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Archive 1Archive 2Archive 3Archive 4

See also

radek just cleaned up the "See also" section, and while I'm sympathetic to cleaning up, I think they got it backwards. My understanding of "See also" is that it should primarily contain things not linked in the main article (here). I'm going to switch the "See also" around. I'm not fixated on my version, it's just that making the change is the easiest way to show what I have in mind.

At least two of the links--Combinatorial game and Game--are things which I think should be linked in the main article, but aren't at the moment. CRETOG8(t/c) 12:54, 24 March 2009 (UTC)

Comments on particulars:
  • Drama theory is otherwise unknown to me, but appears to be a legitimate cousin of game theory, so I think it belongs (can't figure out a snippet summary of it to go with the link, though).
  • Analytic narrative looks to me like one underdeveloped application of game theory, plus the article for it is almost non-existent. I'm taking it out, but if someone wants to lobby for it, I'm on the fence.
  • General equilibrium I'm taking out because the article has plenty of links to overall economics already.
  • Quantum game theory I'm leaving in because it always seems to incite interest when it comes up (although my interest quickly collapsed to disinterest after reading a paper on it).

Except that General equilibrium is described by David K. Levine (above) as "a specialized branch of game theory" and is not linked within the article. Note that he and others are including in "game theory" topics that are neither "classical" nor "combinatorial" as some editors would try to define "classical" here.

But I disagree with the criterion that the internal links section should only be for links not made in the body of the article. It is convenient for readers to pull together important links, especially those considered branches of the main field. Bracton (talk) 15:48, 24 March 2009 (UTC)

Your opinion is contradicted by Wikipedia style guidelines. See Wikipedia:Guide to layout. A direct quote: Links already included in the body of the text are generally not repeated in "See also". —David Eppstein (talk) 17:01, 24 March 2009 (UTC)
Those are "guidelines" not hard rules. One is expected to exercise some judgment that considers the convenience of the reader.Bracton (talk) 02:31, 25 March 2009 (UTC)
As far as General equilibrium goes, I note that the only instances of the word "G|game" in that article are in the "see also" section. I suspect that if it were widely considered to be a branch of game theory, that the article (which looks to be of reasonably high quality to me) would mention that. Pete.Hurd (talk) 17:14, 24 March 2009 (UTC)
Some researchers, like Robert Aumann argue that the whole General Equilibrium strand in economics should be recast in game theoretic terms. And this is a worthwhile research program. But, arguably, General Equilibrium predates game theory. Part of the confusion is that GE is an economic theory while, from the point of view of economics, GT is an analytical tool. Currently most uses and applications of GE are not game theoretic. I would remove it.radek (talk) 02:37, 25 March 2009 (UTC)
Good point about Robert Aumann, but the recasting is already well underway. It should also be pointed out that application fields don't "own" mathematical methods. That is why we classify GT as a branch of mathematics rather than of economics, even though it is used in economics. Its popularity arises from how well it works with many fields. It has emerged as one of the leading bodies of tools for interdisciplinary development. We also see a lot of work to develop new branches that don't fit in the "classical" or "combinatorial" mold. We don't serve our readers to restrict the topic in ways that will only confront us with embarrassment that we didn't allow for expansion. Bracton (talk) 03:40, 25 March 2009 (UTC)
The problem with that article is the capitalization of all its key words, instead of only the first. It also is a stub with a lot needed to flesh it out. For example, much of the recent work relating game theory to communications is for mesh networking, but that is a couple of links removed. Bracton (talk) 22:49, 26 March 2009 (UTC)

I have reverted the deletion of Zero-player game. It is an important concept, even if it is used with at least two distinct meanings (no players or no human players). Both of them are useful for understanding games of various kinds. Disparaging it is like an ancient Roman disparaging the idea of zero in an article on arithmetic or the natural numbers.

Consider, for example, solution of the classic Towers of Hanoi puzzle. The standard method of seeking a solution algorithm is to start with a simplied version with three pegs and only one disk, then increase the number of disks. Similarly, one can "solve" some games by starting with simplified versions of them: fewer or no actions, players, payoffs, etc. Even if a zero-player game may not be the target of interest doesn't mean it may not be worth analyzing on the way to understanding the game with more players.

Any theory which involves values of a parameter n for values n > 0 should, for the sake of completeness, also cover n = 0. Even if the object for a value of zero seems trivial or uninteresting. Mathematical formalisms have their own natural bounds. Bracton (talk) 05:37, 26 March 2009 (UTC)

I don't think it is an important concept at all. Google scholar turns up virtually nil [1]. All (but one) uses of it in scholarly publications, are in the field of cellular automata, not in game theory, and those papers seem to have never been cited. One paper [2] (cited twice according to GS) is not explicitly about cellular automota, but seems quite far afield from game theory. I see no verifiable evidence that Zero-player game is an important concept in game theory. I would be swayed by the appearance of the concept in standard game theory texts... Pete.Hurd (talk) 05:49, 26 March 2009 (UTC)
google Scholar is not the ultimate authority on this. It is a new tool that will take years to fully populate. Bracton (talk) 22:49, 26 March 2009 (UTC)
The fact that you connected the null player property with zero-player games, means that your knowledge of game theory is extremely poor. When I saw the link you added (and that was appropriately deleted few hours later): [3], my fist thought was whether my colleague and friend René had changed field of research ;-) --Fioravante Patrone en (talk) 12:46, 26 March 2009 (UTC)
Your arguments for including zero-player game amount to wp:or. I'm pulling it back out. CRETOG8(t/c) 16:50, 26 March 2009 (UTC)
The WP:OR is for articles, not arguments made in talk pages, where it is reasonable to offer some original insights in explaining editorial decisions or recommendations. However, in this case there is no OR -- merely linking to an existing article authored by someone else.Bracton (talk) 21:55, 26 March 2009 (UTC)
You might have a point about OR on talk pages. Instead, I'll say your arguments are unconvincing. CRETOG8(t/c) 08:34, 27 March 2009 (UTC)
Honestly, I don't think this issue should be joined in the "See also" section. If zero-player games are a recognized notion backed up by reliable sources, then the link from "See also" seems plausible; if they're not, then the zero-player game article should be deleted. I have no well-considered opinion as to which of these two cases holds. --Trovatore (talk) 17:03, 26 March 2009 (UTC)
I lean towards thinking that article should get deleted, but it's not something I want to start right now. I also think it's possible that zero player game is a concept in computer game design or automata theory, but that it still wouldn't belong as a link here. CRETOG8(t/c) 07:52, 27 March 2009 (UTC)

Representation of games (Confusing)

I think the Representation of games section is confusing and should be redone. Very little discussion is given to what a game is and much discussion is given to "forms". The problem lies in trying to balance brevity and depth. Either much greater explanations must be presented across the board or the presentation of the forms should be abandoned, in favor of something along the lines of "matrices and trees can be used to help study games. In this example the matrices represent..."

