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I played against extotionist strategy and I guess I got lucky because I'm leading (my score - 1) : (his score - 1) = 2:1 and won't change into 1:3 as advertised because from this step I will always defect. 25. You defected (1 points) and I defected (1 points) 24. You defected (1 points) and I defected (1 points) 23. You defected (1 points) and I defected (1 points) 22. You defected (1 points) and I defected (1 points…
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Here is the video of this happening on the tv show. http://www.youtube.com/watch?v=S0qjK3TWZE8 . It worth a watch, I recommend it.
There's a twist in this example though. He says he's going to steal (but split after the show) and convinces the other guy to split. At the last minute he changes to split so that the split is governed by the rules of the game.
Did anyone else find that article meandering? The description of the game, in particular, struck me as especially pompous wiring. The metaphor with the elephant and the goldfish had absolutely nothing to offer either, it was just a rehash of the previous sentence.
The metaphor might have been a little over-the-top but I support this sort of creativity in blog posts, if only because it can ripen into something much more aesthetically pleasing. There are places where it goes way too far -- Gödel, Escher, Bach comes to mind -- but this is only a couple paragraphs. In this case it does have something to "offer": it offers the insight that the only value that looking at past states…
This is only true if you know the strategy of the enemy beforehand, though. For instance if you play rock-paper-scissors and decide your move only based on the previous move your enemy can easily exploit that after playing for a while. It is true that the enemy doesn't have to remember more than one move after he learns your strategy but he needs to remember many moves to learn it.
Did anyone else find that article meandering? The description of the game, in particular, struck me as especially pompous wiring. The metaphor with the elephant and the goldfish had absolutely nothing to offer either, it was just a rehash of the previous sentence.
The metaphor might have been a little over-the-top but I support this sort of creativity in blog posts, if only because it can ripen into something much more aesthetically pleasing. There are places where it goes way too far -- Gödel, Escher, Bach comes to mind -- but this is only a couple paragraphs. In this case it does have something to "offer": it offers the insight that the only value that looking at past states…
The metaphor didn't really have anything to offer, before the preceding paragraph made it clear that the strategy is first-order Markov (it did state very plainly that you only remember the last position).
I don't understand the consequence. It seems to me that you aren't forcing the opponent to commit to a first-order Markov strategy themselves, you just make it easier on them to do that, because they don't need any more moves in the past.
Of course, you're doing this to simplify your own life, and because (I guess) first-order strategies work just as well as higher-order ones. Their conclusion seems to verify this, because they state that you really don't need (since you can't do any better than first-order) higher-order strategies, since you can model the opponent effectively with just the last move (which is the exact model the opponent is using).
Taking more moves into account, you would either just be trying to predict randomness (since that's the whole difference, if the opponent only remembers one move), or you would be "decompressing" their strategy into thousands of moves (since you can express a thousand moves of tit-for-tat with just "my move is the opponent's last move").
Literally, knowing any states further than the last gives you exactly zero extra information. Thus, it's useless.
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The thing that always bugged me about Golden Balls (aside from the terrible name) was the way stealers would act like it was just a game when they had in fact taken thousands of pounds from another person through deception. Certainly it was legal and even encouraged by the format of the show but it was never the right thing to do. I've seen people immediately regret doing it when they see that their opponent shared.…
Here is a video of golden balls and instant regret. The regret starts at 3:03 http://www.youtube.com/watch?v=p3Uos2fzIJ0
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The metaphor might have been a little over-the-top but I support this sort of creativity in blog posts, if only because it can ripen into something much more aesthetically pleasing. There are places where it goes way too far -- Gödel, Escher, Bach comes to mind -- but this is only a couple paragraphs. In this case it does have something to "offer": it offers the insight that the only value that looking at past states…
I will answer your comment in two sections, because it's really two comments in one: The metaphor didn't really have anything to offer, before the preceding paragraph made it clear that the strategy is first-order Markov (it did state very plainly that you only remember the last position). I don't understand the consequence. It seems to me that you aren't forcing the opponent to commit to a first-order Markov strateg…
Think of "the consequence" here in a purely security-theory way. In some sense that's what we're doing, securing ourselves from exploitation.
