Instability or crisis in a system is modeled by the emergence of a configuration of coalitions with conflictual goals and endowed with enough blocking power so as to oppose any outcome. The structure of the configuration may either lead to a compromise or to a deadlock. A compromise exists if there is a sequence of friendly delegations that lead to some stable configuration. The distribution of power is modeled by a simplicial complex. We study the topological structure of configurations that contain a compromise.
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