Bret101x (talk) 04:36, 2 August 2009 (UTC)

Representations may be pointless and confusing when one cares primarily about the mathematics of fixed points, but they are crucial when one cares more about the computational complexity of game-theoretic problems. A problem that requires exponential time in one representation may be polynomial in another due to the difference in size between different representations of the same game. So I wouldn't want this subject dropped altogether, but perhaps it belongs more in the computer science section than where it is now. —David Eppstein (talk) 05:13, 2 August 2009 (UTC)

Deleted: Game theory initial developed for (zero sum games)

In the 1944 book Theory of Games and Economic, Von Neumann and Morgenstern clearly state their position that economic theory requires a treatment different from that which they have found thus far in the literature. They draw many parallels between the advances in physics and argue that a mathematical treatment is necessary for the advancement of the field of economics. This would seem to suggests that the primary intention of the authors was the advancement of the field of economics.

This contradicts the notion that game theory was "initially developed to analyze competitions in which one individual does better at another's expense (zero sum games)"

I removed 8/1/2009 Bret101x (talk) 03:45, 2 August 2009 (UTC)Bret101x

So, von Neumann 1928 is irrelevant? I would bet that vNM 1944 would never had appeared without vN 1928 (and 1937...) --Fioravante Patrone en (talk) 08:24, 2 August 2009 (UTC)
I have restored the sentence on zero-sum games that was deleted. --Fioravante Patrone en (talk) 23:20, 23 August 2009 (UTC)

"most famously"

In the paragraph near the beginning, there's a sentence that says the Nash equilibrium is the most famous, but there's no citation for this. Could someone confirm where it's mentioned this is the most famous, as if it's not, the wording should perhaps be changed. --Rebroad (talk) 20:53, 1 November 2009 (UTC)

Just read any game theory book. Nash equilibrium is by far the most basic (hence used, described, etc., and so famous) equilibrium concept in game theory. --Fioravante Patrone en (talk) 21:43, 1 November 2009 (UTC)
Citations are required to support contentious statements. There is no use in adding "ciation needed" tags to every single uncited statement. If there were heated debate about whether the Nash equilibrium is the most famous, then a "cn" tag would be appropriate. Pete.Hurd (talk) 04:23, 2 November 2009 (UTC)

Game Strategy

I made some additions to the article with regards to practial approaches in business under the umbrella of "Game Strategy". A fellow writer removed the addition because of undue weight to the ideas of one particular book. Point taken. However, I feel that a reference to this practial approach towards game theory would benefit the article. I am writing here to discuss how that could be achieved without imposing "undue weight". Or is the consensus here that the entire addition is pretty much worthless and a discussion about the "how" is a waste of time? I also noticed in one talk above that an auxiliary article about game theory in economics and business was planned - which may or may not be a better environment for the concept at hand. Youngtimer (talk) 21:00, 22 March 2010 (UTC)

I was hoping someone else would offer input. O well. Here's the additions Youngtimer made: diff. I reverted them. I haven't read the book in question, but based on the material there, I don't think it merits mention in the article. It's possible that's just because of how the material was presented. For instance, the connection to game theory wasn't clear. If it's a matter of suggesting that businessfolk consider game theory and how to not just play the game, but structure the game, that's a pretty standard part of many business/game theory courses and books. The material added looked too much to me like it was promoting a particular book. CRETOG8(t/c) 16:39, 24 March 2010 (UTC)
I have come to the realization that I may have gone overboard with this addition and apologize. For an explanation about the relevance of game strategy in relation to game theory (and especially the differences) I found a convenient way to read this section of the book without purchasing it. If you go to Amazon and find the book ("The Impossible Advantage") there you can "search inside". The chapter about "How game strategy differs form game theory"is indexed as "back matter" and therefore can be accessed by everybody for free. I do not intend to inconvenience anybody into jumping through all these hoops but since you were asking I thought it would be useful to point you towards first-hand information.

--Youngtimer (talk) 02:00, 31 March 2010 (UTC)

cheeky phrase

I think the phrase

"this profound work contains the method for finding mutually consistent solutions for two-person zero-sum games"

sounds unprofessional. Profound work? What about foundational, important, etc. what about:

17:58, 1 May 2010 (UTC)~~

I agree, "profound" is too strong a word and probably violates WP:NPOV. I changed it to "important". Justin W Smith talk/stalk 18:10, 1 May 2010 (UTC)

It might be more accurate to say that it was editorializing. Justin W Smith talk/stalk 18:15, 1 May 2010 (UTC)
Well, actually you changed to "foundational", not to "important" ;-) Anyway, I agree --Fioravante Patrone en (talk) 19:33, 1 May 2010 (UTC)
Doh... sorry. I went back-and-forth on that decision. Feel free to change it again, so long as it doesn't sound like we're editorializing. Cheers, Justin W Smith talk/stalk 20:03, 1 May 2010 (UTC)

Hawk-dove = chicken?

