For the game theorists out there...

post by CronoDAS · 2011-06-13T20:55:06.755Z · score: 8 (13 votes) · LW · GW · Legacy · 10 comments

Contents

  Which poll answer do you think will be the most popular today?
None
10 comments

Today's Poll of the Day at gamefaqs.com poses an "interesting" question...

I guess it's sort of like the minority game? Anyone want to try to analyze this?

10 comments

Comments sorted by top scores.

comment by AlexMennen · 2011-06-13T21:43:10.812Z · score: 3 (5 votes) · LW · GW

They all form one big loop, so no option really has any distinguishing feature over the others.

comment by Unnamed · 2011-06-14T07:42:27.712Z · score: 2 (4 votes) · LW · GW

The first option is most salient, by virtue of being first.

Level 0 players will tend to choose option 1. Level 1 players will realize that this is what level 0 players will do, so they will tend to choose option 2 ("the first one"). Level 2 players will realize that this is what level 1 players will do, so they will tend to choose option 4 ("the second one"). Level 3 players will realize that this is what level 2 players will do, so they will tend to choose option 5 ("the fourth one"). Apparently there are lots of level 1 & 2 players, but very few level 3 players.

But this analysis does not explain why so many people chose option 3 ("the last one") - I doubt that they are level 4 players. Perhaps it's that the last answer is the second-most-salient, by virtue of being last, making them level 1 players with a twist.

comment by AlexMennen · 2011-06-14T23:19:37.414Z · score: 3 (3 votes) · LW · GW

When trying to choose randomly, people tend to avoid options with salient features. It is not so easy to sort players into levels accurately.

comment by roystgnr · 2011-06-14T21:53:56.552Z · score: 1 (1 votes) · LW · GW

You and DanielLC are right, however:

Just because a game is isomorphic to a symmetric problem doesn't mean that it is a symmetric problem. "Scissors cut Paper wraps Rock smashes Scissors" has an equivalent formalism to "Policeman arrests Murderer kills Mayor bosses Policeman" but I'd bet with the latter (played as a single-round game) you'd see some very different game play in practice.

So what CronoDAS needs isn't a game theorist, it's a psychologist.

comment by CuSithBell · 2011-06-13T23:05:55.395Z · score: 1 (1 votes) · LW · GW

And yet, D is over twice as popular as E. Contradiction!

comment by benelliott · 2011-06-13T23:32:26.270Z · score: 1 (3 votes) · LW · GW

People's internal random number generators are not perfect.

comment by Emile · 2011-06-14T07:55:26.934Z · score: 2 (2 votes) · LW · GW

I find it pretty interesting that what turned out to be the right answer got the least votes.

comment by potato · 2011-06-15T15:55:00.342Z · score: 0 (0 votes) · LW · GW

In a place like this that should never happen. Vote up vote up.

comment by DanielLC · 2011-06-14T04:15:13.849Z · score: 2 (2 votes) · LW · GW

The Nash Equilibrium is to have an equal chance of each answer.

comment by AlephNeil · 2011-06-14T01:21:34.514Z · score: 0 (0 votes) · LW · GW

Might be more interesting if we replace the permutation matrix with an arbitrary 5 x 5 matrix over the reals.

Which of these expressions do you think will be the largest?

1. a[1,1]*(number of people choosing 1) + ... + a[1,5]*(number of people choosing 5)

...

5. a[5,1]*(number of people choosing 1) + ... + a[5,5]*(number of people choosing 5)