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This page is an Archive of the discussions from WikiProject Game theory talk page (Discussion page). (January 2005 - December 2005) - Please Do not edit!

Evolutionary stable state

I redirected evolutionarily stable state to evolutionarily stable strategy. Should this be redirected as well? —Ilmari Karonen

No, evolutionary stable states are broader than evolutionary stable strategies. For instance, there are evolutionary stable states made up of several different strategies, none of which are evolutionarily stable strategies. For instance, in the Nash bargaining game there is an evolutionary stable state where half the population proposes 2/3 and half the population proposes 1/3. Neither of these strategies is an evolutionary stable strategy, but nonetheless the state composed of half 2/3 half 1/3 is evolutionarily stable. --best, kevin ···Kzollman | Talk··· 02:34, August 30, 2005 (UTC)

So we're using ...strategy for pure strategy equilibria and ...state for mixed equilibria? OK, makes sense to me. Will try to add something about the latter tomorrow. —Ilmari Karonen

Yeah, I think this is the standard usage, although I'm pretty new at this and so might be wrong (?!) Thanks in advance for the contributions! --best, kevin ···Kzollman | Talk··· 02:57, August 30, 2005 (UTC)

I think a reference to evolutionarily stable state in use, drawn from the literature would help us sort this out. A related concept (?) Evolutionarily Stable Sets of strategies, ESSets (Thomas 1985, J Math Biol 22:105-115; Schlag & Balkenborg 2001, Int. J. Game Theory 29: 571-595; Cressman 1992, Math Biosci. 108: 179-201). Note also: related to discussion above, no pure ESS can be a member of a mixed ESS, there's a simple proof for this I can't find a reference for right now.

This result (a subset of a mixed ESS cannot be an ESS) is known as the Bishop-Cannings theorem. [1]

I think we probably really ought to have one page (ESS (game theory)?) describing all these concepts, as they are so similar that having them on separate pages would likely involve excessive redundancy and cross-referencing. But let's get some reasonably good content up first before worrying about page splits/merges too much. −Ilmari Karonen 16:01:30, 2005-08-30 (UTC)

I don't understand. Is there a difference between a "evolutionary stable state" and a "mixed strategy"? Is there a signicant difference between "half the population proposes 2/3 and half the population proposes 1/3" vs. "I flip a coin, heads I propose 2/3 and tails I propose 1/3"? --DavidCary 02:03, 22 September 2005 (UTC)

	A	B
A	1, 1	0, 0
B	0, 0	1, 1

Polymorphic evolutionarily stable states are a feature of populations who each choose pure strategies while mixed strategies are strategies taken by single individuals. Your right to notice the similarity, for every evolutionarily stable state, there is a corresponding mixed strategy Nash equilibrium. However, there is not always an evolutionarily stable state for every mixed strategy Nash equilibrium. For instance, in the game to the right, there is a mixed strategy Nash equilibrium where each player plays each strategy with probability 1/2. However, this is not an evolutionarily stable state. Any perturbation away from a population composed of 1/2 A players and 1/2 B players, will benefit one or another type and lead the population toward all A or all B.

However, note that the 50/50 Nash equilibrium above is not stable, and therefore clearly not an evolutionarily stable strategy. To address the question above, I believe the distinction between mixed populations of pure strategies and pure populations of mixed strategies is irrelevant to the stability of the equilibrium, but may be significant for the evolution of a population not in equilibrium. —Ilmari Karonen 11:38, 23 September 2005 (UTC)

Rational actors

What shall we do with references to rational actors and perfect rationality? Does this warrent a special article, or can homo economicus do? --best, kevin ···Kzollman | Talk··· 21:17, August 31, 2005 (UTC)

I looked at homo economicus, and I don't think it will do for our purposes. We need a short and simple article that defines "rationality" in the pure mathematical sense, without the voluminous debate about its applicability to real people. Of course, it should link to homo economicus, for those who are interested in more than just the definition. —Ilmari Karonen 23:43:24, 2005-08-31 (UTC)

Articles for the Wikipedia 1.0 project

Hi, I'm a member of the Wikipedia:Version_1.0_Editorial_Team, which is looking to identify quality articles in Wikipedia for future publication on CD or paper. We recently began assessing using these criteria, and we are looking for A-Class and good B-Class articles, with no POV or copyright problems. Can you recommend any suitable articles? Your main article on Game theory looks like a candidate to me (I'm not an expert!) Please post your suggestions here. Thanks a lot! Walkerma 21:05, 7 October 2005 (UTC)

