Zero-sum game

Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two sides, where the result is an advantage for one side and an equivalent loss for the other.^[1] 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.^[2]

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 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 all participants value each unit of cake equally. Other examples of zero-sum games in daily life include games like poker, chess, and bridge where one person gains and another person loses, which results in a zero-net benefit for every player.^[3] In the markets and financial instruments, futures contracts and options are zero-sum games as well.^[4]

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 linear programming duality,^[5] or with Nash equilibrium. Prisoner's Dilemma is a classic non-zero-sum game.^[6]

^ Cambridge business English dictionary. Cambridge: Cambridge University Press. 2011. ISBN 978-0-521-12250-4. OCLC 741548935.
^ Blakely, Sara. "Zero-Sum Game Meaning: Examples of Zero-Sum Games". Master Class. Master Class. Retrieved 2022-04-28.
^ Von Neumann, John; Oskar Morgenstern (2007). Theory of games and economic behavior (60th anniversary ed.). Princeton: Princeton University Press. ISBN 978-1-4008-2946-0. OCLC 830323721.
^ Kenton, Will. "Zero-Sum Game". Investopedia. Retrieved 2021-04-25.
^ Cite error: The named reference Binmore2007 was invoked but never defined (see the help page).
^ Chiong, Raymond; Jankovic, Lubo (2008). "Learning game strategy design through iterated Prisoner's Dilemma". International Journal of Computer Applications in Technology. 32 (3): 216. doi:10.1504/ijcat.2008.020957. ISSN 0952-8091.

[1] Cambridge business English dictionary. Cambridge: Cambridge University Press. 2011. ISBN 978-0-521-12250-4. OCLC 741548935.

[2] Blakely, Sara. "Zero-Sum Game Meaning: Examples of Zero-Sum Games". Master Class. Master Class. Retrieved 2022-04-28.

[3] Von Neumann, John; Oskar Morgenstern (2007). Theory of games and economic behavior (60th anniversary ed.). Princeton: Princeton University Press. ISBN 978-1-4008-2946-0. OCLC 830323721.

[4] Kenton, Will. "Zero-Sum Game". Investopedia. Retrieved 2021-04-25.

[Binmore2007-5] Cite error: The named reference Binmore2007 was invoked but never defined (see the help page).

[6] Chiong, Raymond; Jankovic, Lubo (2008). "Learning game strategy design through iterated Prisoner's Dilemma". International Journal of Computer Applications in Technology. 32 (3): 216. doi:10.1504/ijcat.2008.020957. ISSN 0952-8091.

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