# Zero-Sum Game

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A Zero-Sum Game is a competitive game in which a game participant's utility change is exactly balanced by the other game participants utility change.

**Context:**- It can range from being a Two-Player Zero-Sum Game to being a Multiplayer Zero-Sum Game."
- It can range from being a Complete Information Zero-Sum Game to being an Imperfect Information Zero-Sum Game."
- It can (typically) be a Winner-Take-All Game.

**Example(s):**- a Chess Game.
- a Poker Game.
- a Game of Life.
- a Futures Market.
- a Stock Market because:
- a stock transaction cannot both be the right time to sell and the right time to buy
- for every unit of currency paid in a unit of currency comes out.
- if everyone decided to sell at the same moment (a run on the market) then the price would be zero.

- …

**Counter-Example(s):**- Non-Zero-Sum Game, such as a labor market.

**See:**Game Theory, Cake Cutting, Marginal Utility, Minimax Theorem, Nash Equilibrium, Lump of Labor Fallacy.

## References

### 2014

- http://www.investopedia.com/terms/z/zero-sumgame.asp
- QUOTE: A situation in which one person’s gain is equivalent to another’s loss, so the net change in wealth or benefit is zero. A zero-sum game may have as few as two players, or millions of participants. Zero-sum games are found in game theory, but are less common than non-zero sumgames. Poker and gambling are popular examples of zero-sum games since the sum of the amounts won by some players equals the combined losses of the others. So are games like chess and tennis, where there is one winner and one loser. In the financial markets, options and futures are examples of zero-sum games, excluding transaction costs. For every person who gains on a contract, there is a counter-party who loses. However, the stock market is not a zero-sum game.

### 2013

- (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/zero-sum_game Retrieved:2013-12-26.
- In game theory and economic theory, a
**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. Thus cutting a cake, where taking a larger piece reduces the amount of cake available for others, is a zero-sum game if all participants value each unit of cake equally (see marginal utility). In contrast, non–zero sum describes a situation in which the interacting parties' aggregate gains and losses are either less than or more than zero. A zero-sum game is also called a*strictly competitive*game while non–zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, or with Nash equilibrium.

- In game theory and economic theory, a

### 1989

- (Friedman et al., 1998) ⇒ Stewart D. Friedman, Perry Christensen, and Jessica DeGroot. (1998). “Work and Life: The End of the Zero-sum Game." Harvard business review 76