Efficient liability assignment under shock propagation

TL;DR

This paper models shock propagation in networks and proposes a liability assignment rule that allocates systemic costs proportionally based on network structure, computable efficiently.

Contribution

It introduces a novel liability rule based on path-structure weights, aligning agent liabilities with systemic losses and computable via polynomial algorithms.

Findings

Liability weights match the Shapley value of a path-counting game.

The proposed rule ensures efficient path selection in the shock propagation model.

Simulation demonstrates the practical application of the liability assignment method.

Abstract

We study a model in which shocks propagate along a path chosen by agents embedded in a network. When a shock hits an agent, the affected agent cancels one of her outgoing edges. This cancellation cascades sequentially along a chosen path until reaching a terminal agent, resulting in a systemic cost equal to the sum of individual cancellation losses. A liability rule determines agent payments for realized losses, and we seek to implement efficient path selection in the induced sequential-move game. Our main axiomatic result characterizes a family of rules, which set each agent's liability to be proportional to the system's total realized losses with agent weights depending only on the network structure. We propose a way to set such weights based on a simple path-based procedure that assigns equal importance to all non-sink agents along each path and then aggregates these contributions across paths. These weights coincide with the Shapley value of an associated "path-counting" cooperative game and can be computed in polynomial time. A simulation study illustrates the mechanics of our approach.