Non-zero-sum game: In game theory, a situation where one decision’s gain (or loss) doesn’t always entail a loss for the other choice (or gain). In other words, when none of the players’ wins or losses equals zero, everyone can gain a win-win game.
Game with Non-Zero Sum
A Non-Zero-Sum Game is one in which a win for one side does not always imply a loss for another, and a loss for one party does not always imply a win for the other. All participants in a non-zero-sum game have the potential to win or lose. This is in stark contrast to a Zero-Sum Game, when one party’s victory automatically results in another party’s defeat, as in competitive basketball games.
Prisoner’s Dilemma In Non Zero Sum Game
The Prisoner’s Dilemma, where two inmates are interviewed separately and are given a deal whereby one confesses, he is released. Still, the other prisoner is sentenced to ten years in jail, which is a classic illustration of a non-zero-sum game scenario. If both admit, they will each get two years in prison.
They each risk receiving two years in prison if they confess. They would each receive six months in prison for a petty offense if they kept their mouths shut. Naturally, remaining silent and serving the required six months would be the best course for both.
However, as they are unaware of one another’s plans, they will each worry that they will have to serve a 10-year sentence if the other person confesses. They will feel pressured to defend what they believe to be in their best interests, and as a result, they will often confess, resulting in both of them losing and receiving a two-year sentence.
What is a Zero Sum Game?
A zero-sum game is one in which a player’s losses in a transaction lead to an equal rise in the opponent’s gains. It has this moniker because the net result of gains and losses on both sides is zero.
Is trading in stocks a zero-sum game?
A zero-sum game exists when comparing investors’ collective stock market performance to an index. An index’s value is always zero-sum because it accounts for both gains and losses.
For instance, when evaluating market outperformance, every outperformance signifies a loss or underperformance somewhere else. But since the stock market system as a whole does not fit the definition of a game with players, it should be viewed as something other than a zero-sum game. The only performance compared to the stock market index is an individual’s.
An example of a non-zero-sum game
A non-zero-sum game is one in which the outcome of the game results in either a net gain or loss for the system.
Even if it can appear to be one at first glance, a competition between commercial ships and pirate ships illustrates what should be regarded as a non-zero-sum game.
But since the stock market system as a whole does not fit the definition of a game with players, it should not be viewed as a zero-sum game. The only performance compared to the stock market index is an individual’s.
Source and Relevance
The origin of the zero-sum idea was that the defeat of a rival could only achieve victory. The concept probably originated from a misunderstood view of finance and economics in which the challenged entity was viewed as fixed and unalterable. So, the only way to turn a profit was to guarantee the death of the competitors.
However, modern knowledge of economics expands the horizon and explains why not all competitions come under this heading. It is feasible for each participant to record a win. For instance, all parties benefit from a trade, according to the traditional (Ricardian) view of trade.
Theory of Non- Zero Sum Games
Since there is always an optimal solution, the concept of zero-sum games differs greatly from that of non-zero-sum games. This, however, rarely reflects the conflicts people deal with daily. In the real world, solutions to problems are rarely simple. The theory of non-zero-sum games is a subfield of game theory that more accurately captures the mechanics of the world we live in.
In contrast to zero-sum games, non-zero-sum games lack an agreed-upon solution. That is to say, neither a conclusion that can be predicted nor a single ideal method that is preferred to all others. Contrary to zero-sum games, which are only strictly competitive, non-zero-sum games typically have both cooperative and competitive features. As a result, they are not strictly competitive. Players involved in a non-zero-sum dispute have some complementing and some wholly antagonistic objectives.
A Standard Case
A straightforward illustration of a common non-zero-sum game is The Battle of the Sexes. In this example, a husband and his wife wish to go for a night. They have decided to attend either a ballet or a boxing event. Both would rather go together than by themselves. Although he would rather go to the ballet with his wife than fight, the man chooses to attend boxing matches.
The wife would also love to attend the dance, but she would rather accompany her husband to the fight than attend the ballet alone. Below is a matrix that represents the game:
A Non-Zero-Sum Game Communication Analysis
According to common wisdom, having the ability to speak could never be detrimental to a player because they could always choose not to do so. But being unable to communicate is different than refusing to communicate. In certain situations, a player may benefit from their incapacity to speak.
In an experiment, Luce and Raiffa examine what occurs when players can converse with what occurs when they cannot. The game that Luce and Raiffa created is as follows:
There is no chance of accusations being made if Susan & Bob cannot converse. Therefore, Susan and Bob cannot play strategy A any better than they currently are.
| Bob | Susan | |
|---|---|---|
| A | 1, 2 | 3, 1 |
| B | 0, -200 | 2, -300 |
The first component of the item set represents the payoff matrix for the wife, whereas the second member of the ordered pair represents the payoff matrix for the husband.
The circumstance exhibits a non-zero-sum, semi-competitive conflict, as observed from the matrix above. The wife and husband have a common interest in attending activities together rather than separately.
| Husband | Wife |
| Boxing Match | Boxing Match |
| 2, 3 | 1, 1 |
| 1, 1 | 3, 2 |
Bob gains two, and Susan gains one as a result. When communication is permitted, the circumstance is challenging. Susan can intimidate Bob by stating that she will use method B if he doesn’t agree. Bob will lose one, and Susan will gain two if Bob gives in (as opposed to Susan gaining one and Bob gaining 2 when communication is not allowed).
