Talk:Game theory/Archive1

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This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

John Nash

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

Computer science?

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

Rule and theory

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

Heuristics

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)

Wikipedia mega topic

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.

von Neumann, Morgenstern and Nash

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)

Monopoly

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)

Poker

I would mention that WSOP winner Chris Ferguson has frequently attributed his success at the poker table to his studies of game theory while spending 18 years gettting his PhD in Computer Science at UCLA. Poker is one of the few real world examples of applied game theory in practice.

Von Neuman loved poker, it was the major motivator in starting his thinking on the topic. Pete.Hurd 20:50, 13 January 2006 (UTC)

Also, David Sklansky actively uses game theory in his discussions of poker strategy. Nothing so deep as von Neumann's analysis, but nonetheless insightful. --best, kevin [kzollman][talk] 20:52, 13 January 2006 (UTC)

Checkers

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)

Revise?

It has applications in a variety of fields, including economics, international relations, evolutionary biology, political science, and military strategy.

Can we make this a little more concise/organized by changing evolutionary biology to biology, and using "political science (including international relations)"? Thanks ~ Dpr 20:27, 23 July 2005 (UTC)

I'm cool with that, although we should also add philosophy. best, Kzollman 22:55, July 24, 2005 (UTC)

Wikiproject anyone?

Hello all - I have had some discussion about starting a wikiproject game theory. There are a lot of missing articles and some standardization issues that it would be nice to deal with in an organized fashion. If you would be interested in participating, drop me a note. With enough interest, we will go a head and start one. --best, kevin ···Kzollman | Talk··· 23:19, July 31, 2005 (UTC)

I'm interested. Our game theory coverage was terrible when I arrived here, and I always intended to do some work on it. It's somewhat better now than it was, but still not comprehensive, clear, or well-polished. Take a look at best response or cooperative game, for example, and there doesn't appear to be an article at all on the concepts of a dominant strategy or dominated strategy. Isomorphic 05:55, 1 August 2005 (UTC)

(Note... I just plugged one of the above gaps with the article dominance (game theory). I'd appreciate some extra pairs of eyes, to check for mistakes or improve the explaniation.) Isomorphic 07:23, 1 August 2005 (UTC)

Question about a game

I am not sure if this is a correct place to ask, but anyway. Consider the following game, which I would call "striking workers". Player 1 are workers in a factory, and player 2 is the owner (capitalist). Workers can work or strike, and capitalist can pay them lower on higher wage. So the payoff matrix is like this:

	Work	Strike
Low wages	(1, 2)	(0, 0)
High wages	(2, 1)	(0, 0)

Can somebody analyze this game for me, please? What will be the outcome? I would like to know, is it rational for workers to strike and enforce high wages in this way (like in cooperative strategies for iterative prisoner's dilemma)? Samohyl Jan 07:25, 9 September 2005 (UTC)

This is a fine place to ask. The game you describe is very similar to the Ultimatum game, which is often used to analyze strike behavior. In the ultimatum game the players move sequentially. So, the employer first decides what wages to pay, and then the workers decide whether they want to strike. In that case, it is never rational to strike. However, the experimental evidence indicates that people are willing to "strike" in the ultimatum game. I'm sure there has been work done on the iterated ultimatum game, although I don't know where. --best, kevin ···Kzollman | Talk··· 16:41, September 9, 2005 (UTC)

Thanks. Samohyl Jan 20:05, 9 September 2005 (UTC)

I don't know of any game-theoretical analisys, but I did hear of tests being made at psychology departments. The game played was 2-player. The 1st palyer gets 100 dollars. He is then allowed to make a single proposal to the 2nd player. The 2nd player then decided weather he takes the money offered to him by the 1st player. If he refuses, no one gets anything. It seems that during actual experiments, players don't agree to get less than about 25% on avarage (I'm not sure about the numbers). mousomer 10:28, 11 September 2005 (UTC)

Mousomer, you're describing the Ultimatum game. In answer to Jan's original question, you could make a Nash equilibrium of the repeated game in which the worker plays some form of "tit for tat" strategy: work as long as the wages stay high, and strike only if the owner played "low" last turn. Isomorphic 03:22, 12 September 2005 (UTC)

