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Money exchange involves a buyer and a seller. A money exchange model isdesigned as follows: at each time step, a pair of socially connected agents areselected to transact. A Fermi function defines the probability of one of theselected pair being a buyer. Their transaction amount is an integral randomvariable with finite states. We argue that achieving equal wealth isunattainable. Additionally, we demonstrate conditions that result in the moneydistribution forming two or more clusters, and we explore circumstances inwhich a connected social graph with more links leads to a reduced number ofstates in the money distribution.

Application of the Fermi function in money exchange