Talk:Risk dominance

Starting from scratch

I propose we're starting from scratch here. In the spirit of writing articles in three segments: 1. Stuff everybody understands, 2. Stuff some people understand, and 3. Stuff nobody but the author understands, we should shoot for a common-sense definition first, then tighten it with a formal definition and an example, then go into a discussion of the stag hunt/strategy revision/Young-KMR applications in evol game theory. Two questions: 1. What should the title of the article be, especially should we discuss risk and payoff dominance in conjunction, and 2. Anyone know of applications outside the stag hunt universe? ~ trialsanderrors 21:04, 5 February 2007 (UTC)

I'm more inclined to keep payoff dominance and risk dominance seperate as they are two different types of equilibria. If we do that, however, we need a consistent naming convention. Currently the two articles are risk dominance and payoff dominant equilibrium. I have a bunch of stuff on risk dominance in EGT, which I will look at. Unfortunately, this is a bad week for that. Perhaps this weekend I'll get back to you about its applications there. --best, kevin [kzollman][talk] 00:36, 6 February 2007 (UTC)

OK. My discussion so far is mostly about RD. I'm not sure there is much more to be said about ΠD, but clearly if you have more it might make sense to reserve for a separate article. ~ trialsanderrors 00:54, 6 February 2007 (UTC)

Stability diagram

I'm looking at the stability diagrams in Harayani and Selton (1988) p 78, and they seem to make things easier to understand mathematically (as for intuition, well.... ::sigh::). Anyway, I don't know if a table or an image will work better. The table might be something like this, but it would be better if we could scale it so the reader can see that (1D,2R) has the largest basin (or did I do it wrong). I hesitate to do an image because I suck at cpu graphics.

	Left	Right
Up	(5-4)(5-4)	(5-4)(2-0)
Down	(2-0)(5-4)	(0-2)(0-2)
Risk dominance

In any case, we could use a description of this (larger basin) characterization of RD, and the perhaps connect it to Nash products. Would that be appropriate? I'm thinking I can probably put in some time in the next week on this article, and it won't be hard now that I have a copy of H&S checked out. Can anyone think of anything I should look for in here that needs to go into the article? Also, basin seems to have a slightly different definition in this article vs the dynamical systems article that links to. Are they fundamentally still the same thing? Smmurphy^(Talk) 05:41, 21 February 2007 (UTC)

Formal Definition?

The article currently gives a technical definition for the example. This is in no way a formal definition which can be generalized to other games. There isn't even an explanation of what the condition equation is derived from, and is not really useful for a reader who is looking for more than general erudation. 195.37.116.2 12:45, 17 August 2007 (UTC)

Very true. So, you don't have any inclination to sign up and fix the problems you pointed out? ~ trialsanderrors 03:07, 18 August 2007 (UTC)