What is a zero-sum game?
In: 115
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.
Answer:
Its actually very simple to put
Any game where: If i win you loose, if you win i loose.
Ie direct advantage for one player is direct disadvantage to opponents
A zero-sum game is an activity that distributes rewards/punishments so that they even out to nothing overall. No net-gain or net-loss when you take *everyone* into account.
* If I win a ranked chess game against you, I might take 5 ELO rating points from you. I go +5 and you go -5.
* If I have $100, and share $50 with you, then that means I am down $50.
* If I fire Alice to hire Bob, the same work gets done and the same amount of money is paid overall.
Zero-sum games are typically ‘win-lose’ scenarios like this.
–
It’s easy to think that every ‘game’ is like this. However, not always. Often, one side wins or loses more than the other loses or wins, or maybe both sides win, or maybe both sides lose:
Some positive-sum “games” might be:
* I’m choking on some food and will die, but you do some first aid and save my life. You spent some minor effort in trying to save me, and if it works, you save my entire life. I gain far more than you lost.
* Imagine that there is a nearby forest that we use as a supply of lumber. I know how to make chairs, and you know how to start fires (and neither of know the other skill). If we didn’t cooperate, I’d sit in a chair in the cold, and you’d sit on the ground next to a warm fire. If we cooporate, we can both sit in chairs by the fire. Cooperation costs us little-to-nothing and we both benefit.
* We play a game of chess and both have a fun time. That’s a win-win, in a sense.
Some negative-sum games might be:
* You accidentally burn down our shared forest. Neither of us have any lumber now, so we both lost.
* We get into a fight over who gets to use the last of the firewood. We both fatally wound each other and die from our injuries. We both lost.
* A protest is a lose-lose, at least in the short-term. The protestors bear the inconvenience of protesting instead of doing other things like study/work/hobbies/leisure/rest/etc, and the protest inconveniences others (perhaps the government).
* Strikes are similar to protests. The workers forgoe the chance to working and collect their wage, and the employer doesn’t get the labor of its workforce.
* We play a game of chess, but neither of us like chess, so the time spent on it is lost and we got no enjoyment from it.
* EDIT: and of course wars, where overall there is a loss of life and wealth and materials, and at most one side wins, but they win less than both sides lost collectively.
Note that ‘lose-lose’ games aren’t always bad. Often they are, but I think protests and strikes can be very good forces for change, but they are, in the short term, lose-lose. I think the value of them is in proving that you’re willing to take a lose-lose, and hence pressure the other side to change in order to stop their losses.
I have an apple and you want it. We play rock, paper, scissors and the winner gets the apple. There is only one apple, so only one person can win by taking from the other person.
Zero sum game is when you fight for the pizza with your brother. If you get more pizza, your brother gets less.
An example of non zero sum game is when you go to steal some apples from neighbor with your brother. You can compete against your brother, but the amount of apples you pick does not hinder the amount of apples your brother can pick as there are plenty.
In that example the neighbor gets less apples, so to include him to the equation makes it zero sum game again. And that is how it is often in the world. However, consider picking lingonberries, there are plenty in the forest and if nobody picks them up, they just rot.
Zero sum game is when you fight for the pizza with your brother. If you get more pizza, your brother gets less.
An example of non zero sum game is when you go to steal some apples from neighbor with your brother. You can compete against your brother, but the amount of apples you pick does not hinder the amount of apples your brother can pick as there are plenty.
In that example the neighbor gets less apples, so to include him to the equation makes it zero sum game again. And that is how it is often in the world. However, consider picking lingonberries, there are plenty in the forest and if nobody picks them up, they just rot.
Latest Answers