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While generic competitive systems exhibit mixtures of hierarchy and cycles, real-world systems are predominantly hierarchical. We demonstrate and extend a mechanism for hierarchy; systems with similar agents approach perfect hierarchy in…
The time-dependent probability density function of a system evolving towards a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex. The frequencies \omega_n, with which…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
We present numerical simulations of a model of social influence, where the opinion of each agent is represented by a binary vector. Agents adjust their opinions as a result of random encounters, whenever the difference between opinions is…
We propose a minimal off-lattice model of living organisms where just a very few dynamical rules of growth are assumed. The stable coexistence of many clusters is detected when we replace the global restriction rule by a locally applied…
We model a dynamic public good contribution game, where players are (naturally) formed into groups. The groups are exogenously placed in a sequence, with limited information available to players about their groups' position in the sequence.…
Many classical models of collective behavior assume that emergent dynamics result from external and observable interactions among individuals. However, how collective dynamics in human populations depend on the internal psychological…
We investigate a social system of agents faced with a binary choice. We assume there is a correct, or beneficial, outcome of this choice. Furthermore, we assume agents are influenced by others in making their decision, and that the agents…
We present a theory which describes a recently introduced model of an evolving, adaptive system in which agents compete to be in the minority. The agents themselves are able to evolve their strategies over time in an attempt to improve…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
We analyse a generalisation of the Galam model of binary opinion dynamics in which iterative discussions take place in local groups of individuals and study the effects of random deviations from the group majority. The probability of a…
When a prediction algorithm serves a collection of users, disparities in prediction quality are likely to emerge. If users respond to accurate predictions by increasing engagement, inviting friends, or adopting trends, repeated learning…
There is a significant amount of online human activity which is either clandestine or illicit in nature, and hence where individuals operate under fear of exposure or capture. Yet there is little theoretical understanding of what models…
The rich set of interactions between individuals in the society results in complex community structure, capturing highly connected circles of friends, families, or professional cliques in a social network. Thanks to frequent changes in the…
We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat's law of proportionate effects as the result of…
We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
We explore the coupled dynamics of the internal states of a set of interacting elements and the network of interactions among them. Interactions are modeled by a spatial game and the network of interaction links evolves adapting to the…