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This paper is concerned with a model in econophysics, the subfield ofstatistical physics that applies concepts from traditional physics toeconomics. In our model, economical agents are represented by the vertices of aconnected graph and are characterized by the number of coins they possess.Agents independently spend one coin at rate one for their basic need, earn onecoin at a rate chosen independently from a fixed distribution $\phi$ andexchange money at rate $\mu$ with one of their nearest neighbors, with therichest neighbor giving one coin to the other neighbor. If an agent needs tospend one coin when her fortune is at zero, she dies, i.e., the correspondingvertex is removed from the graph. Our first results focus on the two extremecases of lack of cooperation $\mu = 0$ and perfect cooperation $\mu = \infty$for finite connected graphs. These results suggest that, when overall theagents earn more than they spend, cooperation is beneficial for the survival ofthe population, whereas when overall the agents earn less than they spend,cooperation becomes detrimental. The infinite one-dimensional system is alsostudied. In this case, when the agents earn less than they spend in average,the density of agents that die eventually is bounded from below by a positiveconstant that does not depend on the initial number of coins per agent or thelevel of cooperation.

The role of cooperation in spatially explicit economical systems