[MUD-Dev] Understanding Simulation (was: Point of View)

[Ted L. Chen]

Derek Licciardi wrote:
> From: Ted L. Chen

>> Things get more interesting and applicable to MMOGs at Road Map
>> #6, where they start to combine the elements learned in
>> "Economics Supply and Demand" Something of interest for anyone
>> interested in player-driven economies.  Most people assume
>> equilibrium from the get go, and the example serves to illustrate
>> the oscillation that occurs in even a simple system that uses the
>> most basic of rules.  For those pondering a purely player-driven
>> economy, I suggest you take and play with the model.  I've been
>> playing with the effects of demand noise and have destablized the
>> system with only 15% noise.  If you want the matlab code or
>> discuss the specifics in detail, email me off list.

> I wanted to comment and add to your statement about player-driven
> economies.  I took something completely different from that
> article.  What I saw was an explanation of what happens when you
> consider inventory(the craftsmen/women) into the supply and demand
> equation.  Most of the stuff seemed obvious from a player driven
> economy standpoint.  It just seemed like what would happen in a
> situation given a supply, given a demand and everyone looking out
> for their own self interest.  It helps the understanding, but I'm
> not sure how it would apply to a player-driven economy from a
> design standpoint.

> Now if you think about NPCs on the other hand, the chapter has
> significantly more use.  I read it and thought of all the data
> structures that I could track from the player-driven economy.  I
> thought about how the model helps us understand the dynamics of
> profit motivated AI.  I thought it was directly applicable to
> things like an NPCs stock level of any given item and the prices
> they would charge, or an items availability in a region of your
> world and the resulting prices.  All of these things can be
> sampled from the player economy and fed to your AI system in an
> effort to make NPC shopkeepers much more realistic.  I took more
> than just a good read for player-driven economies.  I also took it
> as a more significant read for AI developers looking to create and
> model profit driven NPCs in their worlds.

I was afraid the leap I made was rather large.  The article was
primarily concerned with showing readers how to put the previous
dynamic 'elements' together.  I guess I was extrapolating the
article a bit.  The key was to highlight the oscillations that occur
before the model reaches equilibrium.  Let me explain, but first,
let's back up a bit...

The article's model made a few assumptions.  One of which was that
the demand/supply was an aggregate number, not really counting
individual suppliers or people in the economy.  From this, the price
was assumed to be an averaged price across all companies in the
industry.  So, in effect, you could say it's a scaleless model.
Now, the difference in my eyes, between a player economy and a NPC
economy is the size.  Ideally, a stable NPC economy is large, with
the population of whole economic regions, while the player economy
will no doubt number far smaller but hopefully still large enough
(n>1000?) for the assumptions to hold.  The model as is scaleless,
so we still apply it.

Now, perhaps it's too many years learning about control systems, but
I get edgy whenever I see oscillations.  You see, oscillations move
the system away from the equilibrium point for brief periods.  The
general rule is that stability decreases the further you are away.
At some point out the system cannot be stable anymore.  All control
designers want to minimize oscillations as much as they can by
trading off control performance.

When I encounter nonlinear systems, no matter how initially stable
it may seem, my first act is always to examine how it fairs against
noise in its inputs.  It should be easy to envision cases where the
system might be pushed out of the safe zone and into the frying pan.
For a player-driven economy, I assume that because of the lower
number of "n", that any noise in demand is a higher percentage of
overall demand than it would be in the NPC economy.  The NPC
economy, by its sheer size, has more inertia which I factor in as a
lower noise percentage.  As a dramatic simplification, more noise =
less certainty of stability.

So that's why I say the article is useful.  It shows that no system
gets to the equilibrium point immediately, and that many factors
influence how far it stays away from equilibrium and for how long.


P.S.  if you're interested, the model they give does go unstable if
the situation starts when the price becomes so bloody low that
stocks are quickly depleted.  The industry then gears into this
insane production run to meet it the new hyper-inflated price.
Demand drops, but oddly, the hyper-inflated price and inventory
sustains the growth in price.  The economy is dead (or has a good
chance of being dead) by this point and the simulation is useless.

Given a good initialization, the model will never go into this
situation by itself.  It takes noise.  Testing in a very
"non-scientific way" :P, and with MMOG-like numbers (price change
delay = 3 days, inventory in stock = 1 week, a simulation step size
of 1 day, and a random demand bias every week), the economy model
collapses with about 7-10% noise in the demand.


If you believe the assumptions behind the model (and the curves),
then 10% is rather low for a noise level, especially when people are
concerned.  There are a couple of things one can do to increase that
limit.  One of which I found was not to allow backorders (negative
inventory).  I could probably increase the noise up to about 15%.
Which admittedly, still isn't much.

But personally, the numbers above aren't conclusive as I don't
really believe that model as written by the article.  Even they
suggest a couple additions to it.  The numbers were only to get you
thinking and I merely pointed it out as a starting point in your
development (you should at least understand that article if you want
to do anything remotely resembling a player-economy).

And you're quite right in that people interested in NPC economies
should read that article too.  If it's closed, with no player input,
then they can implement the model as is and have a decent
simulation.  If players are involved, I suggest that they also model
it and actually play with the noise.  The bigger the NPC:player
ratio, the smaller the noise should be.  I personally am of the
opinion that active NPCs are required buffers for good stable MMOG
economies.

One thing I'm interested in (and haven't done this yet as of writing
this) is to see how that simple model compares to one where the
industry is subsidized.  Hey, wait, that's what we had in the old
mixed player-NPC economies!  But for any meaning, I think I would
have to explicitly include industry-size in the model instead of
just treating it as variable noise.  Anyone want to do that?


TLC


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