Strategies Defined and Illustrated
When strategies were being introduced in Schelling’s course on rational decisions, the following was included in the original homework.
The Three-Way Duel
Anderson, Barnes, and Cooper are to fight a gun duel. They will stand close to
one another, so that each can kill one of the others or deliberately miss. The
first to fire will be chosen at random, and they will rotate in the order Anderson,
Barnes, and Cooper, each firing one shot at a time.If there is more than one survivor after a number of rounds, one of the contenders will be chosen at random and required to shoot one of the others, and this
will be repeated if there is still more than one alive.Before the duel starts, Anderson may make any statement, followed by
a statement from Barnes, and finally one from Cramer. They will adhere to the
|1. ||A contender may not break any commitment he makes in his statement.|
|2. ||He will act in his own best interest when it does not conflict with Rule One.|
|3. ||He will act randomly when it does not conflict with Rules One and Two.|
There are referees to ensure that the rules are followed. If a contender commits himself to a choice of action on a statistical basis (for example, if Anderson
commits himself to miss with a probability of 1/3), the choice will be determined
objectively (by tossing dice, etc.).What is Anderson’s best strategy and his probability of surviving? That is, what
is the most effective commitment Anderson can make?
|A. ||Anderson’s probability of surviving, if he adopts his best strategy, is:|
|B. ||Anderson’s statement, with explanation:|
If you wish to challenge yourself and attempt this on your own before seeing an
answer, read no further at this point.