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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…

Physics and Society · Physics 2009-10-15 Elena Agliari , Adriano Barra , Raffaella Burioni , Pierluigi Contucci

The large-scale organization of the world economies is exhibiting increasingly levels of local heterogeneity and global interdependency. Understanding the relation between local and global features calls for analytical tools able to uncover…

General Finance · Quantitative Finance 2008-12-10 M. Angeles Serrano , Marian Boguna , Alessandro Vespignani

We study convergence rates of random-order best-response dynamics in games on networks with linear best responses and strategic substitutes. Combining formal analysis with numerical simulations we identify phenomena that lead to slow…

Computer Science and Game Theory · Computer Science 2026-02-19 Wojciech Misiak , Marcin Dziubiński

In this paper we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insuance market by a bipartite graph. Using…

Risk Management · Quantitative Finance 2015-10-05 Oliver Kley , Claudia Klüppelberg , Gesine Reinert

We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the…

Statistical Mechanics · Physics 2007-05-23 Valmir C. Barbosa , Raul Donangelo , Sergio R. Souza

Temporal networks of face-to-face interactions between individuals are useful proxies of the dynamics of social systems on fast time scales. Several empirical statistical properties of these networks have been shown to be robust across a…

Physics and Society · Physics 2023-02-03 Didier Le Bail , Mathieu Génois , Alain Barrat

Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…

Disordered Systems and Neural Networks · Physics 2014-02-25 Imre Kondor , István Csabai , Gábor Papp , Enys Mones , Gábor Czimbalmos , Máté Csaba Sándor

Imitation is widely observed in populations of decision-making agents. Using our recent convergence results for asynchronous imitation dynamics on networks, we consider how such networks can be efficiently driven to a desired equilibrium…

Computer Science and Game Theory · Computer Science 2017-04-17 James Riehl , Pouria Ramazi , Ming Cao

Autonomous and learning agents increasingly participate in markets - setting prices, placing bids, ordering inventory. Such agents are not just aiming to optimize in an uncertain environment; they are making decisions in a game-theoretical…

Computer Science and Game Theory · Computer Science 2025-06-24 Martin Bichler , Julius Durmann , Matthias Oberlechner

We present empirical evidence that land values are scale-free and introduce a network model that reproduces the observations. The network approach to urban modelling is based on the assumption that the market dynamics that generates land…

Disordered Systems and Neural Networks · Physics 2009-11-10 Claes Andersson , Alexander Hellervik , Kristian Lindgren , Anders Hagson , Jonas Tornberg

We model a system of networking agents that seek to optimize their centrality in the network while keeping their cost, the number of connections they are participating in, low. Unlike other game-theory based models for network evolution,…

Populations and Evolution · Quantitative Biology 2007-05-23 Petter Holme , Gourab Ghoshal

This paper presents a multi-agent reinforcement learning algorithm to represent strategic bidding behavior in freight transport markets. Using this algorithm, we investigate whether feasible market equilibriums arise without any central…

Machine Learning · Computer Science 2021-02-19 Wouter van Heeswijk

We present a model in which we investigate the structure and evolution of a random network that connects agents capable of exchanging wealth. Economic interactions between neighbors can occur only if the difference between their wealth is…

Physics and Society · Physics 2015-06-19 A. Agreda , K. Tucci

We present a framework for automatically decomposing ("block-modeling") the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph ("block model") depicting the main patterns of…

Physics and Society · Physics 2008-12-11 Joerg Reichardt , Douglas R. White

We study risk-sharing economies where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled…

Portfolio Management · Quantitative Finance 2020-10-01 Martin Herdegen , Johannes Muhle-Karbe , Dylan Possamaï

Using the minority game as a model for competition dynamics, we investigate the effects of inter-agent communications on the global evolution of the dynamics of a society characterized by competition for limited resources. The agents…

Statistical Mechanics · Physics 2009-11-10 M. Anghel , Zoltan Toroczkai , Kevin E. Bassler , G. Korniss

We introduce a simple network formation model for social networks. Agents are nodes, connecting to another agent by building a directed edge (or accepting a connection from another agent) has a cost, and reaching (or being reached by) other…

Social and Information Networks · Computer Science 2016-04-22 L. Elisa Celis , Aida Sadat Mousavifar

Modeling human dynamics responsible for the formation and evolution of the so-called social networks - structures comprised of individuals or organizations and indicating connectivities existing in a community - is a topic recently…

Computers and Society · Computer Science 2007-05-23 Victor V. Kryssanov , Frank J. Rinaldo , Evgeny L. Kuleshov , Hitoshi Ogawa

We study the competition for partners in two-sided matching markets with heterogeneous agent preferences, with a focus on how the equilibrium outcomes depend on the connectivity in the market. We model random partially connected markets,…

Computer Science and Game Theory · Computer Science 2023-01-12 Yash Kanoria , Seungki Min , Pengyu Qian

This paper presents a pioneering approach for simulation of economic activity, policy implementation, and pricing of goods in token economies. The paper proposes a formal analysis framework for wealth distribution analysis and simulation of…

General Finance · Quantitative Finance 2024-01-17 Rem Sadykhov , Geoffrey Goodell , Denis de Montigny , Martin Schoernig , Philip Treleaven