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Lumifer comments on Thomas C. Schelling's "Strategy of Conflict" - Less Wrong
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In two player zero sum games, vengeance (hurting self to hurt other more) is impossible, as are threats and destruction in general -- because the total score is always the same. They are ruthless in that to gain score you must take it from the other player (also eliminates cooperation), but there can be no nuking. If the game is variable sum (or zero sum with extra players), you again gain the ability to unilaterally and unavoidably lower someone's score (the score can be destroyed in variable sum games, or transferred to the other players in zero sum games, allowing for vengeance, punishment, destruction, team cooperation, etc.
It may be that you're using a restrictive definition of zero-sum games, but generally speaking that is not true because of the difference between the final outcome and the intermediate score-keeping.
Consider e.g. a fight to the death or a computer-game match with a clear winner. The outcome is zero-sum: one player wins, one player loses, the end. But in the process of the fight the score varies and things like hurting self to hurt the other more are perfectly possible and can be rational tactics.
I think you're mixing levels- in a match with a clear winner, "hurting self" properly means "make my probability of losing higher" not "reduce my in-game resources." I can't reduce my chance of winning to reduce my opponent's chance of winning by more- the net effect is increasing my chance of winning.
I am not so much mixing levels as pointing out that different levels exist.
You're confusing yourself because you're mixing scoring systems -- first you say that the game is zero sum, win or lose, then you talk about variable sum game resources. In a zero sum game, the total score is always the same; you can either steal points or give them away, but can never destroy them. If the total score changes throughout the game, then you're not talking about a zero sum game. There's no different levels, though you can play a zero sum game as a variable sum game (I won while at full health!).