Network Flow Routing under Strategic Link Disruptions

TL;DR

This paper models a strategic game between a network defender and attacker, analyzing equilibrium properties and costs in network routing under link disruptions, extending classical max-flow problems to adversarial settings.

Contribution

It introduces a strategic game framework for network routing under link disruptions, deriving equilibrium properties using linear programming duality and max-flow min-cut theorem.

Findings

In equilibrium, both players achieve identical payoffs.

Defender's transportation cost decreases as attacker's marginal value increases.

Attacker's expected attack cost increases with defender’s marginal value.

Abstract

This paper considers a 2-player strategic game for network routing under link disruptions. Player 1 (defender) routes flow through a network to maximize her value of effective flow while facing transportation costs. Player 2 (attacker) simultaneously disrupts one or more links to maximize her value of lost flow but also faces cost of disrupting links. This game is strategically equivalent to a zero-sum game. Linear programming duality and the max-flow min-cut theorem are applied to obtain properties that are satisfied in any mixed Nash equilibrium. In any equilibrium, both players achieve identical payoffs. While the defender's expected transportation cost decreases in attacker's marginal value of lost flow, the attacker's expected cost of attack increases in defender's marginal value of effective flow. Interestingly, the expected amount of effective flow decreases in both these parameters. These results can be viewed as a generalization of the classical max-flow with minimum transportation cost problem to adversarial environments.