Antipersistent dynamics in kinetic models of wealth exchange

TL;DR

This paper explores the antipersistent behavior in wealth exchange models, revealing how agents' gains and losses are correlated, leading to non-random walk dynamics influenced by saving propensities.

Contribution

It uncovers the antipersistent nature of gain-loss dynamics in kinetic wealth exchange models with distributed saving propensities, highlighting microscopic correlations.

Findings

Antipersistence causes correlations in gain-loss sequences.

Distributed saving leads to antipersistent walks with bias.

Differences from simple biased random walks are identified.

Abstract

We investigate the detailed dynamics of gains and losses made by agents in some kinetic models of wealth exchange. The concept of a walk in an abstract gain-loss space for the agents had been introduced in an earlier work. For models in which agents do not save, or save with uniform saving propensity, this walk has diffusive behavior. In case the saving propensity $\lambda$ is distributed randomly ($0 \leq \lambda < 1$), the resultant walk showed a ballistic nature (except at a particular value of $\lambda^* \approx 0.47$). Here we consider several other features of the walk with random $\lambda$. While some macroscopic properties of this walk are comparable to a biased random walk, at microscopic level, there are gross differences. The difference turns out to be due to an antipersistent tendency towards making a gain (loss) immediately after making a loss (gain). This correlation is in fact present in kinetic models without saving or with uniform saving as well, such that the corresponding walks are not identical to ordinary random walks. In the distributed saving case, antipersistence occurs with a simultaneous overall bias.