Income and Wealth Distributions from Stochastic Strategy Minority Game

Abstract

We propose a version of the Minority Game where the agents at each time make investments either in terms of money or stock from their possessions. The amount of investments at each time step, and not the number of people opting for a choice, determines the ‘minority’. The invested money is returned to the stock investors and the invested stock is returned to the money investors in proportion of their respective investments at each time. In this way, agents in the less investment side faces higher demand, and hence are in ‘minority’, receiving higher pay-off for their investments. This dynamics lead the ‘market’ to a self-organized state. We measure the distributions of income of the agents at every step and also the accumulated wealth, both of which have a stationary distribution. The distribution functions follow Pareto’s law when the agents invest random fractions of their wealth. This reflects the role of heterogeneity in economic interactions.