  We introduce noncooperatively optimized tolerance (NOT), a generalization of
highly optimized tolerance (HOT) that involves strategic (game theoretic)
interactions between parties in a complex system. We illustrate our model in
the forest fire (percolation) framework. As the number of players increases,
our model retains features of HOT, such as robustness, high yield combined with
high density, and self-dissimilar landscapes, but also develops features of
self-organized criticality (SOC) when the number of players is large enough.
For example, the forest landscape becomes increasingly homogeneous and
protection from adverse events (lightning strikes) becomes less closely
correlated with the spatial distribution of these events. While HOT is a
special case of our model, the resemblance to SOC is only partial; for example,
the distribution of cascades, while becoming increasingly heavy-tailed as the
number of players increases, also deviates more significantly from a power law
in this regime. Surprisingly, the system retains considerable robustness even
as it becomes fractured, due in part to emergent cooperation between
neighboring players. At the same time, increasing homogeneity promotes
resilience against changes in the lightning distribution, giving rise to
intermediate regimes where the system is robust to a particular distribution of
adverse events, yet not very fragile to changes.
