This paper analyzes empirical income distributions and proposes a simple stochastic model to explain the stationary distribution and deviations from it. Using the individual tax returns data in the U.S. and Japan for 40 years, we first summarize the shape of income distribution by an exponential decay up to about the 90th percentile of income and a power decay for the top 1 percent. We then pro...

The uniform distribution is an important counterexample in game theory as many of the canonical game dynamics have been shown not to converge to the equilibrium in certain cases. In particular none of the canonical game dynamics converge to the uniform distribution in a form of rock-paper-scissors where the amount an agent can lose is more than the agent can win, despite this fact, it is the un...

This article verifies that the ideal free distribution (IFD) is evolutionarily stable, provided the payoff in each patch decreases with an increasing number of individuals. General frequency-dependent models of migratory dynamics that differ in the degree of animal omniscience are then developed. These models do not exclude migration at the IFD where balanced dispersal emerges. It is shown that...

We have derived a quantum distribution function in terms of cumulants that are expectation values of a (anti)symmetric-ordered product of position and momentum fluctuation operators. A second-order approximation leads a Gaussian distribution function, which is positive definite and has proper marginals so that the Shannon entropy can be evaluated.

In this paper we suggest an alternative estimator and an alternative graphical analysis, both developed by Hyndman et al. (1996), to describe the law of motion of cross-sectional distributions of per-capita income and its components in Europe. This estimator has better properties than the kernel density estimator generally used in the literature on intra-distribution dynamics (cf. Quah, 1997). ...

General delay dynamical systems in which uncertainty is present in the form of probability measure dependent dynamics are considered. Several motivating examples arising in biology are discussed. A functional analytic framework for investigating well-posedness (existence, uniqueness and continuous dependence of solutions), inverse problems, sensitivity analysis and approximations of the measure...

Evolutionary tournaments have been used as a tool for comparing game-playing strategies. For instance, in the late 1970’s, Axelrod organized tournaments to compare strategies for playing the iterated prisoner’s dilemma (PD) game. While these tournaments and later research have provided us with a better understanding of successful strategies for iterated PD, our understanding is less clear about...

Simulations of vortex tube dynamics reveal that the non-Gaussian nature of turbulent fluctuation originates in the effect of random advection. A similar non-Gaussian distribution is found numerically in a simplified statistical model of random advection. An analytical solution is obtained in the mean-field case.

Using restricted firm level data from the Kauffman Firm Survey, I document that (a) the distribution of average returns to capital amongst nascent entrepreneurial firms is left skewed, and (b) has higher persistence in the left tail than the right. I find that a model where the entrepreneur’s capital investment is illiquid can largely rationalize this data. On average, a continuing entrepreneur...