Wiretapping a Hidden Network

Authors:
Haris Aziz;Oded Lachish;Mike Paterson;Rahul Savani
Affiliations:
Institut für Informatik, Universität München, München, Germany 80538;Department of Computer Science, University of Warwick, Coventry, UK CV4 7AL;Department of Computer Science, University of Warwick, Coventry, UK CV4 7AL;Department of Computer Science, University of Liverpool, Liverpool, UK L69 3BX
Venue:
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Year:
2009

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Abstract

We consider the problem of maximizing the probability of hitting a strategically chosen hidden virtual network by placing a wiretap on a single link of a communication network. This can be seen as a two-player win-lose (zero-sum) game that we call the wiretap game. The value of this game is the greatest probability that the wiretapper can secure for hitting the virtual network. The value is shown to be equal the reciprocal of the strength of the underlying graph. We provide a polynomial-time algorithm that finds a linear-sized description of the maxmin-polytope, and a characterization of its extreme points. It also provides a succint representation of all equilibrium strategies of the wiretapper that minimize the number of pure best responses of the hider. Among these strategies, we efficiently compute the unique strategy that maximizes the least punishment that the hider incurs for playing a pure strategy that is not a best response. Finally, we show that this unique strategy is the nucleolus of the recently studied simple cooperative spanning connectivity game.