"Finally, biologists have used the hawk-dove game (also known as chicken) to analyze fighting behavior and territoriality." Is it correct that "chicken" is used as a term for "hawk-dove"-games? I always thought, there is a difference! Rieger 13:24, 13 August 2006 (UTC)

Chicken and Hawk-Dove are both symmetrical discoordination games (as long as the standard V<C assumption is made for the Hawk-Dove game). The payoff matrices are essentially the same. In the matrix below, A is either Hawk or Don't Swerve, and B is Dove or Swerve, then they payoffs have the ranking Tempation>Coordination>Neutral>Punishment and the games will have the same reaction correspondences (see Best response#Discoordination games) or appendices in J theor Biol (2006) 241:639-648 :) )
Discoordination game payoff matrix
A B
A Punishment, Punishment Temptation, Neutral
B Neutral, Temptation Coordination, Coordination

Pete.Hurd 14:34, 13 August 2006 (UTC)

Just changed the Hawk-Dove example to a numerical example. Up to now the pay-offs were indicated by variables. Where V > C had to hold. Unfortunately, this was never indicated throughout the text. —Preceding unsigned comment added by 129.13.72.198 (talk) 11:27, 27 July 2010 (UTC)

Outline suggestion

For the types of games to consider, Webb (2007) has the "most encyclopedic" approach, bulldozing over turf wars between applied fields. Tijfo098 (talk) 10:23, 20 March 2011 (UTC)

Economics?

Why in the love of Nash is Game Theory belong in the category of Economics?? This should in the Mathematical category, even then it's more related to evolution than it is to economics! 141.117.178.185 (talk) 03:46, 21 September 2011 (UTC)

Nope, game theory is hugely important in economics. CRETOG8(t/c) 04:52, 21 September 2011 (UTC)
So why then does the article start with the phrase, "Within math?" Just asking. Eleuther (talk) 21:42, 2 October 2011 (UTC)
I don't think merely being important to economics justifies putting the article in category:economics. But if I'm not mistaken, game theory is not merely important to economics, but is actually studied by economists, as a branch of economics. It's a little borderline, but I think I probably come down on the side of including it. --Trovatore (talk) 21:52, 2 October 2011 (UTC)
As an economist who studies game theory, I keep being uncomfortable with the "Within math, game theory..." opening line. From my perspective it seems simply wrong, although it's a matter of perspective. The mathematical parts of game theory involve proving uniqueness/existence/stability of equilibrium given various assumptions. But there's a lot of "game theory" which involves the mapping of the theory to an application, and many of the assumptions underlying various solution concepts were originated by economists based on economic reasoning. Anyway, one of these days I may feel the need to change that, probably should find a reference first. CRETOG8(t/c) 22:54, 2 October 2011 (UTC)
Courses in game theory are overwhelmingly taught within Economics departments, textbooks on game theory are overwhelmingly filed under Economics, and specified as such. The theory may be mathematical, but it is easy to demonstrate that secondary and tertiary sources consider game theory to be a branch of economics. It may be an odd historical accident, but it is the way it is. Pete.Hurd (talk) 15:05, 3 October 2011 (UTC)
My university offered courses in both the math department and the economics department (different courses!). It seems obvious to me that the article should be in some economics category (whether Economics itself or a subcat I have no immediate opinion). CRGreathouse (t | c) 15:13, 3 October 2011 (UTC)

I guess I wasn't thinking clearly enough about categories. For categories, I think the most useful categorization would be economics. Because the importance goes both ways: you really have to study game theory to study modern economics and the bulk of game theory is oriented around economics (although there are certainly lots of other applications). As far as the "Within math, game theory..." opening line, I would simply pull out the "Within math" and not replace it with anything. I think game theory has matured enough to stand on its own, and I wouldn't open the mathematics article with "Within philosophy, math is...". CRETOG8(t/c) 16:28, 3 October 2011 (UTC)

Inconsistency?

If the definition under "Representation of games" in this article is correct: "The games studied in game theory are well-defined mathematical objects ... and a specification of payoffs for each combination of strategies", then the summary of the article needs to change to reflect this. At present there seems to me to be a conflict in definition between a concept of it applying to a mathematical-model or to a general non-mathematical model where payoffs cannot be mathematically specified e.g psychology, where an individual may change the "rules" of the game in this regard at any point. LookingGlass (talk) 12:49, 21 January 2012 (UTC)

Criticism

I removed a section labeled "criticism of game theory" and returned the material to its original place. Labeling it "criticism of game theory" seems inappropriate, as the criticisms do not apply to the use of game theory in biology (biologist do not presume that animals are rationally self-interested in the sense criticized). Rather this is a criticism of game theory as used primarily in economics. As a result, I think its more appropriate there. The bit added about John Nash is merely an bad ad hominem. I say bad, because those assumptions were used in game theory long before Nash. So even if Nash's mental state was relevant, it doesn't explain the assumption. Besides, on matters like this, the BBC is not a reputable source. --best, kevin [kzollman][talk] 17:35, 13 April 2007 (UTC)

Having a "criticism of game theory" section would be like having a "criticism of differential calculus" section. However it is possible to criticize the various ways that game theory has been applied or used. Perhaps there should be an article or section on Applied Game Theory or Uses of Game Theory?radek 21:34, 13 April 2007 (UTC)

We already have some criticism of game theory in the "uses of game theory/economics" section. More could certainly be added there. But adding much criticism to this section as it is would mean that there might be an unbalanced amount of criticism of game theory in economics. In any case, Nash's mental state doesn't really belong in this article.
I have a related comment/question. I think that section could use a little bit more material, both positive and critical discussion. Does anybody agree that the "in economics" section could use some lengthening, or do people think that most lengthening should be done in subarticles, to which this article may link?
The later would entail consigning, for instance, Franklin Fisher's general criticisms of game theory in the article I linked to at folk theorem and to oligopoly (which is the particular application of game theory that Fisher is most interested in). The former would mean bringing his and others' general points to this article, which could be done only if they were adequately balanced with answers (in this case, Carl Shapiro argues that Fisher's point is a straw man)
In case you are wondering, the articles I'm thinking of are: Fisher, Franklin M. Games Economists Play: A Noncooperative View, and Shapiro, Carl. The Theory of Business Strategy, both in The RAND Journal of Economics, Vol. 20, No. 1. (Spring, 1989). Smmurphy(Talk) 17:29, 14 April 2007 (UTC)
Sm - I think this is a nice idea, but probably better for daughter articles. I had hoped that we could write articles like game theory in philosophy, game theory in biology, game theory in economics and business, etc. I have intended for sometime to write the first, but you know how it goes.... --best, kevin [kzollman][talk] 19:57, 23 April 2007 (UTC)

hello, thank you for the response. I wasn't sure how the section would play out. I know this page has had alot of work done on it. That being said, the idea that game theory is uncriticisable is very wrong. Settling this debate only means finding more sources, which i will do. Kzollman's idea that "the BBC is not a reputable source" is contrary to wikipedia's guidelines. Adding a new section does not reduce the value of the article. I concede that calling nash a psychopath is ad hominum. There is much to be criticised about game theory and this section can be valid if done well. I will do more work, but it will not be able to get better unless the section can survive on the page for more than 4 hours. For those unfamilliar with the criticisms of ame theory, please take my word that they are widespread, and the page will be more comprehensive if they are mentioned formally.Spencerk 18:11, 14 April 2007 (UTC)

