In 2001, Russell Crowe starred in A Beautiful Mind, a film based on the life of American mathematician John Nash. A pivotal scene in the movie depicts Nash's eureka moment when developing his thinking around non-cooperative games, or what became widely known as Nash's Equilibrium.
I hope that John Nash, and Russell Crowe for that matter, would excuse my poor attempt to explain such a brilliant theory, but here goes.
While watching his friends jostle for position to ask a group of women to dance, it occurred to Nash that an accepted theory by the eighteenth-century economist Adam Smith was incomplete. Smith had stated that in economics the best result comes from everyone doing what is best for themselves. Nash's insight was that the best result actually comes from everyone in the group doing what is best for themselves, and for the group. Nash's Equilibrium became an important contribution to the field of economic game theory, which is now used in many modern applications, from online gambling to traffic flow analysis. Sadly, I believe, it resulted in none of the men getting to dance with a beautiful woman that night (at least in the movie).
So what does this part-history, part-Hollywood lesson have to do with team productivity? Well, I reckon quite a lot. This is what I call game theory productivity.
Our team is most productive when we work in a way that is productive for ourselves as individuals, and productive for the team as a whole.