I wouldn't yet recomend Game theory although the bits it has are good, it is missing a lot of important information and represents, I think, a skewed picture of the discipline. Soon, hopefully, it will be up to snuff (See Talk:Game theory). I would recomend these pages (others feel free to discuss it):

• Best response A Pete.Hurd 00:47, 24 April 2006 (UTC)
• Centipede Game
• Cheap talk (still B, needs links for important concepts such as "pooling", and the biology section needs help (but not from me) Pete.Hurd 00:47, 24 April 2006 (UTC)
• Common knowledge
• Complete information 2 refs, now A? Pete.Hurd 00:47, 24 April 2006 (UTC)
• Dictator game
• Dominance (game theory) (looks good to me, Kevin?) Pete.Hurd 00:47, 24 April 2006 (UTC)
• Extensive form game A Pete.Hurd 00:47, 24 April 2006 (UTC)
• Evolutionarily stable strategy A-/B , shortcoming is lack of treatment of asymmetric games, and mixed ESSs, (The "ESS & human behaviour" section could also do with a good beating up) Pete.Hurd 00:47, 24 April 2006 (UTC)
• Fictitious play (B?)
• Game of chicken A (but I can imagine more Hawk-Dove material going in there...) Pete.Hurd 01:57, 24 April 2006 (UTC)
• Game theory
• Nash equilibrium (although it could use some more references, I'll try to fix that sometime soon)
• Nash bargaining game (B?)
• Normal form game A, but needs better references, Weibull is a wierd choice for this topic.. Pete.Hurd 01:12, 24 April 2006 (UTC)
• Payoff dominant equilibrium
• Payoff matrix
• Rationalizability
• Replicator equation
• Shapley value
• Perfect information (looks A-ish to me Pete.Hurd 14:17, 11 October 2005 (UTC))
• Prisoner's Dilemma (it was a featured article once)
• Rock, Paper, Scissors (also featured)
• Signaling game A- ? Pete.Hurd 01:12, 24 April 2006 (UTC)
• Stackleberg competition added refs, but image is redlinked Pete.Hurd 01:12, 24 April 2006 (UTC)
• Stag hunt
• Ultimatum game (very good)
• zero sum

Phew. Well, this is no doubt a really biased list, I hope that others will suggest adding and removing from this list. --best, kevin ···Kzollman | Talk··· 22:04, 7 October 2005 (UTC)

Hmmm, I think the ESS page is a B, good B. I think the Evolutionaily Stable State stuff really belongs on it's own age. I've been meaning to figure out how to unredirect, but too busy with science the last couple of weeks. I think Best response could do with some reacton coresspondence graphs, one for Game of chicken, one for Battle of the sexes (comparison and contrast of coordination and discoordination correspindences), another for a strictly dominanted game like the prisoner's dilemma. Pete.Hurd 03:00, 8 October 2005 (UTC)

I added common knowledge to the list, thanks to an anonymous editor, its really good now. --best, kevin ···Kzollman | Talk··· 17:04, 8 October 2005 (UTC)

Thank you so much for this list- you really have a good core of articles in your field. I'm really glad, bearing in mind the recent Nobel Prize announcement (congratulations!). I will record the rough assessments in the WP 1.0 table soon, but please continue to add to this list in the meantime. I will continue to monitor this page, and check in with you again occasionally. Many thanks, Walkerma 07:10, 11 October 2005 (UTC)

I added some to the list that I think meet the criteria. I also alphabetized the list. Pete.Hurd 14:17, 11 October 2005 (UTC)

I think Game theory is now up to snuf, i've added it to the list. I agree with Pete that Best response should be on the list

In case you don't notice the note on our project page, we are working to correct a deficiency in references noted by the 1.0 editorial team. This deficiency is a result of an academic bias on my (and other's) part for not referencing things that are common in every textbook. We are working to overcome this :) Many pages that didn't have references before may have them now or will very soon. --best, kevin ···Kzollman | Talk··· 19:28, 8 November 2005 (UTC)

Thanks a lot! We'll review these again soon. Walkerma 19:05, 3 February 2006 (UTC)

UPDATE: I have re-assessed the articles on your list at WP1.0. I am not an expert on this topic - in fact I barely understand parts of the articles - so can this group check my assessments and change any that seem wrong? Feel free to treat this table as belonging to this project, so you can add more articles and update with GAs or FAs as you see fit. I would suggest any A-Class articles might also be considered as good article candidates. Thanks again! Walkerma 05:19, 21 April 2006 (UTC)

