a game-dynamical system of interacting agents that play repeated games with their neighbors, and adapt their behaviors and network links based on the outcome of those games. The…
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 investigate the evolution of cooperation on a non - growth network model with death/birth dynamics. Nodes reproduce under selection for higher payoffs in a prisoners dilemma game played between network neighbours. The mean field…
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 theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two…
We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…
We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its…
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.…
A stochastic evolutionary dynamics of two strategies given by 2 x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire…
Studying strategy update rules in the framework of evolutionary game theory, one can differentiate between imitation processes and aspiration-driven dynamics. In the former case, individuals imitate the strategy of a more successful peer.…
The replicator equation in evolutionary game theory describes the change in a population's behaviors over time given suitable incentives. It arises when individuals make decisions using a simple learning process - imitation. A recent…
We establish a theoretical framework to address evolutionary dynamics of spatial games under strong selection. As the selection intensity tends to infinity, strategy competition unfolds in the deterministic way of winners taking all. We…
Replicator dynamics, the continuous-time analogue of Multiplicative Weights Updates, is the main dynamic in evolutionary game theory. In simple evolutionary zero-sum games, such as Rock-Paper-Scissors, replicator dynamic is periodic…
A partial differential equation is derived, describing the replicator dynamics with mutations of games with a continuous strategy space. This equation is then applied to continuous versions of symmetric 2x2 games, such as the Prisoners…