Related papers: The long-run behavior of the stochastic replicator…
In this letter, we study distributed optimization and Nash equilibrium-seeking dynamics from a contraction theoretic perspective. Our first result is a novel bound on the logarithmic norm of saddle matrices. Second, for distributed gradient…
Evolutionarily Stable Strategy (ESS) in classical game theory is a refinement of Nash equilibrium concept. We investigate the consequences when a small group of mutants using quantum strategies try to invade a classical ESS in a population…
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…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and…
Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a…
In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
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…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
An ab-initio numerical study of the density-dependent, evolutionary stable dispersal strategy is presented. The simulations are based on a simple discretei generation island model with four processes: reproduction, dispersal, competition…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
The replicator equation is a simple model of evolution that leads to stable form of Nash Equilibrium, Evolutionary Stable Strategy (ESS). It has been studied in connection with Evolutionary Game Theory and was originally developed for…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…
Distributed strategic learning has been getting attention in recent years. As systems become distributed finding Nash equilibria in a distributed fashion is becoming more important for various applications. In this paper, we develop 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…
In this paper, we examine the Nash equilibrium convergence properties of no-regret learning in general N-player games. For concreteness, we focus on the archetypal follow the regularized leader (FTRL) family of algorithms, and we consider…
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…
Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning…