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The Question of Relaxation in the Wealth Exchange Models

By Abhijit Kar Gupta

Abstract

We look at the meaning of ’relaxation ’ in the wealth exchange models that are recently proposed in Econophysics to interpret the wealth distributions. To quantify and characterise the process of relaxation, we define an appropriate quantity and evaluate that numerically for the systems of many agents. Also, it has been supported heuristically by constructing a simple differential equation. Introducing the Models The wealth exchange models are many agent models for wealth distributions where a randomly chosen pair of agents interact and exchange wealth between them in a certain fashion. We here deal with the models that are primarily based on the kinetic theory of gas in statistical physics. The interactions among agents can be thought of as an elastic collision as the total wealth of the interacting agents is kept constant and this in turn ensures the total wealth of all the agents to remain conserved. There has been a great amount of study [1] in this kind of wealth exchange models in econophysics in recent times [1]

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