Talk:Complete information

Game Theory vs. Microeconomics

In the perfect information page, I separated the ideas via headers, I'm trying to figure out the proper procedure to give them their own pages, since my understanding is they are different concepts. Mathematically, games in game theory can be modeled with graph theory graphs, that is, discrete math. Whereas perfect info in the microecon sense would require complete knowledge of the physical state of the universe. I'm not sure I understand the distinction between complete and perfect information in the microecon sense, or maybe there isn't one, and the microecon references should be removed and combined with the perfect information (microecon page). — Preceding unsigned comment added by NoWikiFeedbackLoops (talk • contribs) 23:36, 22 May 2012 (UTC)

Incomplete Information in Chess

The article gives this example:

Examples of incomplete but perfect information are conceptually more difficult to imagine. Suppose you are playing a game of chess against an opponent who will be paid some substantial amount of money if a particular event happens (an arrangement of pieces, for instance), but you do not know what the event is. In this case you have perfect information, since you know what each move of the opponent is. However, since you do not know the payoff function of the other player it is a game of incomplete information.

Unless I am misunderstanding the idea of complete information, this doesn't seem to be a valid example. The objective in chess is checkmate, not to get a particular arrangement of pieces, and the rules don't change because one player has an agreement outside the game. If this player tries to arrange the pieces in such a way, and it causes him to be checkmated in the long run, he has lost the game, regardless of whether he gets paid for arranging the pieces in that way. Whatever financial arrangements one player has made outside the game are irrelevant - the rules of the game are still the same. The other player's objectives do not change at all, even if he were aware of the arrangement; his goal is still checkmate, by the rules of the game. The only payoff in the rules of chess is checkmate. 86.28.197.238 (talk) 13:25, 6 April 2010 (UTC)

I can see it will be about a million years before anyone responds to this, so I am just going to go ahead and remove the reference. As far as I can see, chess is a game of both perfect and complete information, and this example is simply erroneous. The only example I know of where a game has perfect but incomplete information is a boardgame called Labyrinth [1], in which a player can see all the available moves for his opponent, but does not know what his objective is. Anyway, if someone disagrees with my assessment and wishes to put the above text back in, please explain why it is a valid example. 86.28.197.238 (talk) 21:58, 6 April 2010 (UTC)

I can understand the confusion since the "winning conditions" are not affected, but this kind of chess game would still be considered as having incomplete information since the payoff of your opponent is changed (which might affect his playing style and lead him to make unusual moves, for example). I have brought back the paragraph but tried to clarify it a bit. 7804j (talk) 00:28, 17 June 2016 (UTC)

Complete Knowledge

I don't think "a state of complete knowledge" is very helpful as a definition for "complete information". It is defining a term in terms of itself. Knowledge of what? Of the history of moves? Of the payoff functions? What is the difference with "perfect information"?--Frank Guerin 16:26, 8 May 2005 (UTC)

You're right. I've reworded it to make it clearer and less circular. The difference between games of perfect and complete information is that in the former, knowledge of the history of moves is available to each player and in the latter, knowledge about the type of each player is available to each player (i.e. about their payoff functions and strategy spaces). I think this distinction is made clear in the two articles.

Treborbassett 16:37, 8 May 2005 (UTC)

Should this be merged with perfect competition? The definitions given are identical. Inebriatedonkey 28 June 2005 08:38 (UTC)

Merger should no longer be necessary, I have clarified the definitions. 7804j (talk) 00:29, 17 June 2016 (UTC)

Perfect vs complete information

In response to a user's concern I removed the following content. I think it refers to a situation of perfect information not necessarily complete --Kzollman June 29, 2005 00:12 (UTC)

In practice, the assumption of complete information is unlikely to be correct for real world situations. For example, in the stock market, even the most sophisticated financial investors do not receive information instantly and do not react to it instantly. The large financial firms that have institutionalised the financial markets are overwhelmed with the volume of information that they are required to digest. Many of their major decisions are taken by committees or small groups of people that take time to convene, discuss, analyse and take decisions as to what to do. It can take a long time for major institutions to move their funds from one asset to another because they have to manage market impact (the effect of their own actions on asset prices).

Chess and yahtzee are complete information games while Scrabble and poker are not.

Re: Complete vs. perfect information:

Examples of incomplete but perfect information are more difficult. Suppose you are playing a game of chess against an opponent who will be paid some ... In this case, you have perfect information, since you know what each move of the opponent (is?) However, since you do not know the payoff function of the other player it is a game of imperfect information.

