Managing cascading disruptions through optimal liability assignment

TL;DR

This paper analyzes how to assign liabilities among interconnected agents in a supply chain to prevent cascading failures and improve overall investment efficiency, highlighting the importance of indirect liabilities.

Contribution

It characterizes all efficient liability assignment solutions in cascading failure scenarios and identifies a particularly desirable efficient solution.

Findings

Efficient solutions involve later agents bearing some losses despite not being directly liable.

Indirect liabilities are essential to prevent unbounded inefficiencies.

A specific efficient solution with multiple desirable properties is identified.

Abstract

Interconnected agents such as firms in a supply chain make simultaneous preparatory investments to increase chances of honouring their respective bilateral agreements. Failures cascade: if one fails their agreement, then so do all who follow in the chain. Thus, later agents' investments turn out to be pointless when there is an earlier failure. 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.