Gravity model of trade volumes

[Jon F. Zeigler]

I'm over a thousand miles away from my notes, and I don't recall enough to know whether there's just a dropped exponent there, but I suspect there is. What we've really got here is the economic equivalent of Olbers' paradox - and just as the sky is dark at night, you really don't want your model predicting an infinite amount of trade coming in to every world in the galaxy.

If you lot can agree on a reasonable value for the exponent in a three-dimensional universe, and submit an erratum, I'd be happy to nod my head and say "yes" when the buck gets passed to my desk.

[DrTemp]

Originally Posted by Agemegos

[...]
I suggest 3.
[...]

For 3D maps, that is. Maybe one could add "^(number of dimensions on the map)" to the formula in Space. That way, some Infinite Worlds in Space version with 3+1 dimenions would be covered, too, as would be Traveller-like settings with some kind of two-dimensional "jump space structure".

[sir_pudding]

Originally Posted by Agemegos

I suggest 3.

I don't know if you know this, but you actually have to send an email to errata@sjgames.com.

[DrTemp]

Originally Posted by Agemegos

I didn't. Thanks for the pointer.

Is there a consensus for an exponent of three?[...]

For most applications, that's fair enough. It's just that "number of dimensions of the map, normally 3 for a space map" would be even more accurate.

[DrTemp]

Originally Posted by Agemegos

[...]
As for economists who are worth more than their salt, I didn't use gravity models myself, as being too crude.
[...]

I am also pretty sure that the simplifications of the rules ion damage, injury and fatigue in GURPS are less than tolerable from a scientific point of view. But they work as an approximation in a game. ;-)

[DrTemp]

Originally Posted by Agemegos

Just so. And a gravity model for trade volumes will work as an approximation in a game so long as you put an exponent on the distance (or better, cost) that is higher than 2. [...]

Of course, that makes sense, for obvious reasons - unless T is not given in absolutes, which I do not recall at the moment - will have to look it up. (The ISW trade system at least does not work with a trade volume given in absolute amounts, but as an abstract value for use with the trade system's tables.)

But changing to a more detailed model with lots of factors and more complicated formulae does, in my opinion, not help at all.

[DrTemp]

Originally Posted by DrTemp

Of course, that makes sense, for obvious reasons - unless T is not given in absolutes, which I do not recall at the moment - will have to look it up. [...]

No, it is in absolute numbers. However, I find it plausible that the "squared" or "cubed" part was simply forgotten. A rather simple erratum, so to speak.

Question to JFZ: Is that the case?

[Anthony]

I would bet it was based on the gravity trade model in GT:FT, which is using a 2d map where 1/D makes sense. It's unclear what the exponent should be on a 3d map, we don't have any real-world models to look at (the terrestrial case is generally close enough to 2d that it can be called 2d).

[thrash]

Originally Posted by Anthony

I would bet it was based on the gravity trade model in GT:FT, which is using a 2d map where 1/D makes sense.

Can't be, since the gravity trade model in GT:FT uses 1/D^2 (although it is concealed by the logarithms used in the actual tables).

It looks like a simple omission -- there should be another variable as an exponent on the distance factor.

It's unclear what the exponent should be on a 3d map, we don't have any real-world models to look at (the terrestrial case is generally close enough to 2d that it can be called 2d).

When I asked Jim Maclean (the professional economist behind GT:FT, for those who don't know) he suggested that 1/D^3 was probably close enough.

Part of the problem with this subject is that the gravity trade model is an empirical observation, not a theoretical result. There are a number of competing explanations for why it works across such a wide range of applications -- and thus, at least as many possible ways to extend it to three dimensions.

The actual exponent for international trade is more like 1.9 than 2.0, by the way, but that's close enough to the square to make "gravity model" a reasonably accurate description.

[David Johnston2]

Originally Posted by Brett

In the otherwise good planetary design sequence in GURPS Space, there is a formula suggested for estimating the volume of trade (T) between any pair of planets with given economic outputs (V1 and V2), separated by a distance D. The formula is

T = k.V1.V2/D

where k is a constant set by the GM to reflect the specifics of his setting.

Anyone who attempts to map any reasonably large number of worlds and apply this formula pairwise is in for a nasty surprise. .

Well, not anyone. I for example, assumed that no numerically significant trade route was longer than about 15 light years in distance (with trade at longer ranges passing through economically significant planets and thus being subsumed into the trade of those planets) . Thus, it wasn't "any pair of planets". It was "any pair of planets between 15 light years". And, since there would be only about four economically significant planets at most in that range, the problem simply never arose.