Efficient liability assignment under shock propagation

2026-05-14

AI Summary

This study addresses the challenge of designing responsibility allocation mechanisms that incentivize agents to select socially optimal paths when external shocks propagate through a network and trigger cascading edge failures. The authors propose a class of axiomatic responsibility rules grounded in network structure, whose weights correspond to the Shapley values of a path-counting cooperative game and can be computed efficiently in polynomial time. By proportionally linking individual responsibility to each agent’s marginal contribution to the system’s total loss, the proposed rule is theoretically shown to induce socially optimal routing behavior. Numerical simulations further demonstrate the effectiveness and scalability of the approach across diverse network topologies.

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.

Problem

• liability assignment
• shock propagation
• network
• systemic cost
• path selection

Innovation

• liability assignment
• shock propagation
• network games
• Shapley value
• path-based weighting