Meni_Rosenfeld

• Meni_Rosenfeld 19 Apr 2010 16:07 UTC

  8 points

  on: At­ten­tion Lurk­ers: Please say hi

  Hi.

  I intend to become more active in the future, at which point I will introduce myself.

• Meni_Rosenfeld 27 Sep 2010 15:44 UTC

  2 points

  on: Is Ra­tion­al­ity Max­i­miza­tion of Ex­pected Value?

  Suppose someone offers you a (single trial) gamble C in which you stand to gain a nickel with probability 0.95 and stand to lose an arm and a leg with probability 0.05. Even though expectation is (-0.05arm −0.05leg + 0.95nickel), you should still take the gamble since the probability of winning on a single trial is very high − 0.95 to be exact.

  Non-sarcastic version: Losing $100M is much worse than gaining $100K is good, regardless of utility of money being nonlinear. This is something you must consider, rather than looking at just the probabilities—so you shouldn’t take gamble A. This is easier to see if you formulate the problems with gains and losses you can actually visualize.

• Meni_Rosenfeld 28 Sep 2010 12:42 UTC

  0 points

  in reply to: AnlamK’s comment on: Is Ra­tion­al­ity Max­i­miza­tion of Ex­pected Value?

  What exactly does maximizing expected utility yield in these particular cases?

  For one, I could be convinced not to take A (0.01 could be too risky) but I would never take B.

  Depends on how much money you currently have. According to the simple logarithmic model, you should take gamble B if your net worth is at least $2.8M.

• Meni_Rosenfeld 28 Sep 2010 13:55 UTC

  1 point

  in reply to: AnlamK’s comment on: Is Ra­tion­al­ity Max­i­miza­tion of Ex­pected Value?

  You can’t have your cake and eat it too. If the probability is low enough, or the penalty mild enough, that the rational action is to take the gamble, then necessarily the expected utility will be positive.

  Taking your driving example, if I evaluate a day of work as 100 utilons, my life as 10MU, and estimate the probability to die while driving to work as 1/​M, then driving to work has an expected gain of 90U.

• Meni_Rosenfeld 14 Oct 2010 22:25 UTC

  0 points

  in reply to: cousin_it’s comment on: Mixed strat­egy Nash equilibrium

  I actually briefly considered mentioning correlated equilibria, but the post was getting long already.

• Meni_Rosenfeld 14 Oct 2010 22:38 UTC

  2 points

  in reply to: whpearson’s comment on: Mixed strat­egy Nash equilibrium

  But if you can’t look at the current distribution, you still need to use the equilibrium for this single choice. Otherwise, you’re at risk that everyone will think the same as you, except for a few smarter players who will counter it.

• Meni_Rosenfeld 14 Oct 2010 22:57 UTC

  0 points

  in reply to: Steve_Rayhawk’s comment on: Swords and Ar­mor: A Game The­ory Thought Experiment

  Gambit said the only equilibrium was mixed, with ¹⁄₅ each of (blue sword, blue armor), (blue sword, green armor), (yellow sword, yellow armor), (green sword, yellow armor), and (green sword, green armor).

  FWIW, my calculations confirm this—you beat me to posting. One nitpick—this is not the only equilibrium, you can transfer weight from (blue, green) to (red, green) up to 10%.

• Meni_Rosenfeld 15 Oct 2010 12:26 UTC

  0 points

  on: Any LW-ers in Mu­nich, Athens, or Is­rael?

  I don’t know if I qualify as a LW-er, but I’m in Israel. I’ll be happy to meet you two if you are interested. I’m in Tel-Aviv every day.

• Meni_Rosenfeld 15 Oct 2010 12:45 UTC

  5 points

  in reply to: Paul Crowley’s comment on: Mixed strat­egy Nash equilibrium

  Thanks. I’ll move it as soon as I have the required karma.

Mixed strat­egy Nash equilibrium

• Meni_Rosenfeld 16 Oct 2010 17:31 UTC

  2 points

  in reply to: nerzhin’s comment on: Mixed strat­egy Nash equilibrium

  Fixed.

• Meni_Rosenfeld 17 Oct 2010 6:01 UTC

  17 points

  in reply to: paulfchristiano’s comment on: Mixed strat­egy Nash equilibrium

  Short answer: I already addressed this. Is your point that I didn’t emphasize it enough?

  One thing should be kept in mind. A Nash equilibrium strategy, much like a minimax strategy, is “safe”. It makes sure your expected payoff won’t be too low no matter how clever your opponent is. But what if you don’t want to be safe—what if you want to win? If you have good reason to believe you are smarter than your opponent, that he will play a non-equilibrium strategy you’ll be able to predict, then go ahead and counter that strategy. Nash equilibria are for smart people facing smarter people.

  Long answer:

  The distribution of sword/​armor choices in an MMO will not be the Nash equilibrium with overwhelming probability. In fact, it probably won’t be anywhere close if the choice is at all complicated.

