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This is an old revision of this page, as edited by Charles Matthews (talk | contribs) at 15:31, 6 November 2003 (Heuristics). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

The following notes were moved from 'Game Theory'

Game Theory can be broken down into several categories.

- Linear Programming - Prisoner's Dilemma - Berlekamp Theory (John Conway "Winning Ways for your Mathematical Plays") Surreal numbers - Games of perfect information (go, chess) - Games with perfect information, but a random element (backgammon, monopoly) - Games of imperfect information - Multiple player games (where coalition building is an important part of strategy) (Risk, Poker, voting schemes)

As a minor topic, there are several games from "The Price Is Right" that are mathematically interesting. I remember seeing articles on correct bidding strategy in the "Contestant's row game", and the "Big Wheel game". I remember seeing a good article on correct bidding strategy on "Final Jeopardy"

See also the page on Game theory with a lowercase T.

can someone add John Nash here? I'm not really sure where he fits in or how significant he was to this field. Dze27

  • John Nash is extremely significant. Do we want to add a section on key persons in game theory, with links to articles on those persons? The short history really doesn't do justice to the development of the field. JD Jacobson


I removed the claim that Game theory overlaps with computer science, since I can't see any connection except that computers are used to solve the resulting optimization problems. AxelBoldt 22:05 Sep 22, 2002 (UTC)

There is substantial overlap. Many graph optimization problems occur in certain games. "Find the most effecient way to do something" occurs both in computer science and in game theory. Many games have been analyzed for their complexity class. Strategies for "different computers work on a problem with limited communication" is similar to "different players try to cooperate even though they share limited information".

Computers are used to solve game theory problems, and game theory is used to solve computer science problems (eg, AI, game playing). Thus,an overlap. No? - Khendon

I don't know how AI uses game theory, and while computer chess or go could be called computer science, they don't use any game theory. That leaves the fact that computers are used to solve game theory problems, but computers are also used to book vacations. AxelBoldt 04:08 Sep 24, 2002 (UTC)

  • Computer chess programs are definitely an implementation of game theory. The brute force approach of looking ahead n moves is inefficient. I believe a strategy -- a game theory -- combined with brute force is the secret to successful chess programs. JD Jacobson

Well, okay. I'll concede for now until I can work up a comprehensive argument :-) - Khendon

The article states: " The difference between a rule (or law) and a theory. Technically speaking, there is no difference, but a rule tends to be more fundamental to playing the game. For instance in chess saying that you need to take as many pieces as possible is a rule, that you should start with say the Bishop's Gambit is a theory. Note too that rules tend to be more useful in playing the game. Theories (and this includes scientific theories like e=mc2) may be debunked later on. However in life rules too may sometimes be debunked."

I think that this is an erroneous statement. In the game of chess, for example, the rules include: (a) a king may move one square in any direction, but may not move into check; (b) a queen may move along its file, rank, or diagonal for any number of squares to the edge of the board until either (i) blocked by a piece of the same color, or (ii) reaching a square occupied by a piece of the opposite color, in which case the piece occupying the square is captured; (c) ..., etc. Games of all types, including prisoner's dilemma and the other class games, all of rules, or laws, that are immutable; if you change the rule, you have changed the game.

Theories are approaches to winning a game. Thus, "take as many pieces as possible" is a theory in chess. It is usually a successful theory, but not always. Sacrifices and positional approaches to chess achieve success through giving up material for position, tempo, or other advantages. Major theories used in game theory, based in large part on one's personal utility values and degree of risk-adverseness, include mini-max (choose the strategy that yields the greatest adverse result), tit-for-tat (cooperate until betrayed and then retaliate), and diversify (purchase a portfolio of investments so as to reduce the degree of risk, thereby limiting your upside and downside).

I would appreciate any comments anyone has on the foregoing. After reviewing these comments, and considering them, I will attempt an edit of the section on the difference between rules and theories.

--- JD Jacobson

Heuristic is a much better word for 'theory that helps you find a winning strategy'. Which is one concept from the above. I'd expect a theory of a game to be more like game theory, perhaps based on some modelling assumptions.

Charles Matthews 15:31, 6 Nov 2003 (UTC)

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