Common knowledge Dominance (game theory) looks like A-class to me, are B on the WP1.0 list. Ultimatum game, Common knowledge, Nash equilibrium, Evolutionarily stable strategy, Extensive form game, and Best response all A-class, I'll nominate the aforementioned for GA unless someone has concerns about any of them. Note that Zero-sum, Complete information just need references, Rock, Paper, Scissors needs some more references, Stackelberg competition also just needs references and the restoration (?) of File:Stackelbergmodel.jpg. Oh, here's the obligatory link to page of game theory articles needing references). Pete.Hurd 14:33, 21 April 2006 (UTC)

Featured article candidate

Hi all - Martin suggested to me that Game theory might now be good enough to be a featured article. To let you know, before we put it up for candidacy, its recomended (required?) that it have a peer review. I think this would be a tremendous help since we will get smart non-specialists looking at the article and helping to pinpoint problems. One thing they want is that the article be relatively stable (people can keep making changes, just nothing huge). I thought I would check to see if people had things in the pipes for that article, or if I should just go ahead. Comments? --best, kevin ···Kzollman | Talk··· 19:49, 16 October 2005 (UTC)

All clear from me: good for go. Pete.Hurd 21:29, 16 October 2005 (UTC)

The request has been submitted and can be seen at Wikipedia:Peer review/Game theory/archive1. --best, kevin ···Kzollman | Talk··· 03:17, 23 October 2005 (UTC)

Determinacy

(I originally posed this question in response to Kzollman's appeal on the CS project talk page; this seems a better place for it.) Does anyone want to mention Determinacy, either in the Game theory article or elsewhere in the project? It has of course very little to do with the sort of game theory that's of interest to economists, but some of the more "pure"-oriented participants might be interested in it. --Trovatore 02:22, 19 October 2005 (UTC)

I certainly think it ought to be mentioned, where do you see it fitting best into the page? Pete.Hurd 02:32, 19 October 2005 (UTC)

Perhaps a subheader right after Game theory#Perfect information and imperfect information, maybe called "Infinite games" or some such? --Trovatore 03:15, 19 October 2005 (UTC)

How about adding a section about the uses of game theory in mathematics. I know thats a big awkward since its not really the same way that game theory is used in other disciplines, but that seems like the best place to me. --best, kevin ···Kzollman | Talk··· 04:30, 19 October 2005 (UTC)

Well, it's not just that game theory isn't used in the same way--the results of game theory (in the sense of the game theory project) really aren't used at all, beyond maybe Gale-Stewart (Blackwell games might use a tad more for all I know, but they're not the focus of the Determinacy article, in fact at the moment it's an empty section). The connection with game theory is more the objects of study (games); the main difference being that these games can last for infinitely many moves, with the outcome not known until after all infinitely many moves have been played. So I thought that might make for an interesting blurb in the "Types of games" section. --Trovatore 05:12, 19 October 2005 (UTC)

That's cool with me too. I should have added, please put it where-ever you like. If it might go better somewhere else we can always move it. Thanks for the addition, I know very little about this area, but I know someone who is very interested in it. --best, kevin ···Kzollman | Talk··· 05:19, 19 October 2005 (UTC)

OK, I took a crack at it. I tried to keep it short, given that it's a little bit of a sidelight; let me know if there's anything in particular you think should be better elaborated. And I won't be offended if you move it. --Trovatore 06:18, 19 October 2005 (UTC)

Looks good! Thanks Trovatore! --best, kevin ···Kzollman | Talk··· 15:22, 19 October 2005 (UTC)

Solution concept

Okay, this page need help. Its missing many of the important solution concepts and in its current state is not very helpful. One thing I'm thinking about doing is creating a Venn Diagram of the solution concepts to illustrate their relationships to each other. I know I have one, but its currently in the wrong state, and its not complete anyway. So here it is: I would like to make a list of solution concepts that belong in this article and also their relationships to each other. Here's what I got:

