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Rock-paper-scissors is a zero-sum game, however I remember a different phrase that means essentially the same thing - when each member of a group of objects has exactly balanced strengths and weaknesses.

Edit: The phrase I'm looking for is not a synonym for zero-sum game, I'm looking for something that describes a scenario in which A trumps B, B trumps C, and C trumps A. Are there any words that describe non-linear ranking?

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    A zero sum game does not describe a game in which "every participant has exactly balanced strengths and weaknesses", it describes a game where the outcome is such that whatever one member gains, another member must have necessarily lost. There is no input or winnings from the outside to compete for. – Dan Bron Mar 16 '16 at 18:08
  • @DanBron so I'm looking for a word that describes a different trait of Rock-paper-scissors – Jesse Adam Mar 16 '16 at 18:11
  • Since the example is incorrect I'll ignore it. What about deadlock. I've also hear fungible used in push there, pop out here. Does that make it balanced? – user116032 Mar 16 '16 at 19:52
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    It's rather "non-transitive" ordering than "non-linear" ranking. – Graffito Mar 16 '16 at 23:30
  • I'm voting to close this question as off-topic because the premise is incorrect. – jimm101 Mar 17 '16 at 2:09
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I would call that a symmetric opponent game or simply a symmetric game. I don't see it as a common phrase since most games are assumed symmetric unless stated otherwise.

I'm not sure BoardGameGeek.com is a valid citation, but... https://boardgamegeek.com/thread/636692/game-balance-symmetry-vs-asymmetry

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  • I disagree that games are assumed symmetric unless stated otherwise. It may be true in certain contexts though. Would you care to clarify what context you're thinking about? – user152004 Mar 17 '16 at 4:50
  • I suppose it also matter to what degree of symmetry we are talking, but if you were explaining Rock, Paper, Scissors, you would not have make a specific point to clarify that we both can use Rock. Or to say that my bishop in chess has the same movements as your bishop. Most people would assume this is the case. – BenL Mar 17 '16 at 16:26
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A Nash Equilibrium is where nobody can benefit by changing their strategy. That might be what you are thinking of.

In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.

https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=Nash+Equlibrium

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