# What is a zero-sum game?

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What is a zero-sum game?

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In game theory, a zero-sum game is any game where the total winnings equal the total losses.

For example if you and I bet each other \$5 on the outcome of a race – if you win, I give you \$5, and if I win, you give me \$5. That’s a zero-sum game, because the winner gets +\$5, the loser gets -\$5, and the total of wins and losses is \$0.

A zero-sum game means that for every gain that one party makes, another party loses an equivalent amount – if one person wins, another loses. Think of tennis, or baseball, or most sports where if I’ve won a point or a game, the opponent has lost that point. If you and I bet \$5 on the Super Bowl, even odds, it’s a zero-sum game, because one of us will gain \$5 and the other will lose \$5.

Non-zero sum games are uneven, where a win for one side isn’t necessarily balanced on the other. There are such things as win-win situations, or lose-lose, for example. A common example is “A husband and wife want to go out tonight – he wants to see a boxing match, but she wants to see the ballet. Both of them would be happier going with each other than going alone to either event.” So if they go to the ballet , the husband “wins less,” and the wife “wins more,” because he’s still happy not being alone, but neither of them has actually lost in this example.

Another common example is a pirate ship attacking a merchant ship – not really a “game,” but the same idea applies. If the merchant ship wins the fight, they haven’t gained anything from the pirates – they’re just continuing on exactly as they were before. Whereas if the pirate ship wins, they’ll get treasure, while the other side has lost a treasure that wasn’t even really theirs (since they were trading it) and has likely lost their lives as well. Not a zero-sum.

If I steal \$100 from you, you lose 100, I gain 100, that works zero.

But…

You may also become anxious, humiliated, angry, just by the fact I may feel guilty. So suddenly, we all lose something.

It’s a game where the wins and losses, when combined, equal 0. For example, say that you have four buddies that all decide to pitch in part of their lunch. One person puts in a cheese stick. One person puts in a sandwich. One person puts in a chocolate milk. And one person puts in fruit snacks. Then you spin a wheel that points at one of the four people, who gets to keep all of the stuff in the pot. All four people put in 1 item for 4 total items. Then one person got all 4 items. So the gain (3 items) are the same as the losses (3 items). That’s a zero sum game.

A zero sum game is where if someone wins, someone else loses. A lot the routine games that we talk about are zero sum, someone wins while the opponent loses. Chess, checkers, tic tac toe, tennis, battleship, etc are all zero sum games. Some games, like a marathon, we don’t say are zero sum. If winning means finishing the race, then there is no limit on how many winners there are. Or if winning means having a good time, then there are no limits to how many winners there are.

The idea is often brought up in terms of business or politics. Performing an endeavor as if something is a zero sum game means that you are determined in winning because if you don’t win, it means you lose. This is especially true in things like business and politics. If a business is #2 in their field, and they make millions of dollars and have great products and employees then it sounds like they are prosperous. However, if the CEO views the business as a zero sum game, it means that the CEO considers the business a loser because it’s in second place. Someone like this might lash out at employees or maybe pursue some underhanded tricks to either make the company appear to be doing better on some metric, or sabotage the success of a rival company.

That’s kind of the core of it – a zero sum game means that all participants are rivals rather than collaborators, and one of them will be a winner and all the others are losers. It is often a pretty dismal way to look at the world.