Comment on Mixed strategy Nash equilibrium

Thu, 21 Oct 2010 23:26:35 GMT

The true limit would be 0 if everyone was rational, and aware of the rationality of everyone else, but rational people in the real world should be taking into account...

the fact that most people only seem to be able cope with two or three recursions before they get bored and pick an option

So what you should do, based on that, is try to figure out how many iterations "most people" will do, and then estimate the smaller percentage of the "rank one pragmatic rationalists" who will realize this and aim for 2/3 of "most people" and so on until you have accounted for 100% of the population. The trick is knowing that some people aren't logical means logical strategy (that will actually win) requires population modeling rather than game theory. Hearing your average of 30 makes me hypothesize that the distribution of people looks something like this:

0.1% 100 Blind number repeaters

4.9% 66 Blind multipliers

17% 44 Beating the blind!

28% 30 "most people"

20% 20 Read a study or use a "recurse three times" heuristic

15% 13 Contrarian rationalists

10% 9 Meta-contrarian rationalists

4.9% 6 Economists (I kid!)

0.1% 0 Obstinate game theorists

Suppose you run the experiment again (say, on a mixture of people from LW who have read this combined with others) where you expect that a lot of people might have actually seen this hypothesis, but a lot of people will naively play normally. I think the trick might be to figure out what the percentage of LWers you're dealing with is and then figure out what to do based on that.

I'm tempted (because it would be amusing) to try to estimate the percentage of LWers relative to naive, and then model the LWers as people who execute some variant of timeless decision theory in the presence of the baseline people. If I understand timeless decision theory correctly, the trick would be for everyone to independently derive the number all the LWers would have to pick in order for us all to tie at winning given the presence of baselines. It seems kind of far fetched, but it would be ticklesome if it ever happened :-D

OK, now I'm curious! I think I might try this at the next SoCal meetup.

ETA: ...or does utilitarian consequentialism mean we need to calculate the value we'd all have to vote to maximize the number of winners, whether or not they were expected to participate in the calculation? That sounds even harder.

Discuss