Information revealed to the player

If Chess is an example of a game that meets your criteria, I'm not sure I understand your question. There is no hidden information in chess. If you're considering "a player's strategy" to constitute hidden information, then probably the vast majority of games would meet your criteria.

-Jeff

Through the Desert is a game where the full state is known at the beginning, but becomes unknown as the game progresses. It may not be a very interesting example: I'm referring to players claiming "waterholes" which vary in point value. They are face-up (values seen by all) until a player claims and removes them. The players may then keep their collection of waterholes secret until the end of the game, so that nobody knows exactly how many points have been collected (well, unless they have perfect memories or have been taking notes).

Diplomacy is a war game with "perfect information" and no randomness. In one sense, every player always knows everything about the game. But a crucial element in Diplomacy is the formation of secret agreements and alliances. One could argue that these are just an elaboration of the "player's strategy" that Jeff mentioned, but I could also see an argument that they form a part of the game state that is hidden from some players.

Is any of this what you're looking for, or have I completely misunderstood you? :)

A better example than Diplomacy would be a game (anybody got an example? I can't think of one) where players make secret alliances, and are required to honor them by the game rules. In Diplomacy you don't have to honor your agreements, which in my mind puts them more on the "player intentions" side.

Any game in which players can make hidden changes to the state of the board or off-board pieces would also be an example. Say, each player has an identical set of tokens which can be placed on the board face-down. Other players wouldn't know which token you'd placed until some time later, perhaps when they "encounter" the token, or at the end of the game. Would Stratego count as an example of this kind? (Hm, fun mechanic. I might have to try to do something with that, sometime!)

In this thread, an example is proposed. Players have complete knowledge at the start of the game, but during the game if a player buys a "small ship" it might be a fighter, a mine, a transport, or any number of things.

Any time you go from having perfect information to not, it is either the result of chance or a decision by another player. If chance, it could (and IMO should) be argued that you did not have perfect information to start with. But all decisions made by another player make up part of his strategy. So I believe any game meeting your criteria will meet it only by having parts of a strategy that cannot be changed after the fact but are unknown to the opponent for at least some period of time after the part is definitely decided. If that part still is considered part of the other player's strategy, then I conclude there is no way to a) begin with perfect information, and b) at some point have imperfect information not due to opponents' strategies.

Edit: In Stratego, we must assume you know all changes perfectly. Even if *you and I* can't remember them, the ideal player could.

EDIT: I decided probably not because the position of 'special' island tiles (those that do more than just sink) is not known.