Distribution of money on social networks

This talk is concerned with two of the most popular spatial stochastic models in econophysics. Both models consist of a population of individuals who are located on a general connected graph, are characterized by the number of coins they own, and randomly engage in pairwise monetary transactions with their neighbors. In the first model (uniform reshuffling model), the combined amount of coins of the two interacting neighbors is redistributed randomly and uniformly between the neighbors. In the second model (immediate exchange model), the two interacting neighbors simultaneously choose a random number of their coins to give to the other neighbor. Physicists used numerical simulations to conjecture that, when the population is large and interactions are global (complete graph), the distribution of money converges to an exponential distribution for the uniform reshuffling model and to a gamma distribution for the immediate exchange model. In this talk, we not only give rigorous proofs of these two conjectures but also extend these results to the more realistic network models (general connected graphs as opposed to complete graphs) where the individuals interact with their friends or business partners rather than all the other individuals.. This is a joint work with Stephanie Reed.