Related papers: Explicit equilibria in a kinetic model of gambling
For a class of stochastic dynamical models of exchange economies that we call ``fully connected Cobb-Douglas'', the paper proves convergence of the probability distribution to an equilibrium, in total variation metric as time goes to…
The game dynamical equations are derived from Boltzmann-like equations for individual pair interactions by assuming a certain kind of imitation behavior, the so-called proportional imitation rule. They can be extended to a stochastic…
We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By…
We study a recently introduced class of strategic games that is motivated by and generalizes Schelling's well-known residential segregation model. These games are played on undirected graphs, with the set of agents partitioned into multiple…
A continuous variable changing between 0 and 1 is introduced to characterise contentment, or satisfaction with life, of an individual and an equation governing its evolution is postulated from analysis of several factors likely to affect…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
We investigate the dynamics of wealth inequality in an economy where households have positional preferences, with the strength of the positional concern determined endogenously by inequality of wealth distribution in the society. We…
We mathematically analyze a simple market model where trading at each point in time involves only two agents with the sum of their money being conserved and with neither parties resulting with negative money after the interaction process.…
We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…
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…
Numerical experiments of the statistical evolution of an ensemble of non-interacting particles in a time-dependent billiard with inelastic collisions, reveals the existence of three statistical regimes for the evolution of the speeds…
Social and economic inequality is a plague of the XXI Century. It is continuously widening, as the wealth of a relatively small group increases and, therefore, the rest of the world shares a shrinking fraction of resources. This situation…
We consider a simple theoretical model to investigate the impact of inheritances on the wealth distribution. Wealth is described as a finite resource, which remains constant over different generations and is divided equally among offspring.…
We analyze a conservative market model for the competition among economic agents in a close society. A minimum dynamics ensures that the poorest agent has a chance to improve its economic welfare. After a transient, the system…
Transactions are an important aspect of human social life, and represent dynamic flow of information, intangible values, such as trust, as well as monetary and social capital. Although much research has been conducted on the nature of…
A procedure is introduced which allows to represent the dynamics of a non-equilibrium system violating detailed balance by its steady state loop fluxes. It is shown that detailed balance is restored in this representation, such that the…
This paper investigates the dynamics of gambling and how they can affect risk-taking behavior in regions not explored by Kahneman and Tversky's Prospect Theory. Specifically, it questions why extreme outcomes do not fit the theory and…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
We analyze the dynamics of a forecasting game which exhibits the phenomenon of information cascades. Each agent aims at correctly predicting a binary variable and he/she can either look for independent information or herd on the choice of…