Talk:Dominance (game theory)

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The following users are actively contributing to this topic and may be able to help with questions about verification and sources: Kzollman (talk • contribs • email)

[edit] 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)

[edit] 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)