Is this not a contradiction? Is that an example of a game of imperfect information or perfect information? Or is the last statement really meant to be: However, since you do not know the payoff function of the other player it is a "incomplete game"? This would make sense, because the first sentence of the paragraph is "Examples of incomplete but perfect information are more difficult.", seeming to imply that the paragraph is going to show an example of such... Also, why would the previous paragraph have an example of imperfect information, only to supply another example right after, without having an example of perfect but incomplete information?

--Binesh 4 July 2005 23:17 (UTC)

Binesh thanks! That's a silly typo on my part, but its likely to confuse a lot of people. Its fixed now. best, --Kzollman July 5, 2005 18:14 (UTC)

Why is poker incomplete? I can see how it's imperfect: because you cannot see the moves made in determining your opponent's hand.--Frank Guerin 8 July 2005 14:24 (UTC)

Isn't an open cry English auction an example of incomplete but perfect information?--Frank Guerin 8 July 2005 14:36 (UTC)

Poker's incomplete but perfect - you see your opponents' actions but not their cards. An open cry auction is incomplete and perfect too. Treborbassett 21:46, 10 July 2005 (UTC)

What about poker games where players have an opportunity to discard some cards and get new ones, but other players do not see which cards they chose to discard?--Frank Guerin 23:40, 17 July 2005 (UTC)

In terms of complete and perfect information this is the same as most forms of poker, complete but imperfect information --Kzollman 02:22, July 18, 2005 (UTC)

There is a contradiction here between Kzollman and Treborbassett. Is any resolution possible? The main article on Game Theory [[2]] says poker is incomplete. Is it?!?

The book Game Theory by Drew Fudenberg and Jean Tirole (one of the standard graduate texts in game theory) defines incomplete information as:

When some player do not know the payoffs of others, the game is said to have incomplete information (pg 209).

They define perfect information as:

A special case of interest is that of games of perfect information, in which all the information sets are singletons.

These definitions are echoed at gametheory.net [3], [4], and [5].

In poker, you know the size of the pot, i.e. how much money your opponent stands to gain or lose, you know all of the moves available to your opponent (i.e. check, raise, call, fold), and you are aware of all the cards he might hold. So, you have satisfied the conditions for complete information. However, you do not know where you are in the game, because you do not know you opponents cards nor which cards will come. Thus there are information sets which contain more than one node. Therefore you have imperfect information. This is echoed at this website [6]:

The game of poker involves all of the above extensions to traditional studies in computer game playing, being a non-deterministic multi-player zero-sum game with imperfect information.

I think this is the confusion. When representing games like poker, you have a player representing nature (i.e. the random event which results in the cards being shuffled). In poker you do not know the actions of this player (nature) and thus do not have information about nature's moves. I will fix the entry on game theory now, and barring any objections I will add something on poker to both this entry and the entry on perfect information. Thanks for bringing this to my attention. --Kzollman 22:21, July 24, 2005 (UTC)

I'm sorry, but I maintain that poker is perfect but incomplete. Every player sees the actions of the other players, but no player knows the type of the other players - whether they are holding pocket rockets or nothing. There are nonsingleton information sets, but not because of player's moves, but natures move at the start of the round to determine the cards each player holds. It's worth pointing out that in the literature on this subject isn't in agreement over the definitions of perfect and complete information. However, the definitions originally given in Wikipedia reflect those that are mainstream. The definition in Fudenberg and Tirole of complete information is in agreement with this. Players in poker do not know the payoffs of their opponents. Certainly, they know the range of payoffs (i.e. they'll win the pot or nothing), but they do not know what actions of their opponents will lead to what payoffs. The original definitions, I think, should be left intact. Treborbassett 21:22, 28 July 2005 (UTC)

Incidentally, the sketch I give above is supported in both Rasmusen and Gibbons, both standard graduate texts. Treborbassett 21:24, 28 July 2005 (UTC)

Okay, fair enough. I think this is perhaps a grey area where the consensus has yet to be formed about the meaning of terms. For those who care, the dispute is on how to represent games where nature moves. One can characterize nature as a player and have a imperfect but complete information game or one can characterize nature as selecting a payoff function for each player (in a sense, outside of the game) and then it is perfect but incomplete. I honestly don't have a good sense of the game theoretic community, so I'll just trust trebor's statement that this hasn't been resolved. I think perhaps the best idea would be to leave this out of the article. Explaining the dispute is probably worthless to anyone but ourselves. This leaves a bit of trouble however, if poker can be disputed, the example of imperfect complete information in the article can be as well. Does anyone (trebor?) have an example of a imperfect complete information game that would not be contentious? A natural game where an individual does not know the moves of another player perhaps. --Kzollman 02:57, July 29, 2005 (UTC)

I think battleships constitutes an example of such a game. There is no play by nature in the game, but there are nonsingleton information sets because players do not observe all of their opponent's actions.

