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Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models…
The "theory of open sub-functorial dynamics" is a new theory that defines interacting generalized dynamical systems. The interactions between these dynamics produce new dynamics which, of course, can then enter into other interactions. A…
In this paper the general principles and categories of mixed economy that currently exist in almost all countries of the world are presented. The paper also presents an Advanced Model of Mixed Economy with Threshold (AMMET), which is…
This paper studies the optimal investment behavior of renewable electricity producers in a competitive market, where both prices and installation costs are influenced by aggregate industry activity. We model the resulting crowding effects…
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic…
We consider continuous-time mean-field stochastic games with strategic complementarities. The interaction between the representative productive firm and the population of rivals comes through the price at which the produced good is sold and…
Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: active, sensitive and refractory, and obtained a dynamical system…
We propose a unified mean-field framework that bridges the dynamics of informal financial markets and formal markets governed by Limit Order Books (LOBs). Both settings are modeled as interacting particle systems on a 1D price lattice, with…
Physical analogs have shown considerable promise for understanding the behavior of complex adaptive systems, including macroeconomics, biological systems, social networks, and electric power markets. Many of today's most challenging…
We study an agent-based model of evolution of wealth distribution in a macro-economic system. The evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between agents. We…
This article introduces a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents, plays a central role. Building on classical growth theories…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent…
We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…
The application of principles of thermodynamics and statistical mechanics to economic systems is considered in a broad historical perspective, extending from prehistoric times to the present day. The hypothesis of maximum entropy production…
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a…
We briefly review statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the agents…
Unlike the classical kinetic theory of rarefied gases, where microscopic interactions among gas molecules are described as binary collisions, the modelling of socio-economic phenomena in a multi-agent system naturally requires to consider,…
The paper gives picture of enrichment to economic and financial system analysis using agent-based models as a form of advanced study for financial economic data post-statistical-data analysis and micro-simulation analysis. Theoretical…
We present an overview of some representative Agent-Based Models in Economics. We discuss why and how agent-based models represent an important step in order to explain the dynamics and the statistical properties of financial markets beyond…