Talk:Strategic dominance

Lists and such

DavidCary was kind enough to suggest putting all the types of dominance in a list, which I think really helps make the article easier to read. Personally I prefer keeping all the definitions in one section rather than having them spread out, which I have just done. If folks thinks its better spread out (see David's initial version [1]) I'm game. --best, kevin ···Kzollman | Talk··· 21:52, 21 September 2005 (UTC)

Either way is fine with me. However, the "completist" (is that a real word?) in me wants to list *all* possible ways that B compares to A. Currently, the article leaves out at least 2 that I know of:

• B ...... A ( what's the word I'm looking for? ): choosing A is better in some cases, while choosing B is better in other cases, depending on exactly how the opponent chooses to play.
• B is equivalent to A: B has the same payoff as A in every case.

Are there any other ways that B could compare to A?

Should we list *all* of them in the article?

--DavidCary 04:21, 22 September 2005 (UTC)

I find the section redundant. Once you've defined "A dominates B", it's sufficient to say that B is dominated by A if A dominates B. And you don't really even need to say that, since it's intuitively obvious.

Also, that section isn't really about "types of dominance" because there's only strict dominance and weak dominance, and even those I wouldn't call "types" so much as "degrees" of dominance. There are actually other types of dominance besides what's currently in the article; risk dominance, for example. I've renamed the section to "Terminology". Isomorphic 05:21, 22 September 2005 (UTC)

Yes, "terminology" is much better name for that section.

You'd be surprised at how often people somehow miss the "intuitively obvious" conclusion. (See Please don't just end with "The conclusion should be obvious". Say it.) Speaking of terminology, is there a term for the other case of comparing B vs. A, when neither one is dominant? there's only strict dominance and weak dominance. I don't believe it -- for example, in Rock, Paper, Scissors, the strategy of throwing "scissors" neither dominates nor is dominated by the strategy of throwing "paper". --DavidCary 22:19, 22 September 2005 (UTC)

I don't know if there is a term for that. "Undominated" perhaps? But I think adding that would be too much. --best, kevin ···Kzollman | Talk··· 01:30, 23 September 2005 (UTC)

I agree that in general you don't want to say "and this is obvious", but in this case the second set of definitions follows directly from the meaning of the passive voice in English. That really shouldn't be tripping anyone up. To me, the section is actually more confusing in its current state. But if others disagree, there's nothing actually wrong with it. Isomorphic 02:24, 23 September 2005 (UTC)

Oh,, and in answer to your question: no, I've never heard a term like that. I would just say "X is not dominated" or "X is not dominant". Isomorphic 02:27, 23 September 2005 (UTC)

Table in Dominance and Nash Equilibrium

For a game theory neophyte like me this article is quite useful. However, I don't know how to read the strategy table in the Nash Eq. section. Without going into all of game theory, is it possible to at least hint at what the 1,1 and 0,0 pairs mean and explain WHY C dominates D, and WHY D,D is a nash eq. Thanks! -- cmh 17:18, 12 April 2006 (UTC)

Thanks for the suggestion! I have tried to improve the explanation. Rather than explaining the table (which occurs in lots of game theory articles), I have added a link to payoff matrix which explains what those numbers represent. (Although to be honest that page needs work.) For the time being you might read the first couple of sections in game theory for quick introduction. I have also expanded the explanation for why C weakly dominates D and why (D, D) is a Nash equilibrium. Is this clearer? --best, kevin [kzollman][talk] 19:23, 12 April 2006 (UTC)

Yes, thanks very much! -- cmh 19:30, 12 April 2006 (UTC)

in-line citations

The list of external links and references looks pretty comprehensive for an article of this size. However, should the article have in-line citations? Or is the subject pretty much monolithic in terms of what sort of citations are necessary? That is, if I examined each of the seven references, would I find that each of them has includes essentially all of the information presented in this article? (It's a fine article, by the way; applause to the contributors.) — Steve98052 (talk) 09:42, 9 March 2011 (UTC)

Confusing and incorrect(?) descriptions

There seem to be some confusing/incorrect descriptions in this article, e.g.

