  Single- and multi-layer complex networks have been proven as a powerful tool
to study the dynamics within social, technological,or natural systems. An often
observed common goal there is to optimize these systems for specific purposes
by minimizing certain costs while maximizing a desired output. Acknowledging
that especially real-world systems from the coupled socio-ecological realm are
highly intertwined this work exemplifies that in such systems the optimization
of a certain subsystem, e.g., to increase the resilience against external
pressure in an ecological network, may unexpectedly diminish the stability of
the whole coupled system. For this purpose we utilize an adaptation of a
previously proposed conceptual bilayer network model composed of an ecological
network of diffusively coupled resources co-evolving with a social network of
interacting agents that harvest these resources and learn each other's
strategies depending on individual success. We derive an optimal coupling
strength that prevents a collapse in as many resources as possible if one
assumes that the agents' strategies remain constant over time. However, we then
show that if agents socially learn and adapt strategies according to their
neighbors' success, this optimal coupling strength is revealed to be a critical
parameter above which the probability for a global collapse in terms of
irreversibly depleted resources is high -- an effect that we denote the tragedy
of the optimizer. We thus find that measures which stabilize the dynamics
within a certain part of a larger co-evolutionary system may unexpectedly cause
the emergence of novel undesired globally stable states. Our results therefore
underline the importance of holistic approaches for managing socio-ecological
systems because stabilizing effects which focus on single subsystems may be
counter-beneficial for the system as a whole.
