tag:blogger.com,1999:blog-6837159629100463303.post6384019747687115810..comments2023-06-18T01:25:08.748-07:00Comments on Information Transfer Economics: Utility maximization, matching and information equilibriumJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-6837159629100463303.post-81011451243179116852016-01-12T16:36:39.511-08:002016-01-12T16:36:39.511-08:005. I wouldn't say the search cost 4 boxes; tho...5. I wouldn't say the search cost 4 boxes; those left off are more like unemployed labor states.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-33282421972557342012016-01-12T16:35:27.069-08:002016-01-12T16:35:27.069-08:001. There is a lot more ambiguity in the filling pa...1. There is a lot more ambiguity in the filling pattern that maximizes utility as you add boxes. The result would depend on maximizing the overlap integral, but would have a left-right ambiguity.<br /><br />2. I probably should have said "an additional 98.7%" (totaling 100%).<br /><br />3. NI could probably be modeled as unfair dice, but may not be a true random variable and hence might not have a distribution from which it is drawn.<br /><br />4. The probability for the dice rolls aren't whole numbers, but the results of dice rolls (boxes) are whole numbers. It would probably be better to normalize the result at each step of the way, but that is less illustrative.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-19525455028375071482016-01-12T16:20:45.670-08:002016-01-12T16:20:45.670-08:00"[0] Ok, there are 21 boxes here. For those w..."[0] Ok, there are 21 boxes here. For those who counted, you have won this round!" Haha... I did count, and was going to point that out.<br /><br />Also, for the 2nd figure (i.e. "Matching") there are only 16 boxes. Does that mean the search itself 'cost' 4 boxes then?<br /><br />You write:<br /><br />"The sequences consistent with utility maximization at each roll all begin with 7, 6, 8 ... or 7, 8, 6"<br /><br />Ok, so for each allocation, you're maximizing utility then. There's no first allocation that gives you more utility than to start with 7, and then to move onto either 6 or (equivalently) 8. What would the optimal 4th allocations look like? Back to 7 again, or do we start filling in 5 or 9? Is there a way (for us) to tell, or is there a hidden utility function you're using we're not privy too? What price will person 7 pay for his 2nd widget as compared to the price 5 will 5, 6, 8 or 9 will pay for their first?<br /><br />"while the IE-consistent rolls make up more than 98.7% of the possible histories."<br /><br />Here you lose me. If the dice are fair, I don't see why this isn't 100%.<br /><br />"[2] In reality, you'd need to look at a far larger number of widgets to really tell the difference between the ideal and non-ideal cases. The NI distribution is an improbable result of rolling 20 dice, but is not actually significant at the 5-sigma level, for example."<br /><br />Same question: isn't NI just unfair dice?<br /><br />Ah!... you're talking some kind of statistical test to see if the data is 'consistent' with a distribution, aren't you? So there's a chance that with even fair dice you'll find a sequence of 20 rolls for which this statistic indicates an result inconsistent with the distribution.<br /><br />Shoot! You're always making me use my brain. It's not right. ;D<br /><br />Great stuff! Fits right into my questions on more recent posts. BTW, I assume it's just an unfortunate accident that the boxes are not the same dimension vertically as one-unit on the y-axis?Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.com