  This paper is concerned with a model in econophysics, the subfield of
statistical physics that applies concepts from traditional physics to
economics. In our model, economical agents are represented by the vertices of a
connected graph and are characterized by the number of coins they possess.
Agents independently spend one coin at rate one for their basic need, earn one
coin at a rate chosen independently from a fixed distribution $\phi$ and
exchange money at rate $\mu$ with one of their nearest neighbors, with the
richest neighbor giving one coin to the other neighbor. If an agent needs to
spend one coin when her fortune is at zero, she dies, i.e., the corresponding
vertex is removed from the graph. Our first results focus on the two extreme
cases of lack of cooperation $\mu = 0$ and perfect cooperation $\mu = \infty$
for finite connected graphs. These results suggest that, when overall the
agents earn more than they spend, cooperation is beneficial for the survival of
the population, whereas when overall the agents earn less than they spend,
cooperation becomes detrimental. The infinite one-dimensional system is also
studied. 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 positive
constant that does not depend on the initial number of coins per agent or the
level of cooperation.
