Related papers: A note on the consensus time of mean-field majorit…
For some models of relevance in the social sciences we review some examples in which system size plays an important role in the final outcome of the dynamics. We discuss the conditions under which changes of behavior can appear only when…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…
We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant…
Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a…
A general model of opinion dynamics is introduced in which each individual's opinion is measured on a bounded continuous spectrum. Each opinion is influenced heterogeneously by every other opinion in the population. It is demonstrated that…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
We study settings in which agents with incomplete preferences need to make a collective decision. We focus on a process of majority dynamics where issues are addressed one at a time and undecided agents follow the opinion of the majority.…
In this paper, we study opinion dynamics in a balanced social structure consisting of two groups. Agents learn the true state of the world naively learning from their neighbors and from an unbiased source of information. Agents want to…
We study a model for social influence in which the agents' opinion is a continuous variable [G. Weisbuch et al., Complexity \textbf{7}, 2, 55 (2002)]. The convergent opinion adjustment process takes place as a result of random binary…
We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…
In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…
When people collaborate, they expect more in return than a simple sum of their efforts. This observation is at the heart of the so-called public goods game, where the participants' contributions are multiplied by an $r$ synergy factor…
This study investigates how the majority group influences individual judgment formation and expression in anonymous, spontaneous online conversations. Drawing on theories of social conformity and anti-conformity, we analyze everyday…
We developed a statistical mechanics approach to the problem of opinion formation in interacting agents, constrained by a set of social rules, $B$. To provide the agents with an adaptive quality, we represented both the social agents and…
The modelling of evolutionary game dynamics in finite populations requires microscopic processes that determine how strategies spread. The exact details of these processes are often chosen without much further consideration. Different types…