Summary
It is no longer necessary for the player payoffs in a non-zero-sum game to add up to a fixed amount. Both players might now benefit or suffer losses simultaneously.
Limited alternatives
The Battle of the Sexes scenario from before appears to be an impasse. However, the issue can be resolved if the woman or the husband restricts the other’s options.
Bob gains two, and Susan gains one as a result. When communication is permitted, the circumstance is challenging. Susan can intimidate Bob by stating that she will use method B if he doesn’t agree. Susan will gain two if Bob agrees, while Bob will lose one if Bob refuses.
In the game “Chicken,” two players start their two extremely fast cars at different ends of a long, straight road and race them toward each other. One is referred to as a chicken if he turns before the other. Of course, they will collide if neither swerves. The worst potential outcome is colliding. Thus we give this a value of 0. We give this a value of 3 since having your adversary be the chicken is the ideal outcome. Being the chicken is the second-worst possible outcome. Therefore we give it a value of 1. The final scenario involves both drivers swerving. This is better than being the chicken because neither has less honor.
| Swerve | 2, 2 | 1, 3 |
|---|---|---|
| Swerve | Drive Straight | |
| Drive Straight | 3, 1 | 0, 0 |
We give it a value of 2, but winning is less satisfying than winning. This could be given a payoff matrix:
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The worst-case scenario in chicken is mutual defection, unlike the prisoner’s dilemma. The inverse of what the other player does is what both players desire to do.
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The volunteer problem refers to the game of chicken when there are more than two players. In a volunteer’s problem, one participant must behave in a way that will benefit everyone else. Let’s say, Paris Carver, Wai Lin, and James Bond are all locked up in three soundproof rooms by Elliot Carver. If none of the three press a button in an hour, Elliott will inject toxic gas into their cells. We give it a value of 2, but winning is less satisfying than winning. This could be given a payoff matrix:
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The worst-case scenario in chicken is mutual defection, unlike the prisoner’s dilemma. The inverse of what the other player does is what both players desire to do.
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The volunteer problem refers to the game of chicken when there are more than two players. In a volunteer’s problem, one participant must behave in a way that will benefit everyone else. Let’s say, Paris Carver, Wai Lin, and James Bond are all locked up in three soundproof rooms by Elliot Carver. If none of the three press a button in an hour, Elliott will inject toxic gas into their cells.
Assume you are James Bond, and after 59 minutes, Paris & Wai Lin still need to press the button. They appear to have determined that you should make a sacrifice, but you are unwilling to do so. Vowing never to press the button is useless since you will all perish if you do. The ideal time to press the button is just before it disappears. Conflict resolution depends on chance and reactions because it is impossible to predict when this will occur.
Frequently Asked Questions
These frequent questions may help you regarding Non-Zero Sum Game:
1. What does the term “non-zero-sum game” mean?
In game theory, a circumstance in which one decision maker’s gain (or loss) does not always result in the loss of the other choice maker (or gain). In other words, a game that benefits everyone involved when a player wins and losses do not equal zero.
2. Can a non-zero-sum game exist?
Contrary to zero-sum games, which are only strictly competitive, non-zero-sum games typically have both cooperative and competitive features. As a result, they are not strictly competitive. Players in a non-zero-sum dispute have some goals that are complementary and some that are fully at odds with one another.
3. Is NFT a game of zero-sum?
In game theory, a win scenario, also known as a win-win game or a non-zero-sum game, is one in which cooperation, agreement, or group engagement benefits every participant.
4. Is monopoly a game of zero sum?
A good illustration of a zero-sum sport is Monopoly. An inverse relationship between one player’s gain and then another player’s loss defines a zero-sum game.
5. What sort of games doesn’t have a zero-sum outcome?
An example of a non-zero-sum game A non-zero-sum game is one in which the outcome of the game results in either a net gain or loss for the system. Even if it can appear to be one at first glance, a competition between commercial ships and pirate ships is an example of what should be regarded as a non-zero-sum game.
6. What are some non-zero-sum game illustrations?
A non-zero-sum game is one in which the outcome of the game results in either a net gain or loss for the system. Even if it can appear to be one at first glance, a competition between commercial ships and pirate ships is an example of what should be regarded as a non-zero-sum game.
7. Who created non-zero-sum games? 7.
John proposed this group of ideas (zero-sum, nonzero-sum, and positive-sum).In 1944, Oskar Morgenstern and von Neumann created the mathematics of games.
8. What is the mindset of a zero-sum game?
a kind of game in game theory where players’ earnings and losses equal zero. Because the total number of resources accessible to the players is fixed, one player’s success must necessarily result in the failure of all other players.
9. Is romantic love not a zero-sum game?
Love is not a zero-sum game; for instance, loving your mother-in-law does not take away from loving your own mother. However, when we are envious, we think that love is a limited resource and that there isn’t enough of it to go around.
10. Is a game of love non-zero-sum?
Love is not a zero-sum game; for instance, loving your mother-in-law does not take away from loving your own mother. However, when we are envious, we believe that affection is a limited resource and that there isn’t enough of it to go around.
Conclusion
The player payoffs in a non-zero-sum game are no longer required to add up to a fixed amount. Both players can now win or lose, depending on the situation.