Related papers: Kinetic models for the trading of goods
We introduce a system of kinetic equations describing an exchange market consisting of two populations of agents (dealers and speculators) expressing the same preferences for two goods, but applying different strategies in their exchanges.…
We propose a kinetic model to describe the dynamical evolution of wealth and knowledge in national and global markets, starting from a microscopic description of individual interactions. The model is built upon interaction rules that…
An important class of economic models involve agents whose wealth changes due to transactions with other agents. Several authors have pointed out an analogy with kinetic theory, which describes molecules whose momentum and energy changes…
The temporal evolution of a contagious viral disease is modelled as the dynamic progression of different classes of population with individuals interacting pairwise. This interaction follows a binary mechanism typical of kinetic theory,…
We propose a novel kinetic exchange model differing from previous ones in two main aspects. First, the basic dynamics is modified in order to represent economies where immediate wealth exchanges are carried out, instead of reshufflings or…
The Kinetic Gas Theory like two-agent money exchange models, recently introduced in the Econophysics of Wealth distributions, are revisited. The emergence of Boltzmann-Gibbs like distribution of individual money to Pareto's law in the tail…
We briefly review results on nonlinear kinetic equation of Boltzmann type which describe the evolution of wealth in a simple agents market. The mathematical structure of the underlying kinetic equations allows to use well-known techniques…
In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In…
We propose and investigate general kinetic models %of Boltzmann type with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. These models can be applied to many…
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the influence of knowledge in the evolution of wealth in a system of agents which interact through the binary trades introduced in Cordier, Pareschi,…
A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into…
We introduce a class of one-dimensional linear kinetic equations of Boltzmann and Fokker--Planck type, describing the dynamics of individuals of a multi-agent society questing for high status in the social hierarchy. At the Boltzmann level,…
In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to…
We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time…
We consider a nonlinear kinetic equation of Boltzmann type which takes into account the influence of conviction during the formation of opinion in a system of agents which interact through the binary exchanges introduced in [G. Toscani,…
Two kinetic exchange models are proposed to explore the dynamics of closed economic markets characterized by random exchanges, saving propensities, and collective transactions. Model I simulates a system where individual transactions occur…
In this paper, we discuss the large--time behavior of solution of a simple kinetic model of Boltzmann--Maxwell type, such that the temperature is time decreasing and/or time increasing. We show that, under the combined effects of the…
In this paper we study binary interaction schemes with uncertain parameters for a general class of Boltzmann-type equations with applications in classical gas and aggregation dynamics. We consider deterministic (i.e., a priori averaged) and…
Binary kinetic exchange models, where money is shuffled between two agents at a time, reproduce the Boltzmann Gibbs exponential wealth distribution but cannot address the multi party trades common in real markets. We generalize the exchange…
Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock…