Game Theory Example
Consider a military strategist who is trying to prevent an enemy from attacking his base with 1
elite battalion and 1 smaller squadron. There are two paths—Cooper and Center—to the base
from which the enemy can attack, so the strategist is planning to deploy the elite battalion to 1
of the paths and the smaller squadron to the other path. In addition, if the strategist deploys
the elite battalion to same path from which the enemy attacks, the probability the strategist is
successful is much larger than if the enemy’s attacking path is defended by the smaller
squadron. Specifically, the table below shows the probability that the strategist is successful
given the paths of the elite battalion and the enemy attack.
Elite Battalion Enemy Attacking Path
Deployment
Cooper
Center
Cooper
0.95
0.23
Center
0.24
0.91
a) Determine whether the strategist should use a pure strategy. If so, what is the probability
that the strategist is successful? If not, what are the bounds on the probability that the
strategist is successful?
b) Formulate a linear program for the strategist’s strategy. To save some time, you may refer to
Cooper and Center as paths 1 and 2, respectively.
c) Formulate, but do not solve, a linear program for the enemy’s strategy.