Related papers: From Discrete to Continuous Highest-earning Imitat…
We analyze the long term behavior of interacting populations which can be controlled through harvesting. The dynamics is assumed to be discrete in time and stochastic due to the effect of environmental fluctuations. We present extinction…
In many biological processes, the size of a population changes stochastically with time, and recent work in the context of cancer and bacterial growth have focused on the situation when the mean population size grows exponentially. Here,…
Imitation is a key component of human social behavior, and is widely used by both children and adults as a way to navigate uncertain or unfamiliar situations. But in an environment populated by multiple heterogeneous agents pursuing…
We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of…
Despite the huge number of neurons composing a brain network, ongoing activity of local cell assemblies composing cortical columns is intrinsically stochastic. Fluctuations in their instantaneous rate of spike firing $\nu(t)$ scale with the…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of $n$ cities. In the model a fraction $f_{jk}$ of individuals from city $k$ commute to city $j$,…
In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has…
Collective motion in animal groups emerges from the interplay between individual variability and social coordination, yet connecting these scales quantitatively has remained a major challenge.Using high-resolution trajectories of schooling…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Many analyses of resource-allocation problems employ simplistic models of the population. Using the example of a resource-allocation problem of Marecek et al. [arXiv:1406.7639], we introduce rather a general behavioural model, where the…
In the framework of the paradigmatic prisoner's dilemma, we investigate the evolutionary dynamics of social dilemmas in the presence of "cooperation facilitators". In our model, cooperators and defectors interact as in the classical…
Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
We introduce two stochastic chemostat models consisting in a coupled population-nutrient process reflecting the interaction between the nutrient and the bacterias in the chemostat with finite volume. The nutrient concentration evolves…
In the name of meritocracy, modern economies devote increasing amounts of resources to quantifying and ranking the performance of individuals and organisations. Rankings send out powerful signals, which lead to identify the actions of top…
Understanding the evolutionary dynamics of reinforcement learning under multi-agent settings has long remained an open problem. While previous works primarily focus on 2-player games, we consider population games, which model the strategic…
In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of…
Continuous-time empirical dynamic discrete choice games offer notable computational advantages over discrete-time models. This paper addresses remaining computational and econometric challenges to further improve both model solution and…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…