  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.
