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Obscured Information Games

 
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MarkSteere
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PostPosted: Wed Oct 25, 2006 8:18 am    Post subject: Obscured Information Games Reply with quote

While perfect information games by definition do not contain hidden information, I would like to coin a new, admittedly awkward term, "obscured information game." That would apply to games in which all of the current information is not visible at all times, such as that stacking game (Laska?) in which the colored face of a checker in a stack is not visible and can only be known by memorizing the contents of every stack. And of course games in which huge piles of stones can occur, whose exact count is a mystery to all but savants.
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Lexicon



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PostPosted: Wed Oct 25, 2006 8:57 am    Post subject: Re: Obscured Information Games Reply with quote

There should also perhaps be a category in between hidden information and perfect information for simultaneous games. In particular, in frames & pulling strings, both players make their move with all the same information. There is no hidden information such as a deck of cards. I'm still sort of baffled that the game theorists exclude simultaneous games from being perfect information by definition, but I assume they have their reasons, or maybe it was just that one definition. Anyway, for a term, I would just say "no hidden information" or "full information".
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MarkSteere
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PostPosted: Wed Oct 25, 2006 3:43 pm    Post subject: Re: Obscured Information Games Reply with quote

Lexicon wrote:
I'm still sort of baffled that the game theorists exclude simultaneous games from being perfect information by definition, but I assume they have their reasons, or maybe it was just that one definition.


Simultaneous games aren't simultaneous in the sense of a pistol duel. On a given turn, players can commit to their moves days apart, as often happens here at SDG. The only condition for simultaneity is that players must not *reveal* their moves before both players have committed to a move. This is precisely why it was shown in a previous discussion that 55Stones is not a simultaneous game. In 55Stones, one player reveals his move before the other player has committed to a move. (By the way, I would like to apologize to Ralf, Aaron, et al for my agitated behavior the other day. Henceforth I will try to conduct myself in a more dignified manner.)

So imagine you are playing a true simultaneous game such as Frames, and you are pondering your next move. Meanwhile your opponent has already written his move down on a piece of paper and placed it face down on the table between you. That move is now part of the game. Itís information about the game which is unavailable to you at the time of your current turn. For that reason, Frames in no more a perfect information game than Texas Hold'em.
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Personman



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PostPosted: Wed Nov 15, 2006 3:29 pm    Post subject: Reply with quote

Note: The first several paragraphs of this post are kind of rambly, and involve me figuring out for myself what my answer was. I couldn't bring myself to delete them, but feel free to skip to the paragraph in bold, which is my main point.

This is a very interesting question... My gut instinct is to say that Frames is game of perfect information - in chess, you don't know what your opponent will do next either, but you certainly know what he *can* do, as you do in Frames. The fact that the moves are revealed simultaneously and can be offset by whatever margin seems irrelevant - nothing changes from your perspective whether the other player has submitted their move yet or not, except perhaps psychologically - if you know they've already moved, then your move will be irrevocable, while if you know they haven't, you know you can change it. This is a (probably unfortunate, though minor) consequence of the PBW paradigm, in that your move shouldn't ideally be influenced by whether or not you'll be able to change it, since you won't get any more information between now and the last point at which you could change it.

The same goes for your opponent having a scrap of paper face down on the table, I guess, though I've never played Frames that way. Once it's there, there's more pressure on, but no more information.


However, even if we ignore the psychological factor, or assume that the players are able to be unaffected by it, there is a difference between simultaneous and non-simultaneous games of perfect information. The most common example, in Frames anyway, is the RPS situation - move A beats move B but loses to move C, which loses to B. In fact, RPS is probably a simpler game to work with for purposes of analyzing simultaneous games.

While there are obviously differences between simultaneous and sequential games, that difference is best categorized by "simultaneous" and "sequential", rather than by lumping simultaneous games in with games of imperfect or perfect information, because there can be simultaneous games of both types, as well as sequential games of both types. The pairs of terms are talking about unrelated game features, and shouldn't be confused.
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MarkSteere
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PostPosted: Wed Nov 15, 2006 4:34 pm    Post subject: Reply with quote

The game theoretical assertion is that all simultaneous games are hidden information games, which is true. Move decisions are revealed at the same time, but not necessarily made at the same time. When your opponent commits to a move before you do, whether by writing it on paper or entering his move on SDG, that's information about the game which you don't know, i.e. hidden information.

This discussion began when Ralf tried to refute the assertion that all simultaneous games are hidden information games by redefining "simultaneous game" - essentially claiming that game theory is wrong.
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MarkSteere
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PostPosted: Wed Nov 15, 2006 7:44 pm    Post subject: Reply with quote

When your opponent commits to a move before you do, it's as though he blocked your view of the board and made his move. And then the current state of the game is not completely known to you as you ponder your move decision.

Having said that, Frames doesn't precisely fit that description. If both players choose the same point, a neutral piece is placed on that point. In any case, your opponent's intended move, which he committed to before you committed to yours in this example, is still information about the game which is hidden from you. Frames is a simultaneous game, and as such is also a hidden information game.
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