tag:blogger.com,1999:blog-7366878066073177705.post2035607201950476352..comments2014-04-16T19:17:52.143+01:00Comments on The Psy-Fi Blog: Utility, The Deus Ex Machina of Economicstimarrhttp://www.blogger.com/profile/06254802085744425067noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-7366878066073177705.post-68832013391345200112010-04-06T00:32:24.479+01:002010-04-06T00:32:24.479+01:00but when we can compare activity levels in the pre...but when we can compare activity levels in the prefrontal cortex and NAcc and insula and amygdala, who's to say we can't one day measure 'utility'?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-60775640043981198492010-04-05T17:20:17.983+01:002010-04-05T17:20:17.983+01:00I try not to do the eye-rolling thing, I’ve got te...I try not to do the eye-rolling thing, I’ve got teenage daughters to do that for me :)<br /><br />While Phil’s right to focus on the impossibility of actually implementing the paradox I think it’s an understandable approach – to make any progress on complex issues we have to simplify the problem to a point where we can make a start. So I don’t think the fact that it’s not a real problem invalidates the paradox but the fact that most non-economists think it’s a non-problem is itself interesting given that virtually every major economist of the past two hundred years has had a stab at analysing it.<br /><br />I suspect that the problem is that the simplifying assumption that we’re capable of rationally assessing risk, even in terms of our own utility, doesn’t stand up to even a cursory examination unless we define “rational” in a rather odd way.timarrhttp://www.blogger.com/profile/06254802085744425067noreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-78225714596505619142010-04-05T15:54:05.492+01:002010-04-05T15:54:05.492+01:00@Rob, if you do the arithmetic, the sum of an infi...@Rob, if you do the arithmetic, the sum of an infinite series of discounted cashflows converges. In fact, there are / have been traded perpetual bonds: http://en.wikipedia.org/wiki/Perpetuity.<br /><br />@Parker & Chad Wassell, I suspect that this post was inspired by my comment to an earlier post that I didn't think that a preference for a risk-free return over a somewhat higher but risky one was self-evidently irrational. I think that timarr sort of rolled his eyes and thought "it's the utility, stupid". But I don't believe that the price of risk has anything to do with utility.<br /><br />I think the same thing about the St. Petersburg paradox. To interpret it in terms of utility, you need three assumptions:<br /><br />1. The game is played infinitely fast (or else interest rates are zero.)<br />2. The counterparty is risk-free for obligations of unbounded size.<br />3. Rational investors are indifferent to ruin - i.e. the rational price of risk is zero.<br /><br />In short, the "paradox" is founded on two impossibilities and a wrong assumption.Phil Koopnoreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-46147049945274904752010-04-03T16:48:34.682+01:002010-04-03T16:48:34.682+01:00Parker, you have the right idea. Here's a pap...Parker, you have the right idea. Here's a paper that lays out a compelling answer to the paradox -- perhaps not "the answer" but a reasonable one.<br /><br />http://mpra.ub.uni-muenchen.de/5233/1/MPRA_paper_5233.pdf<br /><br />I haven't thought about it much, but the relevant issue probably boils down to counterparty risk. The casino's ability to pay -- and therefore the number of times I'm allowed to play -- is what determines willingness to pay.Chad Wassellhttp://www.blogger.com/profile/02906862879646111636noreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-56117474095273048772010-04-01T12:47:06.317+01:002010-04-01T12:47:06.317+01:00Sure the amount of future dividends is infinite, b...<i>Sure the amount of future dividends is infinite, but it is also being discounted at an infinite rate, which results in a value which gradually approaches zero.</i><br /><br />Thank, Jason. I've learned not to trust my instinctive responses to math puzzles, but what you are saying sounds right to me.<br /><br />RobRob Bennetthttp://arichlife.passionsaving.comnoreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-4376087064089766492010-04-01T07:35:07.723+01:002010-04-01T07:35:07.723+01:00$20 is too much, unless you have LOTS of money. A...$20 is too much, unless you have LOTS of money. According to a Monte Carlo simulation using Excel, even if you play the game 100,000 times, you still usually come out behind when risking $20.<br /><br />I would bet about $12. On 1,000 plays, you come out ahead about half of the time, but the game is pleasantly asymetrical since the upside is unlimited.Parker Bohnhttp://www.blogger.com/profile/11394409575254934751noreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-77840643774043818712010-04-01T07:26:26.922+01:002010-04-01T07:26:26.922+01:00This is super-interesting.
Infinite expected payo...This is super-interesting.<br /><br />Infinite expected payout, but only worth $20?<br /><br />Its taken me about an hour, but I've finally solved this to my satisfaction.<br />I don't know if this is the 'correct' solution, but it seems rational enough, and would tell me how much to wager.<br /><br />Here's my logic:<br />1) If its rational to bet a certain amount once, then it is rational to wager this same amount again.<br />2) A rational investor is averse to permanent loss of capital.<br />3) If you bet too much, then your 'risk-of-ruin' is quite high - if you keep playing you are likely to be wiped out.<br />4) The chance of hitting a really high payout before being wiped out is relative to the size of your capital.<br />5) Therefore, the amount a rational investor should be willing to risk on the St Petersburg game is relative to the size of their capital.<br /><br />So what I would do is take my total amount of capital, and figure out my risk of ruin (which I will define as losing 50% or more of my money), assuming that I continuously played the game with my capital (but not my winnings). I would then set my maximum allowable bet at a level where my risk of ruin is 5% or less.<br /><br />Warren Buffett could play this game a few million times more than me, so he could rationally risk a lot more money per bet and still come out ahead.Parker Bohnhttp://www.blogger.com/profile/11394409575254934751noreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-19108650353531747222010-04-01T00:05:56.109+01:002010-04-01T00:05:56.109+01:00In reply to your second comment, won't in fact...In reply to your second comment, won't in fact the dividend discounted out to eternity approach closer and closer to zero? <br /><br />Sure the amount of future dividends is infinite, but it is also being discounted at an infinite rate, which results in a value which gradually approaches zero.Justinhttp://www.blogger.com/profile/08393391645130692667noreply@blogger.comtag:blogger.com,1999:blog-7366878066073177705.post-27055088022315167672010-03-30T20:50:25.751+01:002010-03-30T20:50:25.751+01:00If I’m on the crest of an infinite money generator...<i>If I’m on the crest of an infinite money generator then the difference between $100 million and $200 million may not appear to offer me much more utility but frankly I’m sure my kids can use it, or my wife’s lawyers.</i><br /><br />It seems to me that the missing element in the analysis might be time. I'd rather have $100 today than $100 million delivered 100 million years from today. Maybe that's just me.<br /><br />A related puzzle that I have pondered is Buffett's explanation of the proper stock price being the discounted value of all future dividends. If you went out long enough, the amount of the future dividends would be infinite and the discounted value of infinity would also be infinity. So I think there has to be a time cut-off to make this sort of thing make sense.<br /><br />RobRob Bennetthttp://arichlife.passionsaving.comnoreply@blogger.com