Well, Isimorphic, you're naturally right. But is Tit-for-Tat optimal? We know it works nicely against a very wide variety of other strategies. But that doesn's make it 'optimal'. The question remains - do we know the optimal strategies for this repeated game? mousomer 20:57, 12 September 2005 (UTC)

The question you ask isn't as simple as you think. Only a dominant strategy can be truly and unequivocably optimal, and no dominant strategy exists here. A strategy that isn't dominant can only be optimal given some assumption about your opponents' strategies. If owner announces that his strategy will be "play 'low' every turn" and the worker believes him, then the optimal response for the worker would be to continue working. That would be a Nash equilibrium. However, if the worker believes that the owner will respond to a strike by playing "high" in subsequent rounds, then his optimal strategy will involve striking when the owner plays "low". Isomorphic 05:54, 15 September 2005 (UTC)

I didn't say it was simple. And I feel some remarks are in order:

We do know for certain that there are optimal strategies, assuming the game has a finite number of repetitions (because then it will be a finite game).

If the game is repeatd infinitely, then there must at least be epsilon-optimal strategies - something Mertens and Neyman have proved for any 2 player stochastic game.

So my first qusetion is: does anyone know what the optimal strategies are?

Next, I disagree as the woker being forced into accepting low wage. True, assuming the employer's strategy is "never pay high", the worker would be well off accepting. Thing is, the worker is a veto player, which gives him considerable strength here. Your argument works both ways - given that the worker will never agree to be low-payed, the employer is better off paying high. So this argument doesn't tell us much about what result we should expect. Now all this is also what we can say about the Ultimatum game, where the second player rarely agree to less then 20%! Remember also, that humans are capable of learning, so "punishing" your oppenent for "unfair" play has it's merits (remember tit for tat! punishing works!).

So the really interesting question is: what is the (infsup of minmax) value of this game? Is it achievable? mousomer 09:03, 15 September 2005 (UTC)

This article needs work

I think that this article needs some work. I would like to make some suggestions for some substantial changes to the article, which I would like other's input on. I suggest the article structure goes like this:

Introduction
Representations of games
1. Normal form
2. Extensive form
Types of games
1. Symmetric/Assymetric
2. Zero sum/Non-zero sum
3. Simultaneous (static) / Sequential (dynamic)
4. Perfect information/Imperfect information
Uses of game theory
1. Economics (including discussion of solution concepts including the Nash Equilibrium, auctions, and mention perfect rationality)
  1. Game theory as empirical study (Here I imagine we would talk about the important experiments like the Ultimatum game)
  2. Game theory as normative recommendation (Here I think some discussion of the Prisoner's Dilemma)
2. Military strategy (I don't know much about this other than it was used for military strategy)
3. Biology (including ESS, Hawk-dove, replicator dynamics, and sex ratios (?))
4. Computer science (I know almost nothing about this)
History of game theory (here I intend to say something about the difference between cooperative and non-cooperative game theory)
See also, external links, references, etc

Importantly, I would like to remove two major things. One I would like to remove the extensive mathematical definition and move those either to Glossary of game theory or create a new article. I would like this article to be readable by people without substantial mathematical knowledge. Second, I would like to remove the section on Risk Aversion. While this is an important part of the study of human decision making, it is more a part of Decision theory than game theory. I don't think it represents a fundamental insight of game theory that needs to be discussed in the main article.

So, please tell me what you think! Feel free to edit and change the structure above as you see fit. In a few weeks, I'll probably implement these changes if consensus is reached. --best, kevin ···Kzollman | Talk··· 01:09, 1 October 2005 (UTC)

Good idea, the normal and extensive forms each have their own pages already. The math in the normal form section could be moved to the normal form game page to satisfy any math fetishists that feel it is essential to keep. as for risk aversion, there's already an entry, risk aversion I suggest moving anything additional to that in the game theory page to that page. Pete.Hurd 03:40, 1 October 2005 (UTC)

I moved some things around, and added what I think are the primary points for each of the sections. Does anyone know anything about the sections where I am ignorant? --best, kevin ···Kzollman | Talk··· 18:13, 1 October 2005 (UTC)

Squinting? Uhhh, did you save the changes? Pete.Hurd 21:15, 1 October 2005 (UTC)