Press and Dyson are expressing the radical idea that "if I protect myself from some stupid attackers, I protect myself from all smarter ones." How does this work? It works precisely because there is a threshold above which "smarter doesn't matter" -- a smarter attacker has the exact same payoffs as a stupid attacker playing a different strategy. In that sense there are no higher-order strategies for exploiting a sufficiently stupid strategy: sure you can program a smarter attack, but it cannot do better than a different, stupid attack.
So if I intentionally choose my strategy to be stupid and show that, for all of your stupid strategies, the expected payoff is the same -- then for all of your smart strategies, the expected payoff is also the same!
It's not quite "trying to predict randomness", it's "if I dumb myself down I can also assume, without loss of generality, that my adversaries are dumb."
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The metaphor might have been a little over-the-top but I support this sort of creativity in blog posts, if only because it can ripen into something much more aesthetically pleasing. There are places where it goes way too far -- Gödel, Escher, Bach comes to mind -- but this is only a couple paragraphs. In this case it does have something to "offer": it offers the insight that the only value that looking at past states…
> It's true, however, that this leads to a very interesting consequence which is not discussed in this context, something quite convoluted: "I will commit to a first-order Markov strategy in order to prevent my opponent from using a higher-order Markov strategy, so that my own analysis of their strategy simplifies." It is a curious statement that your own ignorance forces someone else to be ignorant, which you can th…
2. You would have to define "exploit that," especially with the understanding that this is game theory and probabilistic strategies are certainly encouraged. So for example, you might imagine a genius who can consistently outthink you, knows your entire history and how you like to play Rock-Paper-Scissors and immediately as you throw down Rock, simply is able to guess that this is what you're likely to do, and throws Paper.
You can beat this guy. Or, more precisely, you can equal him. It's very simple: before the day has begun, roll a six-sided die and memorize the sequence. As long as they are not exploiting certain "tells" (as a Japanese robot did in the news a week or two ago) -- as long as they are just making a deduction based upon the sort of person you are, they cannot produce a net win against you and you're safe. Indeed, the Nash equilibrium for RPS is not terribly interesting, it's to choose each of the options with probability 1/3rd -- I don't really have much reason to believe that this changes dramatically in iterated RPS.
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I will answer your comment in two sections, because it's really two comments in one: The metaphor didn't really have anything to offer, before the preceding paragraph made it clear that the strategy is first-order Markov (it did state very plainly that you only remember the last position). I don't understand the consequence. It seems to me that you aren't forcing the opponent to commit to a first-order Markov strateg…
I think in the second half of what you said you began to understand what you started out saying that you "don't understand." Think of "the consequence" here in a purely security-theory way. In some sense that's what we're doing, securing ourselves from exploitation. Press and Dyson are expressing the radical idea that "if I protect myself from some stupid attackers, I protect myself from all smarter ones." How does t…
Unless I'm confused again, it seems to me that there's just no advantage to them remembering more moves, since they know everything you're going to do from that last one. It's not that your strategy being stupid actively forces them to be stupid, they're not losing anything by being cleverer, they just don't gain anything because they already have it all.
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There's a twist in this example though. He says he's going to steal (but split after the show) and convinces the other guy to split. At the last minute he changes to split so that the split is governed by the rules of the game.
I deeply wanted "the other guy" to steal leaving that guy with nothing.
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> It's true, however, that this leads to a very interesting consequence which is not discussed in this context, something quite convoluted: "I will commit to a first-order Markov strategy in order to prevent my opponent from using a higher-order Markov strategy, so that my own analysis of their strategy simplifies." It is a curious statement that your own ignorance forces someone else to be ignorant, which you can th…
1. No, that statement is still true even if you don't know the higher-order strategy of your opponent: no matter what it is, it has the same payoffs as some lower-order strategy. 2. You would have to define "exploit that," especially with the understanding that this is game theory and probabilistic strategies are certainly encouraged. So for example, you might imagine a genius who can consistently outthink you, knows…
2. Well, I was thinking that a strategy would be a mapping from game history to a probability distribution over possible moves. Should this be considered in some other way?
Sure, you can just play according to the Nash equilibrium and you can't be exploited, but probably a more interesting case is when both players try to outsmart the other player and not just aim for a draw.