In StarCraft 2, how do you deal with game-theoretic anticipation chains? (The enemy anticipating that you anticipate that the enemy anticipate that you might do X.)
In other words, the gun and bridge problem illustrated at http://plato.stanford.edu
It's an interesting problem (especially in repeated games, where you're playing against the same player). In repeated games, you ALWAYS have to ask "well, he used hydras last time - so is he going to use a different unit combo to be more unpredictable? or is he going to anticipate that I'll anticipate that, and use hydras again?"
But also in 1v1s where the enemy might not engage in anticipation chains. But there's a chance that he might be totally naive, but also a chance that he might be trying to trick you.
By anticipation chain, I mean this. You spy on the enemy's base, and you see certain units/structures. Except - that the units/structures are decoys designed to trick you into believing that he's producing Y, even when he's producing X.
So if you see structures for Y/small armies of Y, he might be producing Y (he could not be trying to play such mental games, or he might anticipate that you think that he's trying to trick you. Or he goes to even higher orders of thinking [although I don't think that's likely]). But he might be producing X too (he could play that mental game either to the 1st order or the 3rd order [or higher, but that's unlikely])
But it also illustrates within-game behavior too. If he suddenly wiped out a bunch of your units with Z - (he might anticipate that you might produce counters for Z). Or he might not. Or he might anticipate that you might anticipate the above parenthesized statement. The loop goes forever.
This sort of problem does have a game-theoretic solution, but statistically speaking, the game-theoretic solution isn't necessarily going to work because not all agents are rational.
Anyways, I'm sure this doesn't arise often in random 1v1s. But maybe it might arise in SC2 games between people in, say, MIT or Stanford?
==
There was some paper on it some time ago, but it's gone now (http://expertvoices.nsdl
http://expertvoices.nsdl.
It's an interesting problem (especially in repeated games, where you're playing against the same player). In repeated games, you ALWAYS have to ask "well, he used hydras last time - so is he going to use a different unit combo to be more unpredictable? or is he going to anticipate that I'll anticipate that, and use hydras again?"
But also in 1v1s where the enemy might not engage in anticipation chains. But there's a chance that he might be totally naive, but also a chance that he might be trying to trick you.
By anticipation chain, I mean this. You spy on the enemy's base, and you see certain units/structures. Except - that the units/structures are decoys designed to trick you into believing that he's producing Y, even when he's producing X.
So if you see structures for Y/small armies of Y, he might be producing Y (he could not be trying to play such mental games, or he might anticipate that you think that he's trying to trick you. Or he goes to even higher orders of thinking [although I don't think that's likely]). But he might be producing X too (he could play that mental game either to the 1st order or the 3rd order [or higher, but that's unlikely])
But it also illustrates within-game behavior too. If he suddenly wiped out a bunch of your units with Z - (he might anticipate that you might produce counters for Z). Or he might not. Or he might anticipate that you might anticipate the above parenthesized statement. The loop goes forever.
This sort of problem does have a game-theoretic solution, but statistically speaking, the game-theoretic solution isn't necessarily going to work because not all agents are rational.
Anyways, I'm sure this doesn't arise often in random 1v1s. But maybe it might arise in SC2 games between people in, say, MIT or Stanford?
==
There was some paper on it some time ago, but it's gone now (http://expertvoices.nsdl
http://expertvoices.nsdl.
1 Answer
Interesting question. The answer is that you should play as optimally as possible as to limit the number of things that can beat you. The game is still young, and strategies aren't standardized more than a couple minutes into the game.
Keep in mind that even at the very highest levels, games are usually decided on macro ability, micro ability, and decision-making. Of course, there are mind games to some extent, but this kind of "unit/structure" decoy doesn't really happen, because the resources it costs to invest in a different tech path are almost always more than the advantage gained from your opponent having a changed unit composition; that's assuming he doesn't figure out your trick some other way anyhow. The closest that anything gets to this that I've seen is intentionally showing a tech building, and then cancelling it and hiding the fact that it was cancelled.
Anyway, here's an actual game situation and how a player can change his strategy to play optimally rather than guess what level down the anticipation chain his opponent is thinking.
You're a Zerg player, playing against a Protoss on Scrap Station (a popular map for Protoss to 4-gate against Zerg).
You use the drone pass-through trick to get a last-second read of his base before the "dark period" where a base scout isn't possible any more.
What you see with that scout is that the Protoss has used a lot of his chrono boosts, so it is impossible for him to do the optimal 4-gate.
At this point, as a player, you don't rule out 4-gate, but you know that if it's coming you don't have to be prepared for optimal 4-gate any more. If you've seen a lot of probes chrono-boosted, you can pretty safely assume that he is not going for any sort of quick surprise tech (DTs or void rays) either, and that, at the very soonest, he's going to be doing a sub-optimal 4-gate or a 2-base 6-gate push.
Now that you've ruled out some possibilities, you have a smaller set of things you have to worry about. The best way to internalize this is to make a list of "most likely" things in your head. With every new piece of information, change that list. If it's a player you've played before, you may have a different list than when you're playing someone you've never played before.
As Starcraft 2 develops as a game, game theory may play a bigger role. Right now, though, I would say that such a small fraction of games are decided by one person using game theory better than the other that it's not worth thinking about as a player.
This may not be the most interesting answer to hear, but unless you're a high masters level player, mechanics are by far the most important skill to improve upon.
Keep in mind that even at the very highest levels, games are usually decided on macro ability, micro ability, and decision-making. Of course, there are mind games to some extent, but this kind of "unit/structure" decoy doesn't really happen, because the resources it costs to invest in a different tech path are almost always more than the advantage gained from your opponent having a changed unit composition; that's assuming he doesn't figure out your trick some other way anyhow. The closest that anything gets to this that I've seen is intentionally showing a tech building, and then cancelling it and hiding the fact that it was cancelled.
Anyway, here's an actual game situation and how a player can change his strategy to play optimally rather than guess what level down the anticipation chain his opponent is thinking.
You're a Zerg player, playing against a Protoss on Scrap Station (a popular map for Protoss to 4-gate against Zerg).
You use the drone pass-through trick to get a last-second read of his base before the "dark period" where a base scout isn't possible any more.
What you see with that scout is that the Protoss has used a lot of his chrono boosts, so it is impossible for him to do the optimal 4-gate.
At this point, as a player, you don't rule out 4-gate, but you know that if it's coming you don't have to be prepared for optimal 4-gate any more. If you've seen a lot of probes chrono-boosted, you can pretty safely assume that he is not going for any sort of quick surprise tech (DTs or void rays) either, and that, at the very soonest, he's going to be doing a sub-optimal 4-gate or a 2-base 6-gate push.
Now that you've ruled out some possibilities, you have a smaller set of things you have to worry about. The best way to internalize this is to make a list of "most likely" things in your head. With every new piece of information, change that list. If it's a player you've played before, you may have a different list than when you're playing someone you've never played before.
As Starcraft 2 develops as a game, game theory may play a bigger role. Right now, though, I would say that such a small fraction of games are decided by one person using game theory better than the other that it's not worth thinking about as a player.
This may not be the most interesting answer to hear, but unless you're a high masters level player, mechanics are by far the most important skill to improve upon.
