Samenvatting

The Israeli Defense Force (IDF) encountered numerous problems during the invasion
of southern Lebanon in 2006. Division 162, for instance, experienced serious difficulties
while approaching the village of Ghandouriyeh.2 Even though multiple axes of approach
were available the IDF took the route along Wadi Saluki (other possibilities were to
approach either from the south or north). Hezbollah launched a successful ambush
resulting in the death of several IDF soldiers.3 This action stands as an example of IDF’s
failure to obtain accurate tactical ground intelligence during this conflict.4 Ambushes,
raids and IED attacks have been, and still are, tactics most often employed by irregular
fighters.5 Counter-measures consist of physical protection of men and materiel, and
methods to detect, predict and neutralise possible attacks.6 Game theory, the mathematical
analysis of the strategic interaction between actors, offers a coherent analytical framework
that can be used to systematically analyse problems related to counter-insurgency.7
In addition, it offers a framework that helps understand the influence of assumptions
on outcomes of an analytical process.8 Game theory has been used extensively in modeling
military operations as well as in modeling problems of a more strategic nature.9
We argue that game theory can also be useful in predicting and preventing attacks with
improvised explosive devices by reducing the predictability of traffic patterns.
The goal of this chapter is to present an analytical framework that can be used to
optimise routing schemes, knowing that the enemy employs ambushes and IED attacks.
This will be done by considering the possible strategies each player in this `ambush
game’ can employ. Simply put, one player has to choose among the possible routes
between a source and destination, and the other player has to choose the location of an
attack. Game theory is perfectly equipped to analyse such strategic interactions.
Clearly, mathematical modeling always comes at the cost of making simplifying
assumptions. We recognise that other considerations also play a role in deciding what
route to take (such as geography, available time, etc.). However, a game-theoretical
approach can certainly aid in maximizing the unpredictability of routing schemes, consequently
minimizing the expected loss to allied forces.

The layout of this chapter is as follows. A game-theoretical model that captures the
strategic interaction between the player that conducts the ambush and the player that
moves from source to destination on risk-homogeneous networks will be introduced
first. Next, a discussion on approximating the risk of an attack on edges in the network
will be presented. Finally, optimal routing on heterogeneous networks will be presented
in the last section.