• Strategy sets that survive iterated elimination of strictly dominated strategies
• Rationalizable equilibrium (subset of IESDS)
• Nash equilibrium (subset of Rationalizable equilibria) vs Strict Nash equilibrium (Harsanyi, 1973)
• Strategy sets that survive iterated elimination of weakly dominated strategies (overlap with NE)
• ESS (subset of Nash equilibria, overlap with IEWDS)
• Subgame perfect equilibrium (subset of NE, overlap with ESS)
• Correlated equilibrium (I think a superset of NE, but i'm not sure)(defined on pg 45 of Osborne & Rubenstein, sect 2.2 in Fudenberg & Tirole)
• Bayesian Nash equilibrium
• Perfect Bayesian equilibrium
• Trembling hand perfect equilibirum
• Sequential equilibrium (subset PBE, overlap with SPE and ESS)
• Neutrally stable strategy (Maynard Smith, 1982)
• Limit ESS (Selten, 1983, 1988)
• ES Set (Thomas, 1985a,b)
• Nash-Pareto pair (Hofbauer & Sigmund, 1988)
• Symmetric Nash equilibrium

There are more... so many more. --best, kevin [kzollman][talk] 19:41, 1 December 2005 (UTC)

I really like the Venn diagram idea! Some of the above concepts might not fit on two dimensions, I added some to the wish list. This article feels like quite a large task, but a really valuable thing to have once it's done. Pete.Hurd 19:56, 1 December 2005 (UTC)

Thanks pete! I agree, I decided to finally do this because I wanted to know the relationship between two equilibria concepts and it took far longer than needed. Another example that the best way to figure out how to improve wikipedia is to try and use it :) --best, kevin [kzollman][talk] 20:07, 1 December 2005 (UTC)

I added some references mentioned above to the page. Funny, less than an hour ago in lab meeting we were wondering WTF a "symmetric Nash equilibrium" was and how it related to ES Sets... We figured either it was on WP, or we'd have to add it. Rock on. Pete.Hurd 20:13, 1 December 2005 (UTC)

Nash equilibrium
This article is part of the equilibrium refinement series
Relationships
Subset of:	Rationalizability, Correlated equilibrium
Superset of:	Evolutionarily stable strategy, Subgame perfect equilibrium, Trembling hand perfect equilibrium, Perfect Bayesian equilibrium
Neither:	Nothing
Significance
Discoverer:	John Forbes Nash
Used for:	All non-cooperative games
Example:	Prisoner's dilemma

So in a desperate attempt to avoid writting a simulation program, I made this. Does it seem like the sort of thing that would be useful to add to equilibrium refinement pages? If so, should it include anything else? --best, kevin [kzollman][talk] 02:57, 3 December 2005 (UTC) P.S. the attempt was a success.

Solution vs. equilibrium

The solution concept page says, "a solution concept is a condition which identifies the equilibria of a game." I think this should be more general to include non-equilibrium solution concepts such as Level-k reasoning ([http://www.smu.edu.sg/research/knowledgehub/Jan2005/vincent.htm introduction). When I just want to talk about equilibria, I say "equilibrium concept".

How about something like:

"In game theory, a solution concept is a formal rule for predicting how the game will be played. These predictions are called "solutions", and describe what strategies will be adopted by players, and therefore also predicts the result of the game.

"Many solution concepts, for many games, will result in more than one solution. This puts any one of the solutions in doubt, so a game theorist may apply a refinement to narrow down the solutions.

"The most commonly used solution concepts are equilibrium concepts, most famously Nash equilibrium."Cretog8 (talk) 04:36, 15 April 2008 (UTC)

No response, so I'm going for it. Feel free to clean up my wording. Cretog8 (talk) 05:19, 22 May 2008 (UTC)

"Varma Division" - comments?

I just noticed a game theory article, Varma Division, being nominated for deletion as original research. I'd like some comments from the people here — has anyone ever heard of such a concept? Or, better yet, can anyone dig up a reference? —Ilmari Karonen (talk) 05:31, 9 December 2005 (UTC)

Solution concept infobox

So, I went ahead and turned the thing above into a template. It can be accessed at {{infobox equilibrium}}. I need to write up some instructions for it, which I will do soon. I have added it to some of the equilibrium pages (Nash equilibrium, Evolutionarily stable strategy, Subgame perfect equilibrium), so you can see how it works. Please modify it to your hearts content! --best, kevin [kzollman][talk] 06:16, 12 December 2005 (UTC)

Cool, I like it. I'm not sure what "independentof" means, though (of course I will soon, as you will be writing instructions soon, eh ; ). Also, it is nice when comparing concepts to see what sorts of conditions they satisfy, such as pareto optimality or independence of irrelevant alternatives, so another entry could be added called "satisfies", but it could end up being prohibitively lengthy. On the other hand, "subseto" and "supersetof" could get lengthy as well, and that would probably be ok. So, I tried my hand, what do you think of using it at Folk theorem (game theory)? Smmurphy^(Talk) 06:59, 12 December 2005 (UTC)

