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Understanding the statistical dynamics of growth and inequality is a fundamental challenge to ecology and society. Recent analyses of wealth and income dynamics in contemporary societies show that economic inequality is very dynamic and…
Due to climate change, the interest of studying our climatic system using mathematical modeling has become tremendous in recent years. One well-known model is Budyko's system, which represents the coupled evolution of two variables, the…
In this paper, we use tools from sheaf theory to model and analyze optimal network control problems and their associated discrete relaxations. We consider a general problem setting in which pieces of equipment and their causal relations are…
To determine an optimal plan for complex tasks, one often deals with dynamic and hierarchical relationships between several entities. Traditionally, such problems are tackled with optimal control, which relies on the optimization of cost…
The availability of relational data can offer new insights into the functioning of the economy. Nevertheless, modeling the dynamics in network data with multiple types of relationships is still a challenging issue. Stochastic block models…
By generalizing the measurements on the game experiments of mixed strategy Nash equilibrium, we study the dynamical pattern in a representative dynamic stochastic general equilibrium (DSGE). The DSGE model describes the entanglements of the…
We formulate a flexible micro-to-macro kinetic model which is able to explain the emergence of income profiles out of a whole of individual economic interactions. The model is expressed by a system of several nonlinear differential…
In Evolutionary game theory the payoffs are typically fixed or shaped by external environmental variables. Here, we introduce an endogenous-feedback model in which the game played coevolves directly with the population state: the payoff…
The global production (as a system of creating values) is eventually forming a vast web of value chains that explains the transitional structures of global trade and development of the world economy. It is truly a new wave of globalisation,…
We introduce a sheaf-theoretic characterization of task solvability in general distributed computing models, unifying distinct approaches to message-passing models. We establish cellular sheaves as a natural mathematical framework for…
A standard growth model is modified in a straightforward way to incorporate what Keynes (1936) suggests in the "essence" of his general theory. The theoretical essence is the idea that exogenous changes in investment cause changes in…
The structure of the International Trade Network (ITN), whose nodes and links represent world countries and their trade relations respectively, affects key economic processes worldwide, including globalization, economic integration,…
Economic transformation -- change in what an economy produces -- is foundational to development and rising standards of living. Our understanding of this process has been propelled recently by two branches of work in the field of economic…
A dynamic model of the social relations between workers and capitalists is introduced. The model is deduced from the assumption that the law of value is an organising principle of modern economies. The model self-organises into a dynamic…
A key element to understand complex systems is the relationship between the spatial scale of investigation and the structure of the interrelation among its elements. When it comes to economic systems, it is now well-known that the…
This book provides an inviting tour through sheaf theory, from the perspective of applied category theory and pitched at a less specialized audience than is typical with introductions to sheaves. The book makes it as easy as possible for…
We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We…
The paper develops a general methodology for analyzing policies with path-dependency (hysteresis) in stochastic models with forward looking optimizing agents. Our main application is a macro-climate model with a path-dependent climate…
In this work, we analyse the relationship between heterogeneity and cooperation. Previous investigations suggest that this relation is nontrivial, as some authors found that heterogeneity sustains cooperation, while others obtained…
We consider a sharing economy network where agents embedded in a graph share their resources. This is a fundamental model that abstracts numerous emerging applications of collaborative consumption systems. The agents generate a random…