Thank you for being bold. Generally with established articles (and especially featured articles), large discussions are brought to talk first. Even though your addition was reverted, hopefully we can come to a consensus on including the right amount of criticism in the article. One more note, BBC isn't a reliable source on game theory per WP:RS, BBC reporting on game theory fails more than one of the criteria in the section about non-scholarly sources. Its a case where a source has a different degree of reliability in different contexts, and we have many more reliable sources (published journal articles, books by reputable authors, etc) for discussing GT. Smmurphy(Talk) 20:56, 14 April 2007 (UTC)

i tried it in a section called Family, society, and personal relationships. it is incomplete and not properly referenced, but perhaps others can see value in it, that game theory fails to be appropriate in some contexts. If not, i will stop, being bold a third time is just annoying. thanks for discussion, Spencerk 20:36, 16 April 2007 (UTC)

I don't see much of the problem with the material per se (except that it essentially duplicates some things said in the 'Descriptive' section) but I'm not sure that you put it in the right place. My feelings on the broader question are this: If the players are altruistic that's not a problem for game theory. It just means they're playing a different game. If the players are not completely rational, that's not a problem for game theory in many cases. Whatever cognitive or other constrains they face should be incorporated into the structure of the game and voila. I think it's important to distinguish between Game Theory as a tool of analysis, a methadology, and its applications. You can criticize the latter but criticizing the former is like criticizing calculus. But I also think that mentioning that there are many instances where people appear not to play Nash is important. Second, I think that the fact that the predictions of a game can be very sensitive to choice of parameters or structure of the game should also be mentioned. Third "criticism" would be the Folk Theorem - what good is a theory in which anything can happen? Of course all of these should be put in a proper context. radek 20:48, 16 April 2007 (UTC)

hi radek, i think your idea is common amung game theorists, atleast the game theory teacher at my school also feels this way too i think. -"if the player cares about alruism or ethics or something, throw it in the payoffs". - this is psychological egoism. Take the soldier that jumps on the granade to save his soldiers for example. Its possible to explain his actions in somesort of payoff way, like honour or legacy or afterlife, but thats crazy! right!? atleast, this 'tool of analysis' recieves huge criticism in philosophy class. interesting, yes. usefull, yes. accurate, ...is self interest the best way of understanding the soldier jumping on the bomb? no way. soldier jumping on bomb is just one example, friendship eg applies also. i dont know what the folk theorem is. Spencerk 02:11, 18 April 2007 (UTC)

I have removed this new section. Game theory is used widely in many different disciplines in many different ways. For example, game theory as used by biologists presume that the payoffs represent fitness, and that animals simply play a strategy which is (in some sense) biologically determined. Learning models used in evolutionary game theory are similar. The criticism offered in this section are not sufficiently general to apply to all of game theory, but only its use in one field (hence its location in economics). It is controversial whether individuals cooperate in the prisoner's dilemma, but the other examples of non-nash play are already mentioned. The fact that it has been removed from the article does not prevent it from eventually being included there. We can put a draft of such a section here if you like and hammer it out. But I don't think the section is ready for the live version of the article yet. --best, kevin [kzollman][talk] 19:55, 23 April 2007 (UTC)

There is no doubt that the current entry on game theory is biased. As already noted, there are articles and a documentary posing views against the applications of game theory to social sciences. To withdraw any mention of these sources from this article for such a prolonged time is unacceptable. A layperson reading this article will get the impression that there is no ongoing debate over this issue. 21:13, 3 December 2007 (UTC)

Let me stress the point again. This article is strongly biased in favor of game theory. A layperson reading it will leave with a rosy impression of it. I tried to put a single phrase on the article saying that the applications of game theory are not without criticism. This was, of course, a mild statement. Even this trivial modification was deleted from the article. It is unacceptable that pop culture movies such as A Beautiful Mind gets mentioned here while the documentary The Trap from the BBC over this topic is not even listed on the references. It is impressive that ALL scholary articles listed are in favor of game theory; why not to mention the research of Philip Mirowski on this topic? It seems that there is no option besides puting a dispute on this article. 21:12, 3 December 2007 (UTC)

Okay, let's be clear. Game theory is a mathematical theory. One can no more criticize game theory than one can criticize algebra. One can, however, criticize applications of game theory. So, the place for criticism is the application section. Notice, most of the commonly cited criticisms of game theory criticize the high-rationality approach to game theory as used in economics and political science. Those criticisms do not apply to the use of evolutionary game theory in economics, game theory in biology, game theory in computer science, or game theory in philosophy. If you know of criticisms to those applications of game theory, I recommend you add them. With respect to criticisms of high rationality game theory, I think there is substantial discussion of those criticisms. A few quotes:
  1. "This particular view of game theory has come under recent criticism. First, it is criticized because the assumptions made by game theorists are often violated."
  2. "However, additional criticism of this use of game theory has been levied because some experiments have demonstrated that individuals do not play equilibrium strategies."
  3. "However, this use for game theory has also come under criticism. First, in some cases it is appropriate to play a non-equilibrium strategy if one expects others to play non-equilibrium strategies as well."
  4. "Second, the Prisoner's Dilemma presents another potential counterexample."
  5. "Some assumptions used in some parts of game theory have been challenged in philosophy; psychological egoism states that rationality reduces to self-interest - a claim debated among philosopher"
If there are particular criticisms you would like to see added to particular applications of game theory, we can discuss them here. I don't know Mirowski's work, but it looks to me like it may be described by one of the quotes I mentioned. I welcome you adding him as a cite to those claims if it applies. --best, kevin [kzollman][talk] 05:05, 4 December 2007 (UTC)

