Related papers: Population games and Discrete optimal transport
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…
We initiate the study of game dynamics in the population protocol model: $n$ agents each maintain a current local strategy and interact in pairs uniformly at random. Upon each interaction, the agents play a two-person game and receive a…
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…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
Evolutionary game dynamics with two 2-strategy games in a finite population has been investigated in this study. Traditionally, frequency-dependent evolutionary dynamics are modeled by deterministic replicator dynamics under the assumption…
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 Mean Field Markov games with $N$ players, in which each individual in a large population interacts with other randomly selected players. The states and actions of each player in an interaction together determine the…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
We study evolutionary games with a continuous trait space in which replicator dynamics are restricted to the manifold of multidimensional Gaussian distributions. We demonstrate that the replicator equations are natural gradient flow for…
This paper is interested in the description of the density of particles evolving according to some optimal policy of an impulse control problem. We first fix sets on which the particles jump and explain how we can characterize such a…
We propose a control-theoretic framework for evolutionary clustering based on Mean Field Games (MFG). Moving beyond static or heuristic approaches, we formulate the problem as a population dynamics game governed by a coupled…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
In this paper we present a new modelling framework combining replicator dynamics (which is the standard model of frequency dependent selection) with the model of an age-structured population. The new framework allows for the modelling of…
Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. Despite the existence of…
We discuss a population of sequences subject to mutations and frequency-dependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand the evolution…
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…
Decision-making by imitating the highest earners has been observed in experimental studies. In two-strategy decision-making problems, this behavior may result in perpetual fluctuations in the population proportions of the two strategies.…
Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended…
We propose a stochastic model in evolutionary game theory where individuals (or subpopulations) can mutate changing their strategies randomly (but rarely) and explore the external environment. This environment affects the selective pressure…