You are taking a course in the application of game theory to
coaching football. The following problem has been assigned.
You are trying to decide on which offensive play to run in order
to have the best chance of success against your opponent. You have
a choice of five offensive plays, and your scouting report tells
you that the opposing coach always uses one of three defensive
strategies. The payoff matrix below (you are the row player, the
opposing coach is the column player) shows, for each offensive
play/defensive strategy combination, the historically average
number of yards gained or lost for each play.
Defense 1 Defense 2 Defense 3
Play 1 0 − 1 5
Play 2 7 5 10
Play 3 15 − 4 − 5
Play 4 5 0 10
Play 5 5 −10 10
What play should you call, and why? (The explanation is just as
important as the choice of play.)
