From sludmer@princeton.edu Sun Apr 25 15:21:06 2004 Date: Sat, 24 Apr 2004 18:20:53 -0400 From: Sebastian Ludmer To: John F Nash Subject: Re: Charts Dear Prof. Nash, I realized it may also be of interest to you to have the MS Excel file that generates the chart. I am attaching it to this email. Sebastian ----- Original Message ----- From: "Sebastian Ludmer" To: "John F Nash" Sent: Saturday, April 24, 2004 6:08 PM Subject: Re: Charts > Dear Prof Nash, > > I attach the corrected chart. The reason for the discrepancies is that I > was using a wrong measure for the imbalance: Instead of > p1 + p2 - 2*p3, > > I was using > p1 / p3 - 1. > > In my previous run I corrected this criterion discrepancy for the "model > imbalance" measure, but not for the Shapley nor Nucleolus. I apologize for > this glitch. The Nucleolus was computed, for each parameter specification, > using the "nuke" command of exepac. The line is now as straight as MS Excel > (the software used to generate the chart) can produce (!). > > I also attach to this email the output file with the data that was used to > generate the chart. This file can be found in the "sludmer" area of math, > under > > 1G\2Symm\b3to1new > > By the way, that directory contains a file called "exepac.main.a04", with a > routine called "rutina". The latter generates 74 iterations on b3, from 0.01 > to 0.75, in steps of size 1/100. This range was chosen only with the purpose > of generating a chart comparable with Pokharel's. The solution for b3 = > 75/100 is still non-negative, so further results could be obtained by > increasing b3 even more, before reaching an invalid solution. The routine > "rutina" uses the auxiliary piece of code "psgen". > > I hope this is useful to you. I am travelling to Argentina in ten days (May > 3). If you would have time for a coffee this week (Thursday, for instance) > it would be great to see you. And please do not hesitate to tell me if the > chart needs more work. Hopefully, I got it right this time. > > Sebastian > > > ----- Original Message ----- > From: "John F Nash" > To: "Sebastian Ludmer" > Sent: Wednesday, April 21, 2004 8:55 AM > Subject: Re: Charts > > > > > > Dear Sebastian, > > > > I am back from Washington now. > > I just saw your chart, but something seems to have gone wrong > > in your work on it and it seems, in general appearance, quite > > different from the chart you prepared earlier, for b3 varying, > > with larger values of "the epsilons". > > One thing that is a clear signal is that the curve for the > > nucleolus should be formed by two line segments. On your graph > > the nucleolus trace, for b3 above 0.333.. , should be a straight > > line, and your graphic shows it as curved. > > Also, the Shapley value result came out as simply sv = b3 > > and so the graph of that should rise at 45 degrees in slope > > on the scale indicated for your graphic. > > So I think there are some technical errors in getting the > > graphs, but your calculated numbers might be correct. > > (I didn't find your recent work when first looking into > > the sludmer@math files yesterday.) > > > > John > > > > ############################################################ > > > > On Mon, 19 Apr 2004, Sebastian Ludmer wrote: > > > > > Dear Prof. Nash, > > > > > > I attach the chart with the corrections. I hope it looks better now. I > > > changed the imbalance to the appropriate measure, and also did the > aesthetic > > > modifications to make it look closer to Pokharel's. I apologize that it > took > > > me a few days, but I have been rushing with my research (I am trying to > > > extend the results to an environment with uncertainty and it is proving > > > tricky - there seem to exist multiple equilibria). Please tell me if the > > > chart needs more changes, and I will be glad to make them. > > > > > > Oh, I forgot to tell you the other day. The computations to generate > the > > > chart data are stored in the 'sludmer' area of the math server. Do you > want > > > me to send them to you? I also programmed (yet) another procedure to > > > generate and save a sequence of parameter changes (specifically, b3) and > the > > > resulting computation outcomes. Like the bbseq programs, only taylored > to > > > generating the kind of output needed to generate the charts. I use the > > > "FRTC" command that works very very fast when changes are small. > > > > > > I hope the event at Georgetown University was interesting and you had > a > > > good trip. We could meet on Thursday afternoon (in Fisher hall or Fine > hall, > > > as you prefer - or even elsewhere, like Small World cafe) if you have > time > > > available. > > > > > > Sebastian > > > > > > PS: I thought it was more appropriate to sign the chart as "Nash 2004", > > > rather than "Nash and Ludmer". It seems to me that I am just your > research > > > assistant, and the normal practice is not for assistants to sign the > work. > > > Instead, their help is mentioned in the "acknowledgements" footnote at > the > > > beginning of the paper. Perhaps you think differently... > > > > > > > > > ----- Original Message ----- > > > From: "John F Nash" > > > To: "Sebastian Ludmer" > > > Sent: Sunday, April 18, 2004 3:47 PM > > > Subject: Re: Charts > > > > > > > > > > > > > > > > > > Dear Sebastian, > > > > > > > > I am in Washington now. I have finished up at Georgetown U., > > > > participating in most of the program of their meeting, to the extent > > > > possible. > > > > We will be returning to Princeton late Tuesday on the train. > > > > > > > > John > > > > > > > > > > > > ###################################################### > > > > > > > > On Sat, 10 Apr 2004, John F Nash wrote: > > > > > > > > > > > > > > Dear Sebastian, > > > > > > > > > > By coincidence I will be gone by Thursday evening; I am > > > > > going to Washington, D.C. for a few days. One thing there > > > > > is that I will be participating in an event called the > > > > > "Carroll round" involving undergraduate economics students > > > > > at Georgetown Univ. there in Washington, DC. > > > > > Peter Orszag, who was a summa cum laude undergraduate > > > > > economics major at Princeton, will also be lecturing there. > > > > > > > > > > John > > > > > > > > > > ################################################# > > > > > > > > > > On Sat, 10 Apr 2004, Sebastian Ludmer wrote: > > > > > > > > > > > Dear Prof. Nash, > > > > > > I apologize for not replying before, but I was out of town; one > of my > > > > > > advisors moved to the University of Chicago last fall, and I > travel > > > around > > > > > > once a month to meet him up there. I will send you the charts as > soon > > > as I > > > > > > correct them, most probably by Tuesday night. > > > > > > With respect to meeting, how about Thursday evening? We could > look at > > > the > > > > > > charts for any final details besides talking about other things. I > > > don't > > > > > > know much about your "Ideal money" project, but it sounds very > > > interesting > > > > > > (and close to my heart, unfortunately for Argentina...). > > > > > > I hope you have a good weekend, > > > > > > Sebastian > > > > > > > > > > > > > > > > > > ----- Original Message ----- > > > > > > From: "John F Nash" > > > > > > To: "Ludmer" > > > > > > Sent: Wednesday, April 07, 2004 7:52 AM > > > > > > Subject: Re: Charts > > > > > > > > > > > > > > > > > > > > > > > > > > Dear Sebastian, > > > > > > > > > > > > > > Also. > > > > > > > Also, we could meet at some time of bilateral convenience. > > > > > > > I have been continuing with my series of efforts on the "Ideal > > > > > > > Money" line (which is very relevant to the histories of > Argentina, > > > > > > > Brazil, El Salvador, and Panama). > > > > > > > And I am planning for a publication on the game theory > > > > > > > modeling of evolved cooperation. (The specific model studied is > > > > > > > apparently imperfect but it is an example and possible lines > > > > > > > of improvement, which could be studied, can be seen.) > > > > > > > I was at the Timothy Van Zandt lecture in "micro" last > > > > > > > Thursday but I didn't see you there. Tanjim Hossain was there. > > > > > > > Tomorrow I may be too busy to go to a "micro" seminar. > > > > > > > > > > > > > > John > > > > > > > > > > > > > > ######################################### > > > > > > > > > > > > > > On Tue, 6 Apr 2004, John F Nash wrote: > > > > > > > > > > > > > > > > > > > > > > > Dear Sebastian, > > > > > > > > > > > > > > > > A. Pokharel has gotten a pretty nice looking version now > > > > > > > > of a chart for the case of bz varying and b3 = 0 . I am > > > > > > > > attaching it. (I was making some requests in relation to the > > > > > > > > colors of the three different function graphs.) > > > > > > > > > > > > > > > > John > > > > > > > > > > > > > > > > ############################################## > > > > > > > > > > > > > > > > On Mon, 5 Apr 2004, Sebastian Ludmer wrote: > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > [ Part 2, Application/VND.MS-EXCEL 155KB. ] [ Unable to print this part. ]