[Mnet-devel] another paper

[Jim Dixon]

On Mon, 10 May 2004, [iso-8859-1] Some Guy wrote:

> > The big failing is the requirement that the utility function be
> > differentiable.  It just doesn't square with experience.  Most people have
> > low bandwidth connections, so files take a long time to download. A CDROM
> > takes hours, a DVD can take days.  So satisfaction comes in chunks, and
> > often enough the download fails, leaving people frustrated. Or, as a
> > mathematician would say, utility is a step function (and so is not
> > continuously differentiable) and can be negative.  This does not at all
> > match the model in the paper.
>
> You do realise that he's not dirrectly talking about people getting
> utility from downloading files?  He's talking about people getting
> utility out of making a mix of files available to others.

No ... they are actually talking about mobile telephony and say nothing
at all about files.

The paper requires careful reading.  They say "we associate with node n
[an element of] N [where N is the set of all nodes] a utility function
Un(xn) which depends on the transmission rate xn of node n, i.e., the
rate at which node n sends its own traffic."  As I paraphrased in the
earlier email, the utility is zero if xn is zero, and has its maximum
if xn is Cn, the total amount of data transmitted.

In other words, all utility (happiness) is derived from transmitting the
node's own data. Maximum utility is achieved when you carry no traffic at
all for anyone else.

>                                                         This makes
> sense in a politicial or advertising enviroment where people are trying
> to push data out there.  It doesn't make too much sense if people are
> just tring to download data and don't really care if anyone else can
> download anything.

They go on to define a demand function.  The demand is essentially the
difference between the utility derived from transmitting one's own data
and the cost of transmitting it.  In other words, you will transmit as
much as you can afford, all other things being equal.

> His view is like that of a group of people with a webserver with a fixed
> storage capacity.  Some want the world to see more blue data and some
> more red data.  Everyone has his own personal idea of how much blue and
> red there should be and any deviation from this mix gives him less
> utility.

What they call the 'node problem', equation 1, page 3, refines the above.
It takes into account the amount other nodes will pay you to relay their
data.  This offsets the cost of transmitting your own data.  Once again I
quote: "To maximize its own benefit, node n chooses an allocation (xn, yn,
un) which solves [the node problem]".  Here yn is how much data you carry
for others and un how much you charge them for it.

This is nothing whatsoever to do with personal ideas about the traffic
load.  It's a straightforward mathematical calculation carried out by
software. The purpose of the calculation is maximizing the benefit to the
node carrying out the calculation, where benefit is calculated in local
currency units.

In the paper, social benefit is a by-product.  That is, first they try
to show that the local utility functions will converge to a stable
state.  Then they show that this stable state happens to be beneficial
to all.  It's very much Adam Smith and the Invisible Hand.


It's a bit difficult to quote in ASCII.  In the above I have replaced
Greek letters
* epsilon with 'element of'
* mu      with  'u'
and just ignored subscripting, so for example "mu sub n" becomes un.

--
Jim Dixon  jdd at dixons.org   tel +44 117 982 0786  mobile +44 797 373 7881
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