Wealth concentration in a biased asset-exchange model

Economic inequality is a significant and dynamic problem throughout the world. Asset-exchange models have been used to model macroeconomic systems based on microeconomic assumptions about how agents exchange wealth in an economy. Previous studies of a certain asset-exchange model, called the Yard-Sale model, have found that trade alone promotes the condensation of wealth to a single individual in an economy [Chakraborti, 2002, Moukarzel et al., 2007, Boghosian, 2014b]. A later study found that a slight modification of the Yard-Sale model seems to allow for the coexistence of both "condensed wealth" and a normal population in an economy [Boghosian et al., 2016a]. This work formalizes the notion of wealth condensation in a macroeconomic system. This can be done by extending Schwartz's theory of distributions to allow for objects which increase at most linearly at infinity, or by considering condensed wealth to be a nonstandard phenomenon, and describing it as such. Numerical simulations indicate that this continuous description of wealth concentration is a valid approximation of wealth concentration in discrete systems with as few as 256 agents. We then study the properties of the steady-state distribution of wealth in such a system, and mention the fit of our system to the distribution of wealth in the United States in 2016.