## 9/19/12

### Zero-Sum Game Theory By (almost) Dr. Stuart Rhoden

Stuart Rhoden (@ChitownStu) wrote the following at his blog:
"I made the argument that the education policy landscape is a game.  I'd also argue that politics as a whole is a game - some would argue, more often than not, a zero-sum game. A zero-sum game is briefly defined as one making gains and the other side making equally similar gains and therefore the total gains are zero.  As a political science major, and policy wonk in both Washington DC and Chicago, I understand the hand to hand combat of politics - for better or worse.  I am also seeped in a deep, philosophical understanding that there are those in education who believe this divisiveness does not exist."
Here is the definition of a zero-sum game:
zero–sum game is a mathematical representation of a situation in which a participant's gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s). If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero.
So, to be clear, in order for things to sum to zero, one side must win, the other must lose, not have both sides win as Stu says, because then the sum would surely be more than zero, right?

For instance:

Stu would call the equation below 'zero-sum' according to his definition, even though the sum is positively NOT zero:
For this equations, a = gains:
(+a) + a = 2a (not zero, so this is non zero-sum)

Below we see a zero sum equation as defined in the actual definition of zero-sum games.

For this equations, a = gains (and clearly -a equals losses):
(+a) + (-a) = 0 (zero sum)

So Stu, explain yourself and your deep understanding of stuff.