Managing Cascading Disruptions Through Optimal Liability Assignment

Interconnected agents such as firms in a supply chain make simultaneous preparatory investments to increase chances of honoring their respective bilateral agreements. Failures cascade with lasting repercussions further down the chain. How losses are shared affects how agents invest to avoid the losses in the first place. In this way, a solution sets agent liabilities depending on the point of disruption and induces a supermodular investment game. We characterize all efficient solutions. These have the form that later agents—who are not directly liable for the disruption—still shoulder some of the losses, justified on the premise that they might have failed anyway. Importantly, we find that such indirect liabilities are necessary to avoid unbounded inefficiencies. Finally, we pinpoint one efficient solution with several desirable properties. This paper was accepted by Peng Sun, optimization and decision analytics. Funding: This work was supported by the Danmarks Frie Forskningsfond [Grant 4260-00050B] and Carlsbergfondet [Grant CF18-1112].