Talk:Game theory
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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"
Just a query from a non-tech head with only very basic knowledge but isn't "The Weakest Link" also of game theoretic interest, the whole deal with whether you choose to vote off the weakest player and increase overall winnings or the strongest player to increase your chance of beating them - this reminds me a little of the centipede gameAndrew F. 22:34, 11 Apr 2005 (UTC)
See also the page on Game theory with a lowercase T.
In reply to 'Isomorphic': The simplest version of Prisoner's Dilemma is played on a 2 x 2 field. That are the basics as defined by Dresher, Flood and Tucker and elaborated later by Anatol Rapoport. I suggest that you read my book 'Winners and other Losers' described in my original comments on this page before commenting further,
can someone add John Nash here? I'm not really sure where he fits in or how significant he was to this field. User: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. User: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. User: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.
--- User: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)
A lot of extraneous and/or nonsense commentary seems to have gotten into the article. It looks to me like it was all written by the same anonymous user on a dynamic IP (62.64.xxx.xx). I'm going to remove most of it, and restore the article to something resembling David Shay's last edit. Isomorphic 08:15, 8 Dec 2003 (UTC)
Game Theory is like a Wikipedia mega topic, it's talked about far more on Wikipedia in connection with everything else than it is talked about in any other medium I've encountered. For example, the phrase "zero sum game" is used an extreme amount in the wikipedia.
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Nash provided a way to solve non-zero sum games, he is probably as important or more important then Morgenstern and von Neumann (who formalized, 'invented', game theory.
Also I think there should be examples of how to solve a game bi-matrix here, (i.e. find the Nash equilbria). If you take a game theory course a large part is finding these Nash solutions to games. I think I did a solved one, but didnt show the solution steps, in the Nash equilibrium section if you want to copy it over.
I think it is better to view this as a multidisciplinary field like political-economy or cognitive science then as a branch of only mathematics. The problem with only having it as a branch of mathematics is:
1) Those who do game theory are more often then not economists or doctors of economics. Game theory is often taught by economics and not mathematics departments, as game theory is often regarded as the third pillar (behind macro and micro economics) of economics.
2) The prizes most awarded in the field of gametheory is the Nobel prize of economics, not the fields medal.
3) The foundational book of game theory, by Morgenstern and von Neumann, is called "Theory of Games and *economic* behavior.
Because of this, and because of all the overlap, I think that game theory should be regarded as a field of mathematics, economics, and also increasingly psychology (recently Nobel prizes in economics have been going to psychologists for their work on the assumptions of rationality). As a result Game Theory is best described as a multidisciplinary field. --ShaunMacPherson 08:32, 17 Mar 2004 (UTC)
- Agreed with the point about it being multidisciplinary, but I think the current introduction is a bit clunky. I'll try a rewrite. Isomorphic 08:43, 17 Mar 2004 (UTC)
Is monopoly a Zero-Sum Game?
It all depends on what the definition of winner really is.. I mean at the end of the game..there will be one person who will be the wealthiest... but that doesn't mean all others won't gain anything.. There could also be others who have quite an amount of wealth. The net effect is no body loses when person x become the wealthiest.
- It's debatable. In fact, I just commented on this exact problem at Talk:non-zero-sum. The way it's currently argued in the article makes it pretty clear under what conditions Monopoly is zero-sum, so I think it's ok. Isomorphic 20:19, 29 Mar 2004 (UTC)
Monopoly is a very poor example of a (non-)zero sum game. In a zero-sum game one player's loss is another's gain. In Monopoly you can be taxed/reimbursed and this money goes into/comes from the bank. (While one player is designated the banker, this is for administrative purposes and they do not gain from this exchange.) So that element is non-zero sum. However since only one player can win the game, they necessarily do so at the expense of the other competitors. Declaring a winner will always make an activity zero-sum, but it doesn't necessarily mean it's a good example.
The claim that there is always a single winner in zero-sum games is also suspect. If we are dividing a pie then that is clearly zero-sum, anything you don't take will belong to me, yet if we half the pie exactly then who is the winner? Or if I start the game with a full pie and you take a quarter, do I win because I still have more pie? Or do you because you have gained pie at my expense? Win, lose or draw does it really affect the zero-sum nature of dividing up a pie? [User:DaveScotson]
Game Theory: My book: Arnold Arnold:'Winners and Other Losers'(London: Collins/Paladin, 1989) shows that the von Neumann and Morgenstern and the common perceptions of the zero-sum/non-zero-sum game are myths, as defined in the given Wikipedia article on the subject. Zero-sum, pure strategic games (e.g. noughts and crosses,chess, etc. are solely won by deception and lost by inattention or inexperience. The 'draw' is the only description of the non-zero-sum game. This holds even true for 'Prisoner's Dilemma, in which the first moving player always wins in the first round. The next game is also won by the first moving player who would be he (or she) who went second the first time around. That then is a draw in Prisoner's Dilemma.
There is no point in going into all the details here. They are elaborated definitively in my book, cited above. All of thius can be demonstrated easily by use of directed graphs and combinatorial mathematics.
Incidentally, I played Prisoner's Dilemma with Professor Selten some years ago. He insisted on going first to prove his point. When I suggested a return match to demonstrate the draw principle in this instance,he declined, stating that one game was sufficientto prove his point. ???
Games of chance are a different matter. I deal with that subject on my forthcoming book.
- The above sounds like nonsense to me. There is no first mover in the Prisoner's Dilemma; it's a simultaneous-move game by definition. Can't be sure, however, as the comments are too vague. Isomorphic 04:05, 22 Jun 2004 (UTC)
Is checkers a game that can be analyzed with game theory? I love that game. Jaberwocky6669 05:38, Jul 29, 2004 (UTC)
- Depends what you mean by "analyzed." In theory, checkers could be solved by game theory, but the computations involved would be prohibitive.
- Hey! Thanks for your reply. I meant solve but I didn't know it would be so hard to solve the game. Cool, thanks! Jaberwocky6669 19:23, Jul 29, 2004 (UTC)
- Longer answer: the situation for checkers is similar to that for chess. In theory, it is a zero-sum game for two players, with complete information. It is provable that a solution exists. However, such a solution would take a truly insane number of computations. There was extensive discussion of this on Talk:Chess at some point, trying to estimate the total number of possible game states or something. It's enormous, astronomically more than even a supercomputer can handle. I would guess that checkers is a bit less complex, but not nearly within range of calculation. ----
IZ need help
I serched for Jhon Nash, after watching "A beautiful Mind". I was interested in his work. I landed here. Please any one of u can guide me in studies. I am electronic engineer, and programming is my hobby. How can I start for Game theory. reply on "jaffersultan@hotmail.com"
Band?
There is a band called Game Theory, and I have recently created a entry for it at Game Theory (band). I was just wondering if this needed to be disambiguated... --Travlr23 03:59, 6 Apr 2005 (UTC)
- Since the study of game theory is much more common (and likely to be researched), so I believe a small italicized note at the top of the article will do. I've gone ahead and done so; feel free to make any changes, of course. The band's article doesn't need to have anything like that.
- The disambig note at the top is fine, thanks! --Travlr23 15:21, 6 Apr 2005 (UTC)
If your question was about whether the dismabig note should come after the already-existent Game (disambiguation) link or on that page itself, I'm not sure - I've gone ahead and appended it. -Grick(talk to me) 04:57, Apr 6, 2005 (UTC)