Dear editors, seeing; http://plus.maths.org/content/adam-smith-and-invisible-hand I suggest some editting. talk — Preceding unsigned comment added by 83.82.77.119 (talk) 16:00, 31 May 2012 (UTC)


Survey section

Would there be value in adding a kind of survey section containing (pointers to) the major theorems and results of game theory? The current setup covers the history well, and explains the "dimensions" of game theory (types of games, applications of the theory, etc.) but doesn't really map out the terrain at a high level. I'm nowhere near knowledgeable enough to author such a section, but I'd love to read one! --Doradus (talk) 14:44, 21 June 2012 (UTC)

Weasel wording

I've removed the so-called weasel wording in the "Combinatorial games" section. "Some" there was used to give examples, not really in contravention of WP:WEASEL. This is an overview article, so we cannot give all the details. The "Description and modeling" and "Philosophy" sections on the other hand are more difficult to fix. I don't know enough about the proponents and opponents of various things said there to do it myself... Tijfo098 (talk) 00:59, 22 September 2012 (UTC)

Game Theory is not just used in Economics

Why is there an Economics sidebar in article about Game Theory. Game Theory is

(1) a purely subfield of mathematics (2) applied in many other fields of study (economics, biology, social sicence, military science)

ergo Economics doesn't own Game Theory! — Preceding unsigned comment added by 149.172.156.166 (talk) 16:59, 7 January 2013 (UTC)

Pascal's Wager absent from section on Philosophy

Isn't Pascal's Wager a pretty prominent example of game theory being used in philosophy? I'm not going to add anything on it because I'm not very knowledgeable about it, but it seems like a mention of it would be fitting. 2600:1016:B013:8A65:A89B:E735:1022:9646 (talk) 17:03, 8 August 2013 (UTC)

Types of games/Combinatorial games

Quote: "Games in which the difficulty of finding an optimal strategy stems from the multiplicity of possible moves are called combinatorial games."

But then the section later refers to combinatorial game theory which has "Combinatorial game theory (CGT) is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning condition."

It would seem that the more common usage of "combinatorial game" now is in the sense of combinatorial game theory, not just combinatorial move complexity.

At least something like "Games in which the difficulty of finding an optimal strategy stems from the multiplicity of possible moves are called combinatorial games, but the phrase combinatorial game is also be applied to games in a more restrictive manner within combinatorial game theory." — Preceding unsigned comment added by Um297zoa (talk • contribs) 06:09, 4 June 2014 (UTC)

Can there be mention of criticism of Economics Applications of Game Theory here?

Hello I see in the economics section of this article [4] there is a notebox at the beginning saying "This article is incomplete. Please help to improve the section, or discuss the issue on the talk page. (November 2010)" Can someone let me know in what way is it incomplete? Is it missing criticism to keep the article from being POV? Is criticism not the right word? I see other sections such as Philosophy mention how it was challeneged.

Is description and modeling the correct location for such differing views? I see in that section right now there is a sentence: "Alternatively, some[who?] authors claim that Nash equilibria do not provide predictions for human populations, but rather provide an explanation for why populations that play Nash equilibria remain in that state. However, the question of how populations reach those points remains open." It seems that section should have some reliable sources. But it seems an odd place for the info even if relaible sources do exist.

As for sources I was thinking that the sources at [5] would suffice. And that article, I understand game theory is a math theory, but it's infobox in the lede is all about economics, this is in the business and economics portal, and plenty of reliable sources refer to it in economics (this seems to be 90% economics sources [6] Popish Plot (talk) 15:43, 3 April 2015 (UTC)

And I see this was somewhat discussed here [7] but it didn't seem to have a consensus. Popish Plot (talk) 15:56, 3 April 2015 (UTC)
I don't think that tv series would be a reliable source. There are criticisms of applications of game theory out there but they have more to do with the limitations of the approach. What we would like to have here is scholarly sources.Volunteer Marek (talk) 16:12, 3 April 2015 (UTC)
Do you mean a scholarly source in terms of an economist, or a mathmatician? Is Adam Curtis, a journalist no good? Popish Plot (talk) 17:33, 3 April 2015 (UTC)
Either, although you're less likely to find a mathematician. From a mathematical point of view it makes about as much sense to have a "Criticism of Game Theory" section as it does to have a "Criticism of Calculus" or "Criticism of Algebra" section. What can be criticized however is how game theory is applied/used in analyzing real world phenomenon, whether in economics, political science, biology, computer programming or whatever. There you could probably find somebody. In fact probably the people who are most aware of the limitations of the game theoretic approach are those who've spent their lives studying it. But yeah, a journalist, probably no good.Volunteer Marek (talk) 17:55, 3 April 2015 (UTC)
I asked because I wanted to make sure you understood I don't mean mathamatics, but the economics aspect of it which is talked about on this page. And it does say there are criticisms of it on this page but it's unsourced. Do you think someone might have been putting that in without a source which is against the policies here? I was thinking the article could be improved by adding sources but maybe things in the article that are unsourced should be deleted instead? Also should everything in the page that is sourced to a journalist be removed? Popish Plot (talk) 18:19, 3 April 2015 (UTC)
Yeah, there's some problems there. Some of it should be removed, some of it tagged requesting citations. If journalists are being used as sources, better sources should be found if the claim is relatively non-controversial, and removed if it is potentially contentious.Volunteer Marek (talk) 18:33, 3 April 2015 (UTC)
So I'm looking to help, but not sure how to find some good sources, right now it seems like they don't exist so I'd think of removing unsourced things but I'm wary about it being controversial here. Popish Plot (talk) 19:40, 3 April 2015 (UTC)
You can mention specifically what you have in mind here. In terms of sources, I think it does require some substantial familiarity with the topic in order to know where to look. One person who comes to mind who is both a critic and practitioner of game theory would be Ariel Rubinstein.Volunteer Marek (talk) 20:27, 3 April 2015 (UTC)
Specifically what I had in mind was either 1. adding sources for places in the article that have "citation needed" or 2. adding some sort of information about how the economic view of game theory isn't all positive. I showed my sources for that but I guess they are unreliable and/or unnotable? Thanks I will look into Ariel Rubinstein as a possible source of information. Popish Plot (talk) 20:34, 3 April 2015 (UTC)

"Repeated round, open book" in game theory?

