Biblio

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.

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.

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.