I hadn't thought about using it there. Good idea. Adding a satisfies category is not a bad idea, either. I know indepedence is a crappy word, but I could think of another one for two equilibrium concepts that don't overlap at all. Any ideas? --best, kevin [kzollman][talk] 16:40, 12 December 2005 (UTC)

list of game theorists -> category

A while ago I created a list of game theorists. I was wondering if we ought to have a category for game theorists as well? In spite of having read and reread Wikipedia:Categories, lists, and series boxes, I'm not sure when to use which. Smmurphy^(Talk) 07:15, 12 December 2005 (UTC)

I honestly don't think anyone has any good idea. The advantage of a list is that it can include people that might not otherwise warrent articles by themselves. The advantages of a category is that it cleans up the Category:Game theory a little. I'm amazed at how many game theorist articles there are! There's no reason we couldn't have both, I suppose. --best, kevin [kzollman][talk] 16:43, 12 December 2005 (UTC)

• Absolutely. Since there's so much comprehension across a wide thesis. I think having both might be a good idea.-MegamanZero 16:52, 12 December 2005 (UTC)

ok, how's this (Category:Game theorists), go ahead and add any more you can think of to the list and/or category. By the way, we have two articles, Ariel Rubinstein and Ariel Rubenstein, that should be merged. Anybody have a preferential spelling? Someone who is sure should go ahead and merge them. Smmurphy^(Talk) 17:22, 12 December 2005 (UTC)

• • Looks great! Thanks Smmurphy. When I get a chance I'll look into Ariel Rub[e,i]nstein. --best, kevin [kzollman][talk] 17:58, 12 December 2005 (UTC)

Maintainers

Hi there - Recently {{Maintained}} was created. Personally I think this is a great idea. I have raised the idea of adding something similar to {{GameTheoryProject}} instead of adding the template directly to talk pages (see Template talk:Maintained). The more I think about it the more conflicted I am about it. I thought I would get other's input on this. The advantages of adding a line to {{GameTheoryProject}} is that it allows the list of responsible users to be dynamic and saves talk page space (cf. Talk:Prisoner's dilemma). The disadvantages are that it puts our less active users on the hook to verify articles they may not want to and it adds additional effort for someone to contact a possible verifier. Please say both which of these two things you would prefer to do and if you would be willing to be on the hook for some subset of our articles. Thanks. --best, kevin [kzollman][talk] 01:49, 14 December 2005 (UTC)

• This would be nice on controversial pages, where someone would like to make a major edit but would like to make sure that it is ok, and isn't getting any feedback on talk. But for GT articles, it doesn't seem to make sense. Is it to watch for subtle vandalism and edit creep or to watch for non-sourced edits or something else? Plus, it sound nefarious. At the same time, it seems like it would be fun to be an officiall maintainer (different from "upholder" as in upholder of the wiki, I guess). Smmurphy^(Talk) 02:10, 14 December 2005 (UTC)
  • I think the purpose is to distinguish articles that have someone dedicated to them from those articles that are written as jokes. (I.e. to help respond to recent criticism). I understand the worry about cabalism. The fact is, we failed with Sigenthaler. We have to find ways to show that this failure was contained to one bad example. I think this is one way to do it. --best, kevin [kzollman][talk] 03:24, 18 December 2005 (UTC)
• I can see the reasons for doing this, but feel some unease. First, my sense is that some of the really good one-off anon contributions might be deterred. Maybe I'm wrong about that. Second, I'd be kind of reluctant to add my name as a maintainer to a page if I wasn't 100% happy with absolutely all the contents. Most of the game theory (but not the biology) stuff on my watchlist comes close-ish. But this feels like adding my name is an official stamp of approval, and that could send me into editorial paralysis. That being said, I see the sense in it, but fear the potential for increased wiki-reponsibility/workload. Pete.Hurd 07:07, 14 December 2005 (UTC)
  • Yeah, I share this worry too. Initially I thought I'd add it to most of the pages on my watchlist, but then I realized how much information I don't want to be held responsible for. I think we should probably not add a similar note to the game theory project template for just this reason. I add {{GameTheoryProject}} to anything that shows up in our category and sounds close, but I don't want to be held responsible for it. I think I will probably add {{Maintained}} to a few articles and list myself as a maintainer. Anyone else should feel free to do this with others if they like. --best, kevin [kzollman][talk] 03:24, 18 December 2005 (UTC)