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We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying {\em unstable} dynamical critical…
Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…
This paper focuses on the coordination of a large population of dynamic agents with private information over multiple periods. Each agent maximizes the individual utility, while the coordinator determines the market rule to achieve group…
In contrast with unstructured models, structured discrete population models have been able to fit and predict chaotic experimental data. However, most of the chaos control techniques in the literature have been designed and analyzed in a…
We prove under certain assumptions that there exists a solution of the Schrodinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which may be unbounded, not symmetric, or not…
Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by Deffuant et al in 2000. They have raised a fair amount of attention in the communities of social simulation,…
We consider a multiagent system consisting of selfish and heterogeneous agents. Its behavior is modeled by multipopulation replicator dynamics, where payoff functions of populations are different from each other. In general, there exist…
We study the Euler Alignment system of collective behavior, equipped with `topological' interaction protocols, which were introduced to the mathematical literature by Shvydkoy and Tadmor. Interactions subject to these protocols may depend…
A recently introduced concept of "cooperative equilibrium", based on the assumption that players have a natural attitude to cooperation, has been proven a powerful tool in predicting human behaviour in social dilemmas. In this paper, we…
We study the noisy dynamics of a close relative of the sand pile model. Depending on the type of noise and the time scale of observation, we find stationary fluctuations (similar to SOC) or an aging dynamics with punctuated equilibria, a…
Living systems self-organize in ways that conventional physical frameworks-based on forces, energies, and continuous fields-cannot fully capture. Processes like gene regulation and cellular decision-making involve rule-based logic and…
This paper attempts to develop a graph-theoretic multi-agent perspective of population games to study the \quotes{truncation} behavior. The proposed method considers fitness of the population as a dynamical system to address the issue of…
The aim of this work is to establish the personal income distribution from the elementary constituents of a free market; products of a representative good and agents forming the economic network. The economy is treated as a self-organized…
The Non-Commutative (NC) CP(1) model is studied from field theory perspective. Our formalism and definition of the NC CP(1) model differs crucially from the existing one \cite{nccp}. Due to the U(1) gauge invariance, the Seiberg-Witten map…
The purpose of this paper is to present an idealized hypotheses-drawn model describing dynamics of variability in business and other social areas. A new construct is introduced called the Bayesian space of assessments to consider changes in…
Modern socio-technical systems typically consist of many interconnected users and competing service providers, where notions like market equilibrium are tightly connected to the ``evolution'' of the network of users. In this paper, we model…
Game theory studies situations in which strategic players can modify the state of a given system, due to the absence of a central authority. Solution concepts, such as Nash equilibrium, are defined to predict the outcome of such situations.…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
The short-time and long-time dynamics of the Bak-Sneppen model of biological evolution are investigated using the damage spreading technique. By defining a proper Hamming distance measure, we are able to make it exhibits an initial…
We have studied here the self-organising features of the dynamics of a model market, where the agents `trade' for a single commodity with their money. The model market consists of fixed numbers of economic agents, money supply and…