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Over the last decades, the distribution of income and wealth has been deteriorating in many countries, leading to increased inequalities within and between societies. This tendency has revived the interest in the subject greatly, yet it…
A new definition of events of game-theoretic probability zero in continuous time is proposed and used to prove results suggesting that trading in financial markets results in the emergence of properties usually associated with randomness.…
During last two decades it has been discovered that the statistical properties of a number of microscopically rather different random systems at the macroscopic level are described by {\it the same} universal probability distribution…
We study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase ($\alpha\equiv P/N\gtrsim 1$) of the basic Minority Game using sign-payoff, with $N$ agents holding two strategies over $P$ histories. We…
We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of…
This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…
This paper develops a nonparametric statistical model of wealth distribution that imposes little structure on the fluctuations of household wealth. In this setting, we use new techniques to obtain a closed-form household-by-household…
We investigate the unbiased model for money exchanges with collective debt limit: agents give at random time a dollar to one another as long as they have at least one dollar or they can borrow a dollar from a central bank if the bank is not…
We study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed random graphs, where…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…
The proportional odds model gives a method of generating new family of distributions by adding a parameter, called tilt parameter, to expand an existing family of distributions. The new family of distributions so obtained is known as…
The Lucas-Moll system is a mean-field game type model describing the growth of an economy by means of diffusion of knowledge. The individual agents in the economy advance their knowledge by learning from each other and via internal…
In this paper we discuss some examples of systems composed of $N$ units, which exchange a conserved quantity $x$ according to some given stochastic rule, from some standard kinetic model of condensed matter physics to the kinetic exchange…
The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…
We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the…
In this note we give sufficient conditions for the convergence of the iterative algorithm called weighted-average consensus in directed graphs. We study the discrete-time form of this algorithm. We use standard techniques from matrix theory…
I discuss models for a continuum directed random polymer in a disordered environment in which the polymer lives on a fractal called the \textit{diamond hierarchical lattice}, a self-similar metric space forming a network of interweaving…
We present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general…
We consider an inhomogeneous version of the Barak-Erd\H{o}s graph, i.e. a directed Er\H{o}s-R\'enyi random graph on $\{1,\ldots,n\}$ with no loop. Given $f$ a Riemann-integrable non-negative function on $[0,1]^2$ and $\gamma > 0$, we define…