A generative model of income distribution: Formalization with iterated investment game

The purpose of this paper is to formalize a simple model that theoretically connects individuals' rational choice at the micro level to income distribution, which is subject to the Gibrat's law empirically, as social structure at macro level. We use an iterated investment game as a baseline model in which a player has a binary choice between investing and not investing. Given parameters which prescribe the payoff structure of the game are the prize density γ and the rate of return R. Method of analysis is a simulation with computation. We investigate changes in the Gini coefficient and skewness of the total profit distribution, as the parameters varied as follows: 0 ≤ γ ≤ 1, R = 0.5, 1, 2, 3, and n (the number of times that the game is repeated) = 5, 10. As a result of analysis, we derive the implication that the Gini coefficient increases up to critical point, where 0 ≤ γ ≤ 1/(R + 1), then decreases as prize density increases, where 1/(R - 1) < γ ≤ 1. Furthermore, we show that our model, with cumulative effect, generates a lognormal distribution under the condition that 1/(R + 1) < γ ≤ 1.