2022-08-01

Where the term "zero-sum" comes from

In 1925, John von Neumann published one of the first papers introducing "game theory" into popular discourse. In it, he explained that most games are just a series of events. Some of those events depend entirely on chance–which von Neumann calls 'draws'– and others on the decision of a player–what von Neumann calls 'steps.'

Ultimately, he concluded a game, as The Man from the Future explains, "could be represented simply as the choice by each player of a single strategy (effectively an amalgam of all the strategies they play in the game), followed by a calculation of their respective payouts that accounts for everyone's choices (and which factors in their luck)."

But he couldn't get any further in his thinking with multi-player games, so he started thinking about games with two players whose payouts equal 0.

Since there are only two players, one has to win and the other has to lose. What one person wins is equal to what the other person loses. So if Player A wins $5, then Player B has to have lost$5 somehow. The two payouts, when added together equal 0 (5 + (-5) = 0). Therefore, these games were determined to be zero-sum: the sum equals zero.

Why this matters

The terms "zero-sum" and "positive-sum" are popular in the online world I hang out in. The benefits of the world and the creator economy being "positive-sum" or touted and the mindset that the world is "zero-sum" is negative. I always understood what they meant, but didn't know the background behind them. It turns out, John von Neumann helped birth these terms into the world through his earlier work on game theory.

The paper in which he lays out these terms is the one where he describes his 'minimax' strategy. In our example above, Player B wants to minimize the maximum amount of money they can lose and Player A wants to maximize the minimum amount they can win (called the 'maximin' strategy).

People who are described as having a "zero-sum mindset" are those that don't think there can be multiple winners. They'll do anything they can to climb the ladder or make the sale. They are also usually very jealous of other people's success because in their world, if someone else is winning, that means they're losing.

Though that's not how the world really works, so the world can be described as "positive-sum." There is enough winnings for everyone. Thankfully this is the case, because we're a few million years late to the party.

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