I sometimes think of game theory as being roughly divided in three parts, like Gaul. There’s competitive zero-sum game theory, there’s cooperative game theory, and there are games where players compete but also have some shared interest. Except this third part isn’t a middle ground. It’s actually better thought of as ultra-competitive game theory. Zero-sum settings are relatively harmless: you minimax and that’s it. It’s the variable-sum games that make you nuke your neighbour.
Could you clarify that last bit for me? You seem to have a valid point but I don’t think I can glean it from that wording. I can imagine plenty of scenarios in which competitive zero-sum game theory will suggest that I nuke my neighbour. The most obvious example being if I kill them all and take their stuff and I think I can get away with it. Common interests appear not to be necessary.
Of course some real world zero-sum games are ruthless too, but I haven’t seen anything as bad as the nuke game, and it is variable-sum. Peace benefits everyone, but if one side in an arms race starts getting ahead, both sides know there will be war which harms both. If the game was zero-sum, war would’ve happened long ago and with weaker weapons.
The book gives an example of both Soviets and Americans expending effort on submarine-detection technologies while both desperately hoping that such technologies don’t exist, because undetectable submarines with ICBMs are such a great retaliation guarantee that no one attacks anyone.
Just remember that once you nuke (that is destroy) something, you have left the bounds of zero-sum game and quite likely entered a negative sum game (though you may end up having positive outcome, the sum is negative).
(though you may end up having positive outcome, the sum is negative).
Well isn’t this exactly the problem cousin_it is referring to when the game is non-zero sum? It means that I might need to take 1000 utils from you in order to gain 50 utils for myself. (or even: I might need to take 1000 utils from you in order to limit my losses to 50 utils).
It’s possible that it will be a negative sum. It is also possible in principle that it has become a positive sum. The sign of the ‘sum’ doesn’t actually seem to be the important part of the quoted context here, rather the presence or absence of a shared interest.
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.
I have reread the context and I find I concur with wedrifid_2009.
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.
Vengeance is impossible, threats are irrelevant but destruction most certainly is not. Don’t confuse the arbitrary constraint “the total score is always the same” with the notion that nothing ‘destructive’ can occur in such a game. What is prevented (to rational participants) is destruction for the purpose of game theoretic influence.
Consider a spherical cow in (a spaceship with me in a) vacuum. We are stranded and have a fixed reserve of energy. I am going to kill the spherical cow. I will dismember her. I will denature the proteins that make up her flesh. Then I will eat her. Because destroying her means I get to use all the energy and oxygen for myself. This includes the energy that was in the cow before I destroyed her. It’s nothing personal. There was no threat. I was not retaliating. There was neither punishment nor cooperation. Just destruction.
ie. One of these things is not like the other things, one of these things just doesn’t belong:
vengeance, punishment, destruction, team cooperation, etc
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.
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.
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!).
Could you clarify that last bit for me? You seem to have a valid point but I don’t think I can glean it from that wording. I can imagine plenty of scenarios in which competitive zero-sum game theory will suggest that I nuke my neighbour. The most obvious example being if I kill them all and take their stuff and I think I can get away with it. Common interests appear not to be necessary.
Of course some real world zero-sum games are ruthless too, but I haven’t seen anything as bad as the nuke game, and it is variable-sum. Peace benefits everyone, but if one side in an arms race starts getting ahead, both sides know there will be war which harms both. If the game was zero-sum, war would’ve happened long ago and with weaker weapons.
The book gives an example of both Soviets and Americans expending effort on submarine-detection technologies while both desperately hoping that such technologies don’t exist, because undetectable submarines with ICBMs are such a great retaliation guarantee that no one attacks anyone.
Thanks, that makes sense. It also brings to mind some key points from Robin’s talk on existential risks.
Just remember that once you nuke (that is destroy) something, you have left the bounds of zero-sum game and quite likely entered a negative sum game (though you may end up having positive outcome, the sum is negative).
Well isn’t this exactly the problem cousin_it is referring to when the game is non-zero sum? It means that I might need to take 1000 utils from you in order to gain 50 utils for myself. (or even: I might need to take 1000 utils from you in order to limit my losses to 50 utils).
It’s possible that it will be a negative sum. It is also possible in principle that it has become a positive sum. The sign of the ‘sum’ doesn’t actually seem to be the important part of the quoted context here, rather the presence or absence of a shared interest.
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.
I have reread the context and I find I concur with wedrifid_2009.
Vengeance is impossible, threats are irrelevant but destruction most certainly is not. Don’t confuse the arbitrary constraint “the total score is always the same” with the notion that nothing ‘destructive’ can occur in such a game. What is prevented (to rational participants) is destruction for the purpose of game theoretic influence.
Consider a spherical cow in (a spaceship with me in a) vacuum. We are stranded and have a fixed reserve of energy. I am going to kill the spherical cow. I will dismember her. I will denature the proteins that make up her flesh. Then I will eat her. Because destroying her means I get to use all the energy and oxygen for myself. This includes the energy that was in the cow before I destroyed her. It’s nothing personal. There was no threat. I was not retaliating. There was neither punishment nor cooperation. Just destruction.
ie. One of these things is not like the other things, one of these things just doesn’t belong:
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!).