There has been a lot of comment from a range of smart people (Andrew Brandt etc) about Tom Brady's contract extension. A lot of them think there is some sort of underlying trickery - that no person could ever turn down more money. They think every human is a rational economic actor who seeks to maximise his/her utility. And they are right.
Where the commentators are wrong, however, is in equating money with utility. Economics is the study of utility - in simple terms, happiness - and money is merely a proxy for utility (rather than going into great detail, suffice it to say that the more we pay for something, the more we value it.)
So, Tom Brady took short money. Was this motivated by altruism? Unselfishness? A team spirit? No, no, and no. Tom Brady was motivated by selfishness.
What makes Tom happy? Well, money to a certain extent. But there is something called marginal utility. The first $5k you earn give you more pleasure than the next $5k and so on (because the first buy you food and shelter, but the 200th might only let you gold plate your toothbrush). So, Tom figures this: the difference between 9m a year and 20m a year is worth X utility to me. But at this point in time, with all the money I already have, X is *not* a very large number.
However, Tom sees another investment. Investing the difference between 9 and 20 into the team would increase the chance of us winning a Superbowl by Z%. And Z% of Y utility - where Y is the utility he generates from winning another Superbowl - IS GREATER THAN X.
In simple terms, the marginal utility of the extra money he'd get from a "market value" contract is LESS than the utility he anticipates coming from reinvestment in the team.
Tom is selfish. He has acted in a way that is guaranteed to maximise his own utility. But, and this is key, MONEY IS NOT UTILITY. The next time someone tries to tell you that nobody would leave money on the table because we're all selfish, tell him this - "The reason we would leave money on the table is because we are selfish."
Tom Brady: Rational economic self-maximiser. And my quarterback until 2019 :)