Ha, ha... that's what I get for trying to save space. Yeah I did. Instead of having a seperate heading entitles "rationality and game theory" I moved those two subsections to under economics (i.e. descriptive and normative GT). I added computer science as a discipline that used GT. I also added some more parenthetical stuff about what I want to discuss. In particular, Pete, I'd like your input on whether or not sex ratios should go in the main article. --best, kevin ···Kzollman | Talk··· 21:36, 1 October 2005 (UTC)

OK, I get it now, my bad, too much MSG in my brain. Sex ratios should go in, and I suggest they go in before ESS to reflect history (Bill Hamilton & unbeatable sex ratio, then Maynard Smith & ESS - I havn't checked, but I assume the accusation that JMS strategically impeded publication of Hamilton's work is addressed under their respective biography entries). I don't think replicator dynamics belongs under the biology entry. I am open to opposing views here but I think that the EGT/replicator/dynamic systems scene is more of a solution technique/equilibrium refinement than anything related directly to biological interpretations. I suppose one could make the reverse argument, that an ESS is also more of an equilibrium refinement than something particluar to the application of game theory to biology. As for the CS angle, something I'm meaning to educate myself on is this topic of reinforcement learning FAQ which seems to get applied to game theoretical problems by CS types. Pete.Hurd 22:03, 1 October 2005 (UTC)

Actually, reinforcement learning is also used by some economists. For instance, there is an extensive discussion of it in Strategic Learning and Its Limits by Peyton Young, as well as something in Learning in games by Fudenberg and Levine.

I noticed your recent concern with replicator dynamics in biology. I think its fair to say that it is more often used by economists than biologists. I did a quick Google Scholar search [1] which shows about 1 biology publication for every 6 or 7 in economics (mostly in journal of theoretical biology or journal of mathematical biology). I really don't have much of a feel for the biological practice, I'm a mere philosopher. I do know some philosophers sometimes interpret their work as biological in character. Here I'm thinking of some stuff done by Brian Skyrms and Sober and Wilson's Unto others (Doesn't Carl Bergstrom use the replicator dynamics for some of his signalling stuff, too?) --best, kevin ···Kzollman | Talk··· 23:02, 1 October 2005 (UTC)

I think the biology/econ/etc divisions can be made in at least three different dimensions: field of application, discipline of origin, and source of inspiration. I think EGT has a biological source of inspiration, an economics discipline of origin, and (largely) an economics field of application. Field of application is obviously more plastic over time. Carl Bergstrom's knowledge of economic game theory is exceptional, certainly not representative of the typical biologist, not even of the really game theory-savvy ones - and may be genetic ;-). I don't mean to imply that there's something anti- or non- biological about EGT, just that there's no special affiliation between EGT and biological applications, either in theory or in practice, IMHO. Anyway, I think these three different application, origin and inspiration issues all enter into describing how game theory fits together and keeping the differences in mind may avoid confusing stuff. Thanks for the pointers on RL, there goes the rest of my free time. Pete.Hurd 23:51, 1 October 2005 (UTC)

I have added "types of games" as section above. What do others think? I think maybe this stuff should be in the introductory article. Did I miss any important ones? --best, kevin ···Kzollman | Talk··· 17:14, 8 October 2005 (UTC)

Two remarks:

The term "representation of games" for the formal definition of a game is a misleading term. A representation of a game-form is another game (usually a cooperative game) that is used for studying the former game. I suggest returning to the title "Formal definition of a game".

Cooperative games should be added to the definitions. I added "simple games", but that is just one example of coalition-form games. (I would not have the time to do this in the near month.) mousomer 17:58, 8 October 2005 (UTC)

Another "type of game" distinction I would suggest is dynamic vs. static (non-dynamic, static, strategic ?) (dynamic meaning not the EGT sense, but the multiple moves in a single play sense) then I'd suggest moving "types of games" up to preceed "representation of games" to allow the discussion of dynamic games requiring extensive form, and whereas static work fine with strategic form. (I have no problem with "representation" but I may just be naive about the correct definitions, I suppose one could rename "representation of games" to "forms of games" since we're comparing extensive form to strategic form, and it's less intimidating (and maybe more appropriate) than "formal definition". Pete.Hurd 18:44, 8 October 2005 (UTC)

