Econophysics is an interdisciplinary field that leverages tools from physics and mathematics to analyze socioeconomic systems. One major area of interest is the pronounced disparity in wealth distribution observed across different countries, where roughly 20% of the population holds more than 80% of the total wealth. This phenomenon has been consistently observed in various societies throughout history, raising the question of whether such patterns are inherently rooted in social structures.

To explore this issue, we conducted a microscopic analysis of a wealth exchange model known as the Yard-Sale model, which has been widely studied at a macroscopic level over recent decades. This approach allowed us to categorize the strategies used by agents during transactions and to closely examine a critical parameter: risk propensity. We identified a threshold risk level beyond which agents are likely to lose all their wealth as the system approaches equilibrium. Furthermore, we observed that agents' wealth reaches its maximum within a specific range of risk values, which are influenced by particular characteristics of the model, such as the social protection factor. These insights enabled us to define a parameter space where economic agents' strategies are most effective [1].

In a more recent effort to create a realistic model, we examined the behavior of the Yard-Sale model when agents are represented as nodes in a complex network, restricting economic exchanges to those connected through this structure [2]. We analyzed the evolution of these systems using standard economic indicators, such as the Gini coefficient and liquidity, to understand how the number of connections affects agents' economic success. This comparison allowed us to contrast our findings with those from the mean-field version of the Yard-Sale model, where agent interactions are unrestricted.

Our study revealed that some outcomes, like wealth distributions at steady state, are independent of the underlying network connecting the agents. However, the presence of the network becomes significant when analyzing certain indicators more closely, leading to novel findings, such as the non-monotonic behavior of the Gini index and the emergence of a new type of agent whose trading capacity depends on the state of their neighbors. This prompted us to consider the inclusion of the Palma ratio, an inequality measure increasingly used alongside the Gini coefficient in empirical studies. We demonstrated that this ratio could be effectively integrated into the analysis of simulated wealth distributions.

[1] Optimal risk in wealth exchange models: Agent dynamics from a microscopic perspective, Neñer J, Laguna MF, Phys A 566 (2021) 125625.

[2] Influence of Contact Structure on Economic Transactions. Master's Thesis by Santiago Cuevas, Balseiro Institute, UNCuyo, December 2022.