Game theory [interactive decision theory] is mainly used in economics, political science, and psychology, as well as logic and biology.

I believe that I know that tennis serving and football penalty shooting more-or-less stick to their game-theoretical solutions. But are there sports that explicitly use game-theoretical analysis? (Or, perhaps easier to answer, are there game theorists employed or consulted by certain teams or individual players?)

NB: I am particularly interested in play or race strategy, not in acquisition strategy. (Moneyball, besides being statistical, not game-theoretical, isn't relevant to my question.)

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    I am sure the loaning of Romelu Lukaku by Chelsea to other premiership teams is an implementation of Game Theory. Giving your best striker to another team so they can defeat your competitors, yet is barred from playing against yourself.
    – user2096
    Dec 31 '13 at 18:53
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    Interesting article on penalties www2.owen.vanderbilt.edu/mike.shor/courses/game-theory/docs/…
    – RoB
    May 1 '14 at 8:13

Game theory comes into play in American football play-calling. To simplify the game, consider that the offense can run either a running play or a passing play. The passing play generally has potential for more yards gained, but less chance of success than a running play. The defense, on the other hand, also chooses a play that is either focused on stopping a running play or a passing play.

The coach calling the offensive play needs to look at the situation the team is in and balance the risk and reward for each type of play. The Normal-form game matrix might look something like this:

Defense calls running Defense calls passing
Offense calls running 0-3 yards gained 7+ yards gained
Offense calls passing 10-15+ yards gained 0 yards gained

Of course, the numbers in the matrix are just guesses based on how well the players on each team are playing, but coaches have something like this in mind when they are calling plays.

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