I choose "representation" because of the inter-translatability of games in extensive and normal forms. As a result, neither the normal form or the extensive form "define" a game, but, rather, what we call games (i.e. the prisoner's dilemma) is a class of normal form and extensive form representations. This is consistent with standard terminology for instance see [2]. This is far more technical than really ought to be in the article however. With respect to cooperative games and simple games, this is probably where my ignorance comes through. I'm affraid that the definition of "simple game" and of "cooperative game" as they are currently in the article is not sufficient. I say this because, I don't understand them, and I'm certainly more versed in game theory than our target audience. If someone can improve them, I would be very happy to add them in. --best, kevin ···Kzollman | Talk··· 19:29, 8 October 2005 (UTC)

Since Aumann won the Nobel Prize, I thought I would put up the version of the page that I have. It not quite as clean as I was hoping but there it is. Hack away! --best, kevin ···Kzollman | Talk··· 18:23, 11 October 2005 (UTC)

P.S. Pete - I initially tried your suggestion of putting type of games before the representations section, but I thought it was better to be able to present examples of the different type (as is in the article). While its a bit awkward, I think its better this way. --best, kevin ···Kzollman | Talk··· 18:26, 11 October 2005 (UTC)

Very nice, good work! Pete.Hurd 21:15, 11 October 2005 (UTC)

I think a new section that works out problems and gives solutions would be a good new addition. —The preceding unsigned comment was added by 68.123.254.142 (talk • contribs) 23:28, 25 March 2006 (UTC)

No, that wouldn't be encyclopedic. It's the sort of thing you might want to do at Wikibooks, though. --Trovatore 01:56, 26 March 2006 (UTC)

To the extent that there are solutions presented, they are presented on the pages of the specific games they are solutions for, not here on this page. Pete.Hurd 02:23, 26 March 2006 (UTC)

Combinatorial Game Theory

I just find it strange that this article doesn't mention combinatorial game theory at all even though that article does. I guess most people only care about economic game theory, but the only real text I have read on game theory was Winning Ways, and feel it deservese proper recognition here even if it is a less popular feild.

You're invited to write! The article contains what the people who write it know. mousomer 10:03, 17 October 2005 (UTC)

I've mentioned it in the history section. Charles Matthews 10:40, 17 October 2005 (UTC)

I removed the bit from the history section, because I don't really know when the split occured and I was altering the history section to be more cronological. I have already added a dab link at the top of the page. If someone knows when this split occured, please add it back to the history section. --best, kevin _└ ^KZOLLMAN/ _TALK^┐ 23:46, 27 November 2005 (UTC)

Picture

At the Featured article vote, someone suggested that we add a picture to the lead section. I thought this was a good idea, but I have had a hard time finding one. My ideas were: a picture of stock traders, a picture of an auction, or a picture of animals fighting (or at least obviously threatening). I have had little luck finding any such pictures. (I really don't like our picture on auction, its not really obviously an auction and its doesn't show bidding which is the centeral thing at auctions.) Any ideas either where to find these pictures or any other ideas? BTW, I considered a picture of John Forbes Nash, but that picture is used under fair use which will not allow us to use it on this page. Also, I think pictures of board games will only further add to the confusion between game theory and combinatorial game theory, although I'm open to be convinced otherwise. Thanks! --best, kevin [kzollman][talk] 19:31, 7 December 2005 (UTC)

I'll see if I can find a nice photograph of threat displays that has two individuals counter-signalling, the game theory connection might be a bit abstract. Maybe a little picture per section. In any case, I'll look through what I have rights to and see if there's a good biological game theory example. Pete.Hurd 19:59, 7 December 2005 (UTC)

Removed bit

I removed the following part from the Representation of Games section: "a way to determine the outcome from the strategies selected by the players", this is redudant with "and a specification of payoffs for each combination of strategies" (which immeadiately followed it). I don't actually have a strong feeling about which wording is included, but both are unnecissary. In addition, I removed the {{tl:planetmath}} template because, that bit was the only part taken from planet math. --best, kevin [kzollman][talk] 03:59, 16 December 2005 (UTC)

Nobel prize

I removed an added paragraph regarding the recent nobel prize from the intro section. I don't think that this is important enough to warrent discussion in the intro paragraph. It is not the first Nobel prize to be awarded in game theory and the article is about the topic of game theory not game theorists. The most recent prize is mentioned in the history section, but perhaps it could be expanded? --best, kevin [kzollman][talk] 18:22, 21 December 2005 (UTC)

Game theory and nuclear strategy

I remember studying game theory and strategies in nuclear war at university. There was a paper by David Lewis which I will dig out and look at. Basically it was all to do with the strategies which the different sides in the cold war would employ in the case of an all out assault by an enemy.