  Correct. Do you know what the distribution is? Can you gather statistics? Do you understand the mentality of your opponents so well that you can predict their actions? Can you put the game in some reference class and generalize from that? If any of the above, knock yourself out. Otherwise there’s no justification to use anything but the equilibrium.

  If you are playing an MMO with random pvp, populated by people the people who play MMOs, and you choose the Nash equilibrium, you will probably do worse than me.

  If you assume I will continue to use the NE, even after collecting sufficient statistics to show that the players follow some specific distribution (as opposed to “not Nash equilibrium”), then this is a strawman. If you’re just saying you’re very good at understanding the mind of the MMOer then that’s likely, but doesn’t have much to do with the post.

  But saying that someone who talks about what their opponents are likely to do is “wrong” is itself quite wrong.

  I did not criticize the rare swords&armor posts that actually tried to profile their opponents and predict their actions. I criticized the posts that tried to do some fancy math to arrive at the “optimal” solution inherent to the game, and then failed to either acknowledge or reconcile the fact that their solution is unstable.

  Reasoning about the distribution of strategies your opponents play is the correct approach to this problem, not reasoning about the Nash equilibrium.

  One should first learn how to do Nash equilibrium, then learn how to not do Nash equilibrium. NE is the baseline default choice. If someone doesn’t understand the problem well enough to realize that any suggested deterministic strategy will be unstable and that the NE is the answer to that, what hope does he have with the harder problem of reasoning about the distribution of opponents?

  If 90% of American generals in the past have chosen to attack West, it is probably wrong to defend East with the “optimal” probability.

  Even under the strong assumption that there is some clear reference class about which you can collect these statistics, this is true only if one of the following conditions holds:

  • The attacker hasn’t heard about those statistics.

  • The attacker is stupid.

  • The attacker is plagued with the same inside-view biases that made all his predecessors attack west.

  The plausibility of each depends on the exact setting. If one holds, and we know it, and we really do expect to be attacked west with 90% probability, then this is no longer a two-player game. It’s a one-player decision theory problem where we should take the action that maximizes our expected utility, based on the probability of each contingency.

  But if all fail, we have the same problem all over again. The attacker will think, “paulfchristiano will look at the statistics and defend west! I’ll go east”. How many levels of recursion are “correct”?

• Meni_Rosenfeld 17 Oct 2010 6:10 UTC

  0 points

  in reply to: [deleted]’s comment on: Mixed strat­egy Nash equilibrium

  I’ll consider it, But I don’t know if I’m the right person for that, or if I’ll have the time.

• Meni_Rosenfeld 18 Oct 2010 7:32 UTC

  1 point

  in reply to: paulfchristiano’s comment on: Mixed strat­egy Nash equilibrium

  Okay, then it looks like we are in agreement.

• Meni_Rosenfeld 18 Oct 2010 7:59 UTC

  1 point

  in reply to: adsenanim’s comment on: Mixed strat­egy Nash equilibrium

  Now that I’ve looked it up, I don’t think it really has the same intuitions behind it as mixed strategy NE. But it does have an interesting connection with swings. If you try to push a heavy pendulum one way, you won’t get very far. Trying the other way you’ll also be out of luck. But if you push and pull alternately at the right frequency, you will obtain an impressive amplitude and height. Maybe it is because I’ve had firsthand experience with this that I don’t find Parrondo’s paradox all that puzzling.

• Meni_Rosenfeld 18 Oct 2010 19:23 UTC

  14 points

  0

  on: Eliezer Yud­kowsky Facts

  When Eliezer Yudkowsky divides by zero, he gets a singularity.

• Meni_Rosenfeld 18 Oct 2010 19:28 UTC

  0 points

  in reply to: Meni_Rosenfeld’s comment on: Eliezer Yud­kowsky Facts

  Just in case anyone didn’t get the joke (rot13):

  Gur novyvgl gb qvivqr ol mreb vf pbzzbayl nggevohgrq gb Puhpx Abeevf, naq n fvathynevgl, n gbcvp bs vagrerfg gb RL, vf nyfb n zngurzngvpny grez eryngrq gb qvivfvba ol mreb (uggc://​ra.jvxvcrqvn.bet/​jvxv/​Zngurzngvpny_fvathynevgl).

• Meni_Rosenfeld 18 Oct 2010 19:30 UTC

  0 points

  in reply to: adsenanim’s comment on: Mixed strat­egy Nash equilibrium

  Sorry, I’m not sure I know how to answer that.

• Meni_Rosenfeld 19 Oct 2010 15:21 UTC

  11 points

  in reply to: CronoDAS’s comment on: Eliezer Yud­kowsky Facts

  Eliezer Yudkowski can solve EXPTIME-complete problems in polynomial time.

• Meni_Rosenfeld 8 Nov 2010 20:29 UTC

  7 points

  in reply to: PhilGoetz’s comment on: An Xtra­nor­mal In­tel­li­gence Explosion

  At the risk of stating the obvious: The information content of a datum is its surprisal, the logarithm of the prior probability that it is true. If I currently give 1% chance that the cat in the box is dead, discovering that it is dead gives me 6.64 bits of information.