Related papers: Mean-potential law in evolutionary games

We study an atomic signaling game under stochastic evolutionary dynamics. There is a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with…

In this paper, we formulate an evolutionary multiple access channel game with continuous-variable actions and coupled rate constraints. We characterize Nash equilibria of the game and show that the pure Nash equilibria are Pareto optimal…

The study of the density evolution naturally arises in Mean Field Game theory for the estimation of the density of the large population dynamics. In this paper, we study the density evolution of McKean-Vlasov stochastic differential…

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We…

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…

Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…

We study the population genetics of Evolution in the important special case of weak selection, in which all fitness values are assumed to be close to one another. We show that in this regime natural selection is tantamount to the…

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…

Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…

Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…

We study stochastic mean-field games among finite number of teams with large finite as well as infinite number of decision makers. For this class of games within static and dynamic settings, we establish the existence of a Nash equilibrium,…

We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…

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 review, we summarize recent developments in stochastic evolutionary game dynamics of finite populations.

In [12] we formulated an evolutionary game theory model as a dynamical system on the state space of finite signed Borel measures under the weak* topology. The focus of this paper is to extend the analysis to include the long-time behavior…

Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This…

Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…

Studying continuous time counterpart of some discrete time dynamics is now a standard and fruitful technique, as some properties hold in both setups. In game theory, this is usually done by considering differential games on Euclidean…

We analyze the stability of a nonlinear dynamical model describing the noncooperative strategic interactions among the agents of a finite collection of populations. Each agent selects one strategy at a time and revises it repeatedly…

With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…