That's great, one of the things this article is short on is the use of Game Theory in nuclear strategy and political science more generally. I look forward to your addition! --best, kevin [kzollman][talk] 01:59, 13 January 2006 (UTC)

Deal or no deal

Amongst the vandalism, there has been a dispute about whether or not Deal or No Deal ought to be included in the list of game shows using game theory. The anon who is removing it suggests that the problem in deal or no deal is an optimization problem, and hence part of decision theory not of game theory. I don't have a strong opinion about it, but my understanding of the show is that the producers choose which boxes to open knowing which boxes contain different amounts of money. In this case, the producers actions are important in deciding what to do as a player and the player's actions are important in the producer's decisions. This makes it a game theory problem. Anyone else have any feeling about the matter? --best, kevin [kzollman][talk] 20:56, 13 January 2006 (UTC)

The contestent chooses which boxes to open, not the producer. IN this game, the influence of the producer is limited to the 'bank offers' -- my AUD0.02 - it is not really a game in the sense of game theory thing as well (but then, I don't think Monty Hall is either...) novacatz 14:27, 14 January 2006 (UTC)

I've never seen Deal or no deal, but I'd say the Monte Hall problem is a straight-up optimization. After the player chooses a door, the other move is to reveal that one of the other two doors is a distractor. That decision isn't strategic, it's a move by nature which either 1) identifies the distractor if the unchosen doors include a distractor and the prize, or 2) chooses a door at random if both unchosen doors are distractors. Presenting the MHP in the extensive form may help a lot in explaining it, but I would not say that this makes it a game theoretical problem. Pete.Hurd 15:05, 14 January 2006 (UTC)

There's a subtle point here. Whether this is a game or not depends on how the Banker decides what amount to offer. It sounds like the Banker doesn't always offer the mean of the remaining boxes... in fact, there's a sentence in the article implying that the offer is occasionally MORE than the mean. If the Banker is free to offer any amount, and doesn't have a predetermined offer for each possible set of remaining boxes, then this is a game.

Further, even if the Banker is acting on a predetermined strategy, the player has to have full knowledge of the Banker's strategy in order for this to be a true decision problem. As long as the player is unsure what the banker might offer for a particular future arrangement of boxes, the player could treat the banker as another player, and try to guess his actions. Isomorphic 15:55, 14 January 2006 (UTC)

As the anonymous user who initially took out the show, I have to concede that this is a game. The banker's strategy is critical. Presumably the banker's strategy is intended to maximize profits for the network (viewers are good, but giving away too much is bad). If someone wants to put it up I won't take it down, but I don't see any reason to confuse more people like me. I think the discussion is more appropriate on the "Deal or No Deal" page, which suggests that the strategy is governed by decision theory.

Cooperative vs. non-cooperative GT

This distinction should be made somewhere in the article and relevant links (to cooperative game) providedradek 06:50, 14 January 2006 (UTC)

I agree entirely! It was left out because no one knowledgable enough has added it in. If you know something about cooperative games please add it in. I would suggest discuss it under the Game theory in economics section. Although, if you think it would fit better somewhere else, feel free. --best, kevin [kzollman][talk] 08:45, 14 January 2006 (UTC)

I noticed this omission a few days ago, but I don't know enough about cooperative game theory to write it. Isomorphic 15:57, 14 January 2006 (UTC)

I will try to come up with something. However, since the article is already quite long I'm worried that the addition will make it too long. We could retitle the present article "non-cooperative game theory" and have a "game theory" page which gives a more general overview (basically the intro of this one) and then provides links to nc-gt and c-gt seperately. If that's too much, maybe we could keep the title and then add a sentence at the beginning along the lines of "This article deals with nc-gt, for c-gt see ..." - this might be enough since nc-gt is more common and more widely applied. radek 06:56, 15 January 2006 (UTC)

Ok, I see there is a pretty good article on cooperative game already, so maybe this one just needs a sentence or a link - maybe also a statement that Nash thought that all coop games could be reduced to non-coop games. (And I think the definition of the Core in that article is a bit inaccurate but I'll mention it on the talk page there). radek 07:07, 15 January 2006 (UTC)

Rawls?