I just read a mention of what they termed "repeated-round, open-book" theory. Viz:

"Game theorists show that the surest way to boost cooperation is “repeated-round, open-book” play — you interact with an array of individuals multiple times (a known social group) that can access your play history. In other words, the more we're known, the less we act like jerks."

Where does this fit in with the Game theory article or its linked articles. Is this subsumed within Repeated game? Shenme (talk) 18:18, 8 June 2015 (UTC)

FourthKind Resolution - The vos Savant “Goat” is Revealed, the 40 Year-Old Question Solved!

Off topic and WP:NOTAFORUM. Any attempt to reinstate will result in page protection and possible blocks.--Salix alba (talk): 09:50, 1 March 2016 (UTC)
The following discussion has been closed. Please do not modify it.

FourthKind Resolution

FourthKind Resolution - The vos Savant “Goat” is Revealed, the 40 Year-Old Question Solved!


The Paradox Question: Is it to your advantage to switch your choice? (Whitaker, 1990, as quoted by vos Savant 1990a)

The Answer: "No" — Preceding unsigned comment added by FourthKind (talk • contribs) 09:50, 1 March 2016 (UTC)


Without a “random” choice in the vos Savant Model (VSM) it should NEVER be compared with the Monty Hall Show. Flaw of Reasoning: THE FALSE DILEMMA: is a type of informal fallacy that involves a situation in which only limited alternatives are considered, when in fact there is at least one additional option. From Wikipedia: https://en.wikipedia.org/wiki/False_dilemma


In VSM there is no room for a “random” choice at Q2. Only “always-stay” or “always-switch”. This forces the “Model’ into a 2 element Sample Space “model”, through out the entire “game”.


In The Monty Hall Show the Sample Space 2 members are undetermined before Q2. The answer at Q2 sets the Sample Space at 2 equal members. Thus the 1/2 possible outcomes in the Sample Space. Just toss a coin, choose “random” and that’s it. ALWAYS a 1/2 probability. As simple as that. In VSM the Sample Space is essential ‘locked” into a “rigged” 2 member of the Sample Space from the start. Now it drives the contestant to it’s destination of: “always-stay” or “always-switch”, essentially then “always-lose” or “always” switch”. Not much fun.


It’s like trying to compare apples to oranges. One never can.


Without that simple real “choice “ of “random” the VSM cannot and should not be compared to The Monty Hall Show. That’s it in a nutshell.


A simple 1/2 probability at Q2 got turned into “rigged” outcome by VSM and then got “labeled” the VSM model for “proving a probability advantage of 2/3 vs. 1/2 in the Monty Hall Show. Think again. A 40 year-old hoax.


I will elaborate more why 3-Card Game, Million Door Example, Finger On Pea are also explained as “examples” to have an edge in any of the games/examples. Without a real “random” there is no game at all. The illusion. The flaw of reasoning here: False Dilemma: There ARE more than 2 choices, there is a 3rd real choice, choose “random” at Q2 in the Monty Hall Show, choose “random”. Just toss a coin. No model can beat that at a one-time event with 2 elements/embers of the Sample Space set at Q2. The literal moment of truth. It’s a simple coin toss, nothing more.


This is why: At Q1 in The Monty Hall Show there is:


0 probability for the Contestant winning.

0 probability for the Contestant losing.

0 probability for the Host winning.

0 probability for the Host losing.


This sample space of 3 used in argument’s for 1/3-2/3 models are then compared vs. the sample space of 2 in MHP.

There is a 0 (zero) probability, meaning impossible that a win or loss takes place at Q1. This is statistically insignificant, really.


At Q1 answer “always-stay” in VSM there is:


1/3 probability for the Contestant winning.

2/3 probability for the Contestant losing.

2/3 probability for the Host winning.

1/3 probability for the Host losing.


At Q1 answer “always-switch” in VSM there is: 2/3 probability for the Contestant winning.

1/3 probability for the Contestant losing.

1/3 probability for the Host winning.

2/3 probability for the Host losing.


You can see the difference. The reference door was fluff (sorry Monty) for the show and literally inconsequential probability wise to the argument.


Redefining a key term “choice” is fuel to run the models. It is everything. It sets the Sample Space at 3 at that moment. A Sample Space of statistical consequence and then the vehicle rides itself to it’s destination. Choose “always-switch” and win 2/3! A great model to show that. The vos Savant Model ONLY proves itself within It’s own model. Not in reality or the Monty Hall Show, or the Monty Hall Problem.


Flaw of Reasoning: UNFAIRLY REDEFINING A KEY TERM: The argument proceeds by redefining a term in a way that is favorable to the argument. The term is “choice”. A simple “reference door” got exchanged (flaw here) to then mean “choice” in all the models to help “prove” (remember ONLY WITHIN THE MODEL ITSELF) the 2/3 advantage. An Illusion.


More later.

FourthKind FourthKind (talk) 09:42, 1 March 2016 (UTC)

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Political game theory

You are invited to join the discussion at Wikipedia:Articles_for_deletion/Political_game_theory. Spirit Ethanol (talk) 19:18, 13 March 2016 (UTC)

Dr. Benchekroun's comment on this article

Dr. Benchekroun has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:


Infinitely long games : clarify the distinction with infinite horizon games (for example in differential games)

In the differential games section: needs the definition of open-loop and closed-loop strategies.

References for differential games: Dockner Jorgenson Long and Sorger (2000). Basar and Older. Jorgenson and Zaccour (2003) for applications in management. A survey in dynamic games by Long (2010). Also Haurie, Krawczyk and Zaccour , Games and Dynamic Games (2012).


