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Ezekiel comments on Nash Equilibria and Schelling Points - Less Wrong
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Comments (76)
This is a minor quibble, but while reading I got stuck at this point:
followed by a description of a game that didn't seem to have a Nash equilibrium and confirming text "Here there is no pure Nash equilibrium." and "So every option has someone regretting their choice, and there is no simple Nash equilibrium. What do you do?"
I kept re-reading this section, trying to work out how to reconcile these statements since it seemed like you have just offered an irrefutable counterexample to John Nash's theorem. It could use a bit of clarification (maybe something like "This game does have a Nash equilibrium, but one that is a little more subtle" or something similar.
Other than that I'm finding this sequence excellent so far.
No simple Nash equilibrium. Both players adopting the mixed (coin-flipping) strategy is the Nash equilibrium in this case. Remember: a Nash equilibrium isn't a specific choice-per-player, but a specific strategy-per-player.
If this is actually an introductory post to game theory, is this really the right approach?
If the post contains the information in question (it does) then there doesn't seem to be a problem using 'remember' as a pseudo-reference from the comments section to the post itself.
The words "pure," "simple," and "mixed" are not meaningful to newcomers, and so Yvain's post, which assumes that readers know the meanings of those terms with regards to game theory, is not introducing the topic as smoothly as it could. That's what I got out of Maelin's post.
I've never heard the word "simple" used in game-theoretic context either. It just seemed that word was better suited to describe a [do x] strategy than a [do x with probability p and y with probability (1-p)] strategy.
If the word "remember" is bothering you, I've found people tend to be more receptive to explanations if you pretend you're reminding them of something they knew already. And the definition of a Nash equilibrium was in the main post.
Agreed. Your original response was fine as an explanation to Maelin; I singled out 'remember' in an attempt to imply the content of my second post (to Yvain), but did so in a fashion that was probably too obscure.