(And all the actual game theorists groan at all the comments after being Wiki's featured article...)

I noticed in the discussion of philosophy and game theory there's no mention of John Rawls ("A Theory of Justice"). There's a mention on the page that starting at least with Hobbes, social-contract theorists have attempted to motivate morality in terms of self-interest. To my (very limited) knowledge, Rawls was the first one to use the formal methods of game theory, welfare economics, et al. to try to arrive at a specific contract (his two principles of justice). Either way, his work seems to be significant and maybe should be mentioned. Dstrozzi 05:59, 15 January 2006 (UTC)

Yeah, some choices had to be made in choosing who to include. Although Rawls used some economics and game theory, I don't think that game theoretic considerations were primary. If you think he ought to be included feel free to add it in. I have toyed with the idea of writting a game theory in philosophy article... but there are so many things to do. :) --best, kevin [kzollman][talk] 08:49, 15 January 2006 (UTC)

As an actual game theorist, what amazed me was the intensity of the vandalism. It's really changed my view of wikipedia's place in the world. I'm wondering how wikipedia is going to deal with automated vandalism from throwaway acounts... Pete.Hurd 15:27, 15 January 2006 (UTC)

I am a philosophic dilettante and a non-game theorist so I'll defer to others' judgement. Plus I don't have enough expertise to write anything beyond "Rawls did something really clever with game theory and political philosophy." Although not being qualified never stops some people...

As for vandalism, I bleed for you. I'm not active on pages where much has happened besides an occasional 'hi mom.' A real game theorist should construct a game model for vandalism - is it a zero-sum game, what's the payoff matrix, etc :)

Seriously, it surprised me when I first started with wiki to learn that _anyone_ can edit _anything_. While that allowed me to contribute something very quickly, it seems like a disaster waiting to happen. I'm sufficiently risk averse (like those in Rawls' original positionn) that if I were Jim Wales I'd have formed a cirlce of 'editors' who had the power to grant a person the right to edit in certain areas, only after 'proving their worth' by showing they had real knowledge, and who could revoke the right. But who knows how much drag that would introduce.

A good econ/game theory PhD thesis would be to develop a theory of 'fluctations' (vandalism, misinformation, errors) in wiki (or any encyclopedia) under different policy regimes. Should we 'expect' wiki or brittannica to be more accurate? Maybe Levi flights dominate the distribution - a few bad apples... But I'm just a lowly physicist - humans are too pathological! Dstrozzi 07:31, 16 January 2006 (UTC)

Real world success stories

Are there any? Has game theory actually produced any significant improvement in society? For example, are there documented instances of economies benefitting from a non-obvious insight derived solely from game theory? If so, they might be worth a mention. Eiler7 17:32, 28 March 2006 (UTC)

As far as I know using game theory to study macroeconomics is a relatively small field. Game theory is more often used to study the behavior of individuals (human or other living things). It has had predictive success in these areas (and some predictive failures as well), but I'm not sure its had anything like obvious direct improvement. The closest case I can think of, is that a game theorist designed the US's FCC auction of radio bands, and the result was generally considered good. But, I only know this through hearsay. --best, kevin [kzollman][talk] 17:58, 28 March 2006 (UTC)

determinacy/indeterminacy

Relating to the following passage:

he focus of attention is usually not so much on what is the best way to play such a game, but simply on whether one or the other player has a winning strategy. (It can be proved, using the axiom of choice, that there are games—even with perfect information, and where the only outcomes are "win" or "lose"—for which neither player has a winning strategy.) The existence of such strategies, for cleverly designed games, has important consequences in descriptive set theory.

An anon editor recently changed "existence" to "nonexistence" in the last sentence. I reverted, because it's usually the existence of strategies that has the consequences (for example, if a class of Banach-Mazur games is determined, then certain sets of reals must have the property of Baire). But it's sort of an understandable mistake, given the fact that the sentence comes immediately after a parenthetical remark talking about nonexistence of strategies. Without the parenthetical remark, though, the reader might think that the existence of winning strategies is trivial.

Anyone want to take a crack at this? --Trovatore 19:27, 6 April 2006 (UTC)

Single player game

Can someone point me to single player games theory introduction article or web resource? Thanks !! 195.137.203.137

"Single-player game theory" is nothing more than optimization (mathematics). Samohyl Jan 16:50, 14 June 2006 (UTC)

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