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Dr. Benchekroun has published scholarly research which seems to be relevant to this Wikipedia article:


  • Reference 1: Hassan Benchekroun & Cees Withagen, 2012. "On Price Taking Behaviour in a Non-renewable Resource Cartel-Fringe Game," OxCarre Working Papers 080, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
  • Reference 2: Hassan Benchekroun & Ngo Van Long, 2013. "Do Increases in Environmental Risk Reduce Welfare? A Dynamic Game Perspective," CIRANO Working Papers 2013s-08, CIRANO.

ExpertIdeasBot (talk) 15:33, 24 June 2016 (UTC)

Dr. Peleg's comment on this article

Dr. Peleg has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:


I restrict my comments to Subsection 1.3 (Characteristic function form). I will rely exclusively on the textbook: Bezalel Peleg and Peter Sudholter (2007) Introduction to the theory of cooperative games, 2nd edition, Springer, Berlin. I shall use the abbreviation PS for the book. First, the term characteristic function is an anachronism (and is overused in mathematics). The current term is "coalitional function". For a definition of a TRANSRFERABLE utility game see Section 2.1 of PS. For the relationship to the von Neumann Morgenstern book see Section 2.4 in PS For coalitional functions of games with no transferable utility (NTU games) see Chapter 11 in PS.


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  • Reference : Peleg B. & Peters H.J.M., 2014. "Choosing k from m: feasible elimination procedures reconsidered," Research Memorandum 033, Maastricht University, Graduate School of Business and Economics (GSBE).

ExpertIdeasBot (talk) 20:35, 1 July 2016 (UTC)

Dr. Herings's comment on this article

Dr. Herings has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:


General comment:

One would expect a description of pure versus mixed strategies and the fact that mixed strategies are needed to guarantee the existence of a Nash equilibrium.

(which in real-world terms can be interpreted in many ways, the simplest of which is in terms of money but could mean things such as eight days of vacation or eight countries conquered or even eight more opportunities to play the same game against other players) and Player 2 gets a payoff of "two".

Comment: The most important interpretation is that payoff represents utility, typically von Neumann-Morgenstern utility.

When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other.

Comment: Since strategies are formulated contingent on the available information, the statement without knowing the actions of the other is misleading.

In games that possess removable utility, separate rewards are not given; rather, the characteristic function decides the payoff of each unity. The idea is that the unity that is 'empty', so to speak, does not receive a reward at all.

The origin of this form is to be found in John von Neumann and Oskar Morgenstern's book; when looking at these instances, they guessed that when a union C {\displaystyle \mathbf {C} } \mathbf {C} appears, it works against the fraction ( N C ) {\displaystyle \left({\frac {\mathbf {N} }{\mathbf {C}

\right)} \left({\frac {\mathbf {N} }{\mathbf {C} }}\right) as if two individuals were playing a normal game. The balanced payoff of C is a basic function. Although there are differing examples that help determine coalitional amounts from normal games, not all appear that in their function form can be derived from such.

Formally, a characteristic function is seen as: (N,v), where N represents the group of people and v : 2 N → R {\displaystyle v:2^{N}\to \mathbf {R} } v:2^{N}\to \mathbf {R} is a normal utility.

Such characteristic functions have expanded to describe games where there is no removable utility.

Comment: This part is incomprehensible and should be rewritten. 

For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players.

Comment: Since affine transformations of payoffs do not affect the strategic aspects of the game, this asymmetric game could well be considered to be a symmetric game, so is not a good example of an asymmetric game.

Zero-sum games are a special case of constant-sum games, in which choices by players can neither increase nor decrease the available resources. In zero-sum games the total benefit to all players in the game, for every combination of strategies, always adds to zero (more informally, a player benefits only at the equal expense of others).[44] Poker exemplifies a zero-sum game (ignoring the possibility of the house's cut), because one wins exactly the amount one's opponents lose. Other zero-sum games include matching pennies and most classical board games including Go and chess.

Comment: This is ignoring the intrinsic utility derived from playing games. Taking this into account, it is very hard to think of real-world games that are really zero-sum.

Games of incomplete information can be reduced, however, to games of imperfect information by introducing "moves by nature".[46]

Comment: Games of incomplete information can be reduced to games of complete information by introducing "moves by nature".

For instance, Cournot competition is typically modeled with players' strategies being any non-negative quantities, including fractional quantities

Comment: Replace "including fractional quantities" by "including quantities that are not integers."

Pooling Games[edit]

These are games prevailing over all forms of society. Pooling games are repeated plays with changing payoff table in general over an experienced path and their equilibrium strategies usually take a form of evolutionary social convention and economic convention. Pooling Game Theory emerges to formally recognize the interaction between optimal choice in one play and the emergence of forthcoming payoff table update path, identify the invariance existence and robustness, and predict variance over time. The theory is based upon topological transformation classification of payoff table update over time to predict variance and invariance, and is also within the jurisdiction of the computational law of reachable optimality for ordered system.[58]

Comment: This paragraph could be deleted.

This equilibrium is sufficiently general to allow for the analysis of non-cooperative games in addition to cooperative ones.

Comment: Nash equilibrium is used for the analysis of non-cooperative games, not for cooperative ones.

In 2007, Leonid Hurwicz, together with Eric Maskin and Roger Myerson, was awarded the Nobel Prize in Economics "for having laid the foundations of mechanism design theory." Myerson's contributions include the notion of proper equilibrium, and an important graduate text: Game Theory, Analysis of Conflict.[1] Hurwicz introduced and formalized the concept of incentive compatibility

Comment: This paragraph does not really do justice to Roger Myerson's contributions. Eric Maskin's contributions are not discussed at all.}}


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  • Reference : Herings P.J.J. & Predtetchinski A., 2013. "Voting in collective stopping games," Research Memorandum 014, Maastricht University, Graduate School of Business and Economics (GSBE).

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Dr. Carfi's comment on this article

Dr. Carfi has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:


The Wikipedia article lacks of a clear discussion of the analytical models and solutions of infinite games, that is game with infinite many profile strategies. For this games very good references could be devised in the following books:

Aubin, J.P. (1997). Mathematical Methods of Game and Economic Theory, (Revised Edition) North-Holland. Aubin, J.P. (1998). Optima and Equilibria, Springer Verlag (1998).

