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Abstract

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 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 bi-layer 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 collapse in as many resources as possible if one assumes that the agents' strategies remain constant over time. 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.