Two-Person Zero-Sum Games pp 123-141 | Cite as

# Network Interdiction

## Abstract

This chapter deals with a variety of competitive problems that occur on networks. Such problems deserve their own chapter because networks are becoming increasingly important in modern life. The Internet is a network, transportation systems are networks, power distribution systems are networks, communication systems are networks, social systems can be thought of as networks, and all of these are subject to competition between the intended users of the network and another player who wishes to interfere with that usage. In this chapter we will consistently refer to the two competing players as User and Breaker, rather than player 1 and player 2. Depending on the model, either player may be the maximizer. The models in Sect. 7.1 are maxmin formulations where Breaker’s actions are known to User. In Sect. 7.2 we consider games where Breaker can keep his actions secret.

## Keywords

Survival Probability Dual Variable Maxmin Problem Network Optimization Problem Network Interdiction## References

- Alderson, D., Brown, G., Carlyle, M., & Wood, K. (2011). Solving defender-attacker-defender models for infrastructure defense. In R. K. Wood & R. F. Dell (Eds.),
*Operations research, computing, and homeland defense*(pp. 28–49). Hanover, MD: INFORMS.Google Scholar - Altner, D., Ergun, O., & Uhan, N. (2010). The maximum flow network interdiction problem: Valid inequalities, integrality gaps, and approximability.
*Operations Research Letters, 38*(1), 33–38.CrossRefGoogle Scholar - Brown, G., Kline, J., Thomas, A., Washburn, A., & Wood, K. (2011). A game-theoretic model for defense of an oceanic bastion against submarines.
*Military Operations Research, 16*(4), 25–40.CrossRefGoogle Scholar - Burch, C., Carr, R., Krumke, S., Marathe, M., Phillips, C., & Sundberg, E. (2003). A decomposition-based pseudoapproximation algorithm for network flow inhibition. in
*Network Interdiction and Stochastic Programming*, D.L. Woodruff (Ed.), Kluwer.Google Scholar - Cormican, K., Morton, D., & Wood, K. (1998). Stochastic network interdiction.
*Operations Research, 46*(2), 184–197.CrossRefGoogle Scholar - Ford, L. & Fulkerson D. (1962).
*Flows in Networks*. Princeton University Press.Google Scholar - Fulkerson, D., & Hardin, G. (1977). Maximizing the minimum source-sink path subject to a budget constraint.
*Mathematical Programming, 13*(1), 116–118.CrossRefGoogle Scholar - Gerards, A. (1995). Theorem 14 in chapter 3 of
*Handbooks in Operations Research and Management Science*, In M. Ball, T. Magnanti, C. Monma, & G. Nemhauser (Eds.), North Holland.Google Scholar - Harris, T., & Ross, F. (1955).
*Fundamentals of a method for evaluating rail network capacities*. Memorandum RM-1573, RAND Corporation, Santa Monica, CA.Google Scholar - Hemmecke, R., Schultz, R., & Woodruff, D. (2003). Interdicting stochastic networks with binary interdiction effort. In D. L. Woodruff (Ed.)
*Network interdiction and stochastic programming*, Kluwer.Google Scholar - Jain, M., Korzhyk, D., Vanek, O., Conitzer, V., Pechouochk, M., & Tambe, M. (2011). A double oracle algorithm for zero-sum security games on graphs. In
*The 10th International Conference on Autonomous Agents and Multiagent Systems*(Vol. 1). International Foundation for Autonomous Agents and Multiagent Systems, Richland.Google Scholar - Morton, D., Pan, F., & Saeger, L. (2007). Models for nuclear smuggling interdiction.
*IIE Transactions, 39*(1), 3–14.CrossRefGoogle Scholar - Phillips, C. (1993). The network inhibition problem,
*Proceedings of the 25th Annual ACM Symposium on the Theory of Computing*, (pp. 776–785), ACM.Google Scholar - Wood, K. (1993). Deterministic network interdiction.
*Mathematical and Computer Modelling, 17*, 1–18.CrossRefGoogle Scholar