Osborne, Martin J.; Rubinstein, Ariel (1994), A course in game theory. MIT Press,


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  • Reference : Carfi, David & Musolino, Francesco, 2012. "A coopetitive approach to financial markets stabilization and risk management," MPRA Paper 37098, University Library of Munich, Germany.

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“In addition to being used to describe, predict, and explain behavior, game theory has also been used to develop theories of ethical or normative behavior and to prescribe such behavior.[6] In economics and philosophy, scholars have applied game theory to help in the understanding of good or proper behavior.”

An interesting aspect of game theory is that associated with the possible influence of culture or even gender (of the players) in the outcome of the game (see, among others, Fehr & Schmidt (1999), Henrich (2000), Oosterbeek et al. (2004) and/or Solnick (2001)).

Fehr, E.; Schmidt, K. M. (1999). A theory of fairness, competition, and cooperation. Quarterly Journal of Economics, 114: 3, 817-868. Henrich, J. (2000). Does Culture Matter in Economic Behavior? Ultimatum Game Bargaining Among the Machiguenga of the Peruvian Amazon. American Economic Review, 90, 973-979. Oosterbeek, H.; Sloof, R.; van de Kuilen, G. (2004). Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis. Experimental Economics 7: 2, 171-188.

Solnick, S.J. (2001). Gender Differences in the Ultimatum Game. Economic Inquiry, 39, 189-200.


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  • Reference : Antonio Caleiro, 2006. "On the Synchronisation of Elections: A Differential Games Approach," Economics Working Papers 05_2006, University of Evora, Department of Economics (Portugal).

ExpertIdeasBot (talk) 19:07, 30 August 2016 (UTC)

Dr. Koczy's comment on this article

Dr. Koczy has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:


"works against the fraction {\displaystyle \left({\frac {\mathbf {N} }{\mathbf {C}

\right)}" sounds really weird. Now we would just talk about the complementer set (especially that N has not been defined), or just say \mathbf {N}\setminus \mathbf {C}. By the way, why bold?

"removable utility" is odd \mathbf {R} is the symbol for reals? a method of applied mathematics? I think it is rather a subfield. " Ronald Fisher's studies of animal behavior during the 1930s. This work predates the name "game theory"," this is incorrect as von Neumann has already published a paper in 1928 with game theory in the title (though in German). A recently published book (Von Neumann, Morgenstern and the Creation of Game Theory) supposedly (so a well known game theorist told me) explains that "game theory" was a common term in the café's of Budapest about using mathematics in strategic board games and that it must have been totally clear for von Neumann that his work belongs to this "field". "The primary use of game theory is to describe and model how human populations behave" - this is simply not true. Game theory rarely models human interactions, rather interactions between companies or countries. The Economics and Business section is way too short. For game types: cooperative games may be with or without transferable utility and with or without externalities. The "See also" section seems a little random.

}}


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  • Reference : Laszlo A. Koczy, 2006. "Strategic power indices: Quarrelling in coalitions," Working Paper Series 0803, Obuda University, Keleti Faculty of Business and Management, revised May 2008.

ExpertIdeasBot (talk) 19:08, 30 August 2016 (UTC)

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Hawk-Dove-Retaliator Game

A more general version of the hawk-dove game, the hawk-dove-retaliator game, is found in John Maynard Smith, Evolution and the Theory of Games. --Jbergquist (talk) 10:44, 20 September 2016 (UTC)

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Removal of cites

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Not sure if all are valid removals. Jonpatterns (talk) 13:19, 9 April 2017 (UTC)

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Removal of Economics Sidebar

I think that the economics sidebar should be removed, since Game Theory doesn't seem to be primarily concerned with Economics. — Preceding unsigned comment added by Get Learnt (talk • contribs) 05:33, 30 May 2018 (UTC)

Yes I would be in agreement with you, there are much more approproate imagges. Fro exampel a symbolic depiction of the a network or the proziners Dilema.

I first met Game Theory in Apllied Mathematics II - Dynamic Programming — Preceding unsigned comment added by Philipdc (talk • contribs) 12:46, 28 June 2018 (UTC)

(Non-)determinstic: in terminology?

I hesitate to add this, as I am not familiar with the usual terminology, but surely there is an important distinction, worth adding under Game types, between games whose course is entirely determined by the decisions of the players and those influenced by an element of chance. (This is of course not the same as Determinacy or a determined game.) If added, it would also belong in Glossary of game theory. @David Eppstein: since you just edited the article! PJTraill (talk) 14:28, 18 August 2018 (UTC)

Behavioral game theory, decision-making, and rethinking the design of "economics and business" heading's content

This article needs to refer to (and link to) behavioral game theory. Behavioral game theory has grown from economics, but also the psychology of judgement and decision-making. It's basically game theory applied to human decision-making that includes considerations for bounded rationality, "natural" preferences, norms, etc. It's now used in everything from anthropology to resource management, hardly restricted to economics and business. In the "General and Applied Uses" > "Economics and Business" subheading of the article, behavioral economics is mentioned, but behavioral game theory is not, even though it's in the titles of several citations. The content itself under that heading has become fairly redundant with the rest of the article, and doesn't have much content specific to business or economics. Of course, since econ, sociology, psych, etc are all social sciences, there's going to be a decent amount of overlap and fuzziness of topics. Still, I'd suggest that 1. "Economics and Business" be reworked with some content that's specific to business and economics. 2. A "Decision-Making and Social Behavior" heading be added that includes some of the content from behavioral game theory, links to it, and refers to it by name. Alternatively, the heading could just be "Behavioral Game Theory." 174.52.240.90 (talk) 20:56, 13 November 2019 (UTC)

Algorithmic Game Theory

A very hot modern area of game theoretic research. Tied to econ AI and distributed algos. Lots of robust results. Should be mentioned in the article. 2601:14D:4002:6D00:F557:B35D:C52A:CAD4 (talk) 08:28, 29 January 2020 (UTC)

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