Editing Zero-sum game (section)

== Definition ==

{{Payoff matrix | Name = Generic zero-sum game
                | 2L = Choice 1          | 2R = Choice 2          |
1U = Choice 1          | UL = −A, A      | UR = B, −B      |
1D = Choice 2          | DL = C, −C       | DR = −D, D    }}

{{Payoff matrix | Name = Another example of the classic zero-sum game
               | 2L = Option 1          | 2R = Option 2          |
1U = Option 1          | UL = 2, −2     | UR = −2, 2      |
1D = Option 2          | DL = −2, 2       | DR = 2, −2    }}
The zero-sum property (if one gains, another loses) means that any result of a zero-sum situation is [[Pareto optimal]]. Generally, any game where all strategies are Pareto optimal is called a conflict game.<ref>{{cite book |first=Samuel |last=Bowles |title=Microeconomics: Behavior, Institutions, and Evolution |url=https://archive.org/details/microeconomicsbe00bowl |url-access=limited |publisher=[[Princeton University Press]] |pages=[https://archive.org/details/microeconomicsbe00bowl/page/n47 33]–36 |year=2004 |isbn=0-691-09163-3 }}</ref><ref>{{cite web |title=Two-Person Zero-Sum Games: Basic Concepts |url=https://neos-guide.org/content/game-theory-basics |access-date=2022-04-28 |website=Neos Guide |publisher=Neos Guide}}</ref>

Zero-sum games are a specific example of constant sum games where the sum of each outcome is always zero.<ref>{{Cite book|last=Washburn|first=Alan|url=http://link.springer.com/10.1007/978-1-4614-9050-0|title=Two-Person Zero-Sum Games|date=2014|publisher=Springer US|isbn=978-1-4614-9049-4|series=International Series in Operations Research & Management Science|volume=201|location=Boston, MA|doi=10.1007/978-1-4614-9050-0}}</ref> Such games are distributive, not integrative; the pie cannot be enlarged by good negotiation.

In situation where one decision maker's gain (or loss) does not necessarily result in the other decision makers' loss (or gain), they are referred to as non-zero-sum.<ref>{{Cite web|title=Non Zero Sum Game|url=https://www.monash.edu/business/marketing/marketing-dictionary/n/non-zero-sum-game|access-date=2021-04-25|website=Monash Business School|language=en}}</ref> Thus, a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, is in a non-zero-sum situation.  Other non-zero-sum games are games in which the sum of gains and losses by the players is sometimes more or less than what they began with.

The idea of Pareto optimal payoff in a zero-sum game gives rise to a generalized relative selfish rationality standard, the punishing-the-opponent standard, where both players always seek to minimize the opponent's payoff at a favourable cost to themselves rather than prefer more over less. The punishing-the-opponent standard can be used in both zero-sum games (e.g. warfare game, chess) and non-zero-sum games (e.g. pooling selection games).<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. {{ISBN|978-1507658246}}. Chapter 1 and Chapter 4.</ref> The player in the game has a simple enough desire to maximise the profit for them, and the opponent wishes to minimise it.<ref>{{Cite book|last=Von Neumann|first=John |title=Theory of games and economic behavior|date=2007|publisher=Princeton University Press|author2=Oskar Morgenstern|isbn=978-1-4008-2946-0|edition=60th anniversary |location=Princeton|pages=98|oclc=830323721}}</ref>