Kinetic modeling of economic markets with heterogeneous saving propensities

TL;DR

This paper introduces a simplified kinetic model for economic markets with heterogeneous saving behaviors, analyzing wealth distribution and inequality using numerical simulations and efficiency comparisons.

Contribution

It proposes a reduced lattice gas automaton model without propagation, incorporating new transaction rules and sampling methods, enhancing computational efficiency and analytical insights.

Findings

The reduced model is more computationally efficient than the standard LGA.

Different transaction rules and sampling methods produce similar wealth distributions.

The model effectively analyzes wealth inequality using Gini and Kolkata indices.

Abstract

The lattice gas automaton (LGA) is proposed for a closed economic market of agents with heterogeneous saving interests. There are two procedures in the standard LGA, i.e., "propagation" + "transaction". If the propagation step is removed and the transaction is conducted among all agents, the LGA reduces to a more simplified kinetic model. In addition, two dealing rules are imposed on the transaction phase. Under Rule I, the trading volume depends on the average saving propensities of an arbitrary pair of agents in trade. Under Rule II, the exchange is governed by a stochastic parameter between the saving propensities of two traders. Besides, two sampling methods are introduced for the random selection of two agents in the iterative process. Specifically, Sampling I is the sampling with replacement and is easier to program. Sampling II is the sampling without replacement and owns a higher computing efficiency. There are slight differences between the stationary wealth distributions simulated by using the two transaction rules and sampling approaches. In addition, the accuracy, robustness and efficiency of the econophysics models are validated by typical numerical tests. The reduced LGA without the propagation step owns a higher computational efficiency than the standard LGA. Moreover, the impact of saving propensities of agents in two groups on the wealth distributions is studied, and the influence of proportions of agents is investigated as well. To quantitatively measure the wealth inequality, the Gini coefficients, Kolkata indices, and deviation degrees of all agents and two groups are simulated and analyzed in detail. This work is helpful to further analyze and predict the dynamic process of wealth distribution in the realistic economic market.