By the way, I'm not sure of your distinction of characterisations of nature, Kzollman. True, I think one could adequately describe games where nature moves in the way you have. But I think are really equivalent and are incomplete information games. Where nature is treated as a player, it is as an aid to modelling, but does not change the game from being incomplete to complete. Furthermore, when one models nature as a player, players can be treated as having one payoff function only, which is a partial function of nature's moves. However, this is the same as having a single payoff function that is a partial function of nature's choice as opposed to its selecting a payoff function.

I think that the disagreement over the definitions of 'perfect' and 'complete' is simply a non-uniformity in the literature - different authors define them differently. But I don't think it is the centre of any academic debate because at the end of the day the definitions are just stipulative: different people might find different definitions more convenient. Moreover, I think there is pretty much agreement over how they are used (not like, for example, 'certain' information). Precise definitions may vary, but I think the general spirit is perfect information concerns players and complete information regards nature (or at least, nature's choice before any player moves). I think Wikipedia should give readers some information about this. 84.68.134.234 07:18, 29 July 2005 (UTC)

The above was me by the way! Treborbassett 07:21, 29 July 2005 (UTC)

Of course, in a discussion like this I would get the thing backward. I meant finding an example of perfect and incomplete information. Sorry, I must be getting tired :) --Kzollman 07:58, July 29, 2005 (UTC)

Haha! Well I persist with the claim that poker (and lots of other card games) are perfect and incomplete. Scrabble and dominoes are too. Examples not tinged with doubt by the above discussion are harder to find. Open cry auctions and haggling are (non-recreational - at least not normally!) examples. Every bidder is unsure about the valuations of the others, but can see (or hear) all their actions and hagglers do not know each other's valuations, but hear what price is being bargained. Industrial economics examples are fairly common. Many firms might see a competitor lower prices or increase output, but might be unsure of what (for example) its cost structure is. In fact, there has been much research in this area - see e.g.limit pricing (which is in need of much attention incidentally). Treborbassett 16:22, 29 July 2005 (UTC)

I've just realised the limit pricing article does not at all illustrate my point. The idea is that a monopolist signals its cost structure to potential entrants by having a low price that could not be sustained by a high cost structure monopolist. All actions are seen, but the entrant does not know the type of the monopolist - high or low cost. Treborbassett 16:29, 29 July 2005 (UTC)

The non-uniformity in the literature is mentioned in Ken Binmore's book (Fun and Games, Chap. 11); he says Harsanyi's theory can "complete a structure in which information is incomplete ... the result will be a game of imperfect information". In Binmore's view: "strictly speaking, there is no such thing as a game of incomplete information". --Frank Guerin 09:40, 10 August 2005 (UTC)

I can not agree with Binmore in this sense. The differences between ‘complete information’ and ‘Perfect information’, have been nicely clarified by @ARTICLE{Harsanyi1967-8, AUTHOR = {John C. Harsanyi}, TITLE = {Games with incomplete information played by Bayesian players}, JOURNAL = {Management Science}, YEAR = {1967-1968}, volume = {14}, pages 163 footnote 2.

Obviously this debate stopped a few years back, but I would like to make the following points as regards game terminology. Game theory does not appear have strict definitions of these terms and there is usage in academic papers that differ slightly from each other.

The terms while needed by game theory are based upon ideas from game strategy. The terms Complete information and Perfect information are often used synonymously.

Complete information should mean that there is no hidden information

Perfect Information should mean that there is no unknown information in the game

Normally these two terms are used to the same effect. However, it is possible to define a die-roll as open information (as opposed to hidden). In poker, though, the event has been determined as soon as the deal is complete and so the other hands are still hidden information.

This means that almost all card games have neither complete nor perfect information. An example of a game which could be described as perfect information but not complete is roulette. However, this is still not universal as it depends on whether the non-deterministic event of spinning the wheel is treated as hidden.Tetron76 (talk) 13:39, 23 February 2011 (UTC)