Optimal risk in wealth exchange models: Agent dynamics from a microscopic perspective

Abstract

In this work we present a new type of microscopic analysis for two well-known wealth exchange models that have been deeply studied at the macroscopic level for the past decades. This approach allowed us to study and classify the individual strategies carried out by the agents undergoing transactions. We analyze the role of their interaction parameter, the risk propensity, and find a critical risk such that agents with risk above that value always end up losing everything when the system approaches equilibrium. Moreover, we find that the wealth of the agents is maximum for a range of risk values that depend on particular characteristics of the model, such as the social protection factor. Our findings allow to determine a region of parameters for which the strategies of the economic agents are successful.