example_network.nb

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The goal here is to produce a small trilevel program instance that can be \
solved exactly for use in testing the solution algorithms. The size of the \
network, itself, does not really matter, but the sizes of the \
defensible/destructible arc sets should be small enough to enumerate the \
entire game tree so that we can solve the model via exhaustive game tree \
search and minimax.\
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In the example below the defensible arc set includes 7 arcs and up to 3 arcs \
may be defended, for 35 choices of defensive move (assuming that the maximum \
number is defended). The destructible arc set includes 8 arcs (the 7 \
defensible arcs plus 1 extra) and up to 3 arcs may be destroyed, however \
because 3 will be defended, there are actually only 5 choices of arc to \
destroy, for 10 choices of attack move (assuming that the maximum number is \
attacked). Then the game tree has 350 leaves, each of which requires solving \
a MILP or LP to evaluate the objective value.\
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