Security Games in Network Flow Problems

TL;DR

This paper models a strategic security game on network flows, analyzing how defenders and attackers choose links to maximize their respective benefits and costs, extending classical flow and cut problems with game-theoretic insights.

Contribution

It introduces a game-theoretic framework for network flow security, applying linear programming duality and graph theory to characterize equilibrium strategies and extend classical flow problems.

Findings

Characterization of Nash equilibrium strategies using graph-theoretic methods

Conditions for equilibrium extension to budget-constrained scenarios

Extension of classical flow and cut problems to security game settings

Abstract

This article considers a two-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. Linear programming duality in zero-sum games and the Max-Flow Min-Cut Theorem are applied to obtain properties that are satisfied in any Nash equilibrium. A characterization of the support of the equilibrium strategies is provided using graph-theoretic arguments. Finally, conditions under which these results extend to budget-constrained environments are also studied. These results extend the classical minimum cost maximum flow problem and the minimum cut problem to a class of security games on flow networks.