  Cooperation between individuals is emergent in all parts of society, yet
mechanistic reasons for this emergence is ill understood in the literature. A
specific example of this is insurance. Recent work has, though, shown that
assuming the risk individuals face is proportional to their wealth and
optimising the time average growth rate rather than the ensemble average
results in a non-zero-sum game, where both parties benefit from cooperation
through insurance contracts. In a recent paper, Peters and Skjold present a
simple agent-based model and show how, over time, agents that enter into such
cooperatives outperform agents that do not. Here, we extend this work by
restricting the possible connections between agents via a lattice network.
Under these restrictions, we still find that all agents profit from cooperating
through insurance. We, though, further find that clusters of poor and rich
agents emerge endogenously on the two-dimensional map and that wealth
inequalities persist for a long duration, consistent with the phenomenon known
as the poverty trap. By tuning the parameters which control the risk levels, we
simulate both highly advantageous and extremely risky gambles and show that
despite the qualitative shift in the type of risk, the findings are consistent.
