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The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all…
We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms,…
In this paper we introduce kinetic equations for the evolution of the probability distribution of two goods among a huge population of agents. The leading idea is to describe the trading of these goods by means of some fundamental rules in…
The dynamics of urban systems can be understood from an evolutionary perspective, in some sense extending biological and cultural evolution. Models for systems of cities implementing elementary evolutionary processes remain however to be…
Axelrod's model for the dissemination of culture contains two key factors required to model the process of diffusion of innovations, namely, social influence (i.e., individuals become more similar when they interact) and homophily (i.e.,…
Dynamic pricing of goods in a competitive environment to maximize revenue is a natural objective and has been a subject of research over the years. In this paper, we focus on a class of markets exhibiting the substitutes property with…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
This paper shows that in suitable markets, even with out-of-equilibrium trade allowed, a simple price update rule leads to rapid convergence toward the equilibrium. In particular, this paper considers a Fisher market repeated over an…
We present a dynamical model for the price evolution of financial assets. The model is based in a two level structure. In the first stage one finds an agent-based model that describes the present state of the investors' beliefs,…
We consider a non acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the…
Consumer behavior under social influence is a well-known phenomenon and computer scientists and economists are prevalently trying to analyze the dynamics behind decision making during the consumption process through agent-based modeling…
Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The…
This paper is concerned with the determination of pricing strategies for a firm that in each period of a finite horizon receives replenishment quantities of a single product which it sells in two markets, e.g., a long-distance market and an…
Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…
We study the equilibrium points of a system of equations corresponding to a Bass based model that describes the diffusion of two brands in competition. To increase the understanding of the effects of the cross-brand parameters, we perform a…
We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, $1- \varepsilon > 0$ or $ - (1 + \varepsilon) < 0$. We study the specific case where the…
We discuss the stationary states of a model economy in which $N$ heterogeneous adaptive consumers purchase commodity bundles repeatedly from $P$ sellers. The system undergoes a transition from an inefficient to an efficient state as the…
This work demonstrates the application of a birth-death Markov process, inspired by radioactive decay, to capture the dynamics of innovation processes. Leveraging the Bass diffusion model, we derive a Gompertz-like function explaining the…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
Network effects are the added value derived solely from the popularity of a product in an economic market. Using agent-based models inspired by statistical physics, we propose a minimal theory of a competitive market for (nearly)…