   B dominates A: choosing B always gives as good as or a better outcome than choosing A.

I don't think this is true if, for instance, two strategies always give the same payoff for a player. As far as I can tell, neither of these would dominate, although I haven't had a good look for some good references (http://www.gametheory.net/dictionary/DominantStrategy.html doesn't help in this case). I thought about changing the description to be more accurate, but realised I would just be repeating the definition for weak dominance. (All strong dominance is weak, and all dominance satisfies the description in the article, but not all strategies that fit the description in the article are dominance i.e. two equal strategies.) There's a similar problem with

   B is dominated by A: choosing B never gives a better outcome than choosing A, no matter what the other player(s) do.  — Preceding unsigned comment added by Mtjh (talk • contribs) 15:53, 10 November 2015 (UTC) 

@Mtjh: I agree. Simply stated, the definitions are wrong. Under the correct definition of "dominates", a strategy does not dominate an equivalent strategy. But these incorrect definitions would lead you to believe that any strategy dominates an equivalent strategy (or indeed, that any strategy dominates itself). Mathew5000 (talk) 23:15, 10 November 2018 (UTC)

I made a correction to address this issue: [2]. Mathew5000 (talk) 23:28, 10 November 2018 (UTC)

Dr. Moldovanu's comment on this article

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

Reasonably good description of the concept. Some references to more game theory texts and to some of the main primary research articles would be welcome

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Moldovanu has expertise on the topic of this article, since he has published relevant scholarly research:

• Reference : Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2011. "Bayesian and Dominant Strategy Implementation Revisited," Working Papers tecipa-422, University of Toronto, Department of Economics.

ExpertIdeasBot (talk) 15:55, 24 August 2016 (UTC)

Weak Dominance Deletion Step-by-Step Example

In the example of Weak Dominance Deletion Step-by-Step Example, the strategy U (resp. T) does not weakly dominates T (resp. U) (after the deletion of player one's strategy). To show that the order of deletion has an impact, more strategies should be added (for instance player one could have 1 more strategy). Comment added by QBramas

"Dominanza (teoria dei giochi)" listed at Redirects for discussion

An editor has identified a potential problem with the redirect Dominanza (teoria dei giochi) and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 February 12#Dominanza (teoria dei giochi) until a consensus is reached, and readers of this page are welcome to contribute to the discussion. ~~~~
User:1234qwer1234qwer4 (talk) 02:09, 12 February 2022 (UTC)

Mixed Strategy Dominance Deletion Step-by-Step Example with Detailed Explanation

As part of a University of Michigan Game Theory course, we are helping improve this Game Theory wikipage by adding an example of Mixed Strategy Dominance. In particular, we added an explanation of how to assign tester q values for Player 2's strategy and test them to see if that mixed strategy will dominate the pure strategy. The existing example of Mixed did not offer calculations on how to prove mixed dominance, nor did it end by solving the game. My teammate made the step-by-step IDSDS graph, based off a game out of our textbook, Strategy: An Introduction to Game Theory by Joel Watson. — Preceding unsigned comment added by MeltedKeyboard (talk • contribs) 17:45, 16 December 2022 (UTC)

The calculation in this section appears to me to be incorrect (even after I fixed an apparent repeated error where it said ½X+½Z when it should have said ½Y+½Z). To dominate, the mixed strategy has to be better *no matter what the opponent does*. It is impossible to capture that condition in a single inequality (unless it contains variables representing what the opponent's strategy is). The approach you've used would never incorrectly reject a strategy that was actually dominant, but would incorrectly accept strategies that are not dominant. In particular, by not weighting the opponent's strategies, the calculation implicitly assumes that the opponent plays a mixed strategy of 1/3 U, 1/3 M, and 1/3 D. 50.197.48.113 (talk) 13:00, 9 October 2023 (UTC)