Editing Zero-sum game (section)

{{Short description|Situation where total gains match total losses}}
{{Distinguish|Empty sum|Zero game}}
{{Other uses|Zero sum (disambiguation)}}
'''Zero-sum game''' is a [[Mathematical model|mathematical representation]] in [[game theory]] and [[economic theory]] of a situation that involves two [[competition|competing]] entities, where the result is an advantage for one side and an equivalent loss for the other.<ref>{{Cite book |title=Cambridge business English dictionary |date=2011|publisher=Cambridge University Press|isbn=978-0-521-12250-4|location=Cambridge|oclc=741548935}}</ref> In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero.<ref>{{cite web |last1=Blakely |first1=Sara |title=Zero-Sum Game Meaning: Examples of Zero-Sum Games |url=https://www.masterclass.com/articles/zero-sum-game-meaning#what-is-a-zerosum-game |website=Master Class |publisher=Master Class |access-date=2022-04-28}}</ref>

If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Thus, [[Fair cake-cutting|cutting a cake]], where taking a more significant piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if [[marginal utility|all participants value each unit of cake equally]]. Other examples of zero-sum games in daily life include games like [[poker]], [[chess]], [[sport]] and [[Contract bridge|bridge]] where one person gains and another person loses, which results in a zero-net benefit for every player.<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|oclc=830323721}}</ref> In the markets and financial instruments, futures contracts and options are zero-sum games as well.<ref>{{Cite web|last=Kenton|first=Will|title=Zero-Sum Game|url=https://www.investopedia.com/terms/z/zero-sumgame.asp|access-date=2021-04-25|website=Investopedia|language=en}}</ref>

{{anchor|Non-zero-sum}}In contrast, '''non-zero-sum''' describes a situation in which the interacting parties' aggregate gains and losses can be 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 [[LP duality|linear programming duality]],<ref name="Binmore2007"/> or with [[Nash equilibrium]]. [[Prisoner's dilemma|Prisoner's Dilemma]] is a classic non-zero-sum game.<ref>{{Cite journal|last1=Chiong|first1=Raymond|last2=Jankovic|first2=Lubo|date=2008|title=Learning game strategy design through iterated Prisoner's Dilemma|url=http://www.inderscience.com/papers/../offer.php?id=20957|journal=International Journal of Computer Applications in Technology|language=en|volume=32|issue=3|pages=216|doi=10.1504/ijcat.2008.020957|issn=0952-8091|url-access=subscription}}</ref>