Galaxy Size and Tech Costs

For what's not in 'Top Priority Game Design'. Post your ideas, visions, suggestions for the game, rules, modifications, etc.

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Ray K
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#16 Post by Ray K »

Black_Dawn wrote:How about we end this argument by doing the easy thing:

Put in a changeable setting at the beginning of the game...
arrgh.

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skdiw
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#17 Post by skdiw »

What do you mean by "function of the growth of the game"?
You were worrying about how a factor would change the early game, since early game should be the same for a small map and large map. I'm saying if you use a power, expo, or e^x function, the early game will remain the same, while tech cost will increase for latter game.

What do you mean by "'a' can be approximate with x^a"
It's common knowledge that things magically grow by e^t. I just thought x^a looks more or less similar and would be easier to implement and balance the tech costs of each branches later on. 'a' is again the scalar factor tagged along each galaxy size. 'x' is the base tech cost.

I said 'a' can be approx by x^a because you were thinking that if I multiply a and x, the early game would be different. I'm saying do x^(a+b) or do x^(ab)

'a' should be just a fixed number on each galaxy. We don't want 'a' be dependent on empire size, since each player style, enviornment, and empire advantages are all different.
What advantages (or disadvantages) does it have, in your mind, compared to other possibilities, besides being "simple" ?
I think just moving the scalar from a multiplier up the exponent would solve your problem.

I also think that we need a normal scalar factor anyway as a game option because people have a lot of opinions on how fast tech should progress like in moo3.
:mrgreen:

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Geoff the Medio
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#18 Post by Geoff the Medio »

Black_Dawn wrote:Put in a changeable setting at the beginning of the game which will allow you to change scientific progress from "very slow" to "very fast" and everything in between.
That's fine and good; as I said above, "I have no problem with an option to speed / slow research overall as an option at the start of a game."
You could set it so that when you change galaxy size, the research speed changes appropriately (very fast for tiny galaxies), but could then be changed to whatever speed the player prefers.
It's not enough to say we'll change the speed "appropriately". We need to actually figure out what "appropriately" means.

Even if you can adjust the overall tech progress rate, we still (may) need to correct for the different sizes of empires after all space is filled up, which varies with galaxy size and number of empires... but not also cause the tech rate at the start of the game when empires are all the same size to vary (when empires are the same size no matter how big the galaxy is or how many empires there are).

See this chart:
Image

Notice that at the start of the game, empires in both sized galaxies have the same RP production. It's only at the end, when all space is filled up, that RP production depends directly on galaxy size. At the end, we can vary RP costs by galaxy size without problem... but at the start, this creates problems. We need an adjustment that fixes the end-game without messing up the start... in addition to a simple fast / slow tech progress rate control that the user can adjust.

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#19 Post by Geoff the Medio »

skdiw wrote:I'm saying if you use a power, expo, or e^x function, the early game will remain the same, while tech cost will increase for latter game.
So you want something like:

Corrected_Tech_Cost = (Base_Tech_Cost) ^ (Galaxy_Size)

Why do you claim this won't vary at the start of the game? 2^20 is much different from 2^80, 1.05 ^ 20 is quite different from 1.05 ^ 80, etc... exponentials grow so fast that there's probably no useful middle region between no growth at x = 1 and hugely explosive growth.

And IMO this would be a bad formula to use anyway, because assuming RP production grows roughly linearly with galaxy size, if tech costs grow exponentially with galaxy size, more expensive tech will get more expensive much faster than RP will grow with galaxy size, making expensive techs far too expensive in big galaxies.
I said 'a' can be approx by x^a because you were thinking that if I multiply a and x, the early game would be different. I'm saying do x^(a+b) or do x^(ab)
So a is a function of galaxy size, and x is base tech cost... but what's b?
We don't want 'a' be dependent on empire size, since each player style, enviornment, and empire advantages are all different.
You could vary a with the average empire size, rather than separately varying it for each empire... But I suspect a better correction that doesn't depend on empire sizes at all could be found.

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#20 Post by Impaler »

Black_Dawns sugjestion is quite reasonable and I would like to see it implemented. At game set up the player will get a "Sugjested Research Speed" based on the input of several factors most notibly Galaxy Size and # of races. The player is free to keep that speed OR change it if they wish.

But as Geoff has pointed out the main problem is the scaling of cost as the game progresses. In essense their are two multipliers on tec cost a "Galactic Scallar" and a "Progress Scaler" that both multiply the base tec cost.

The Galactic Scalar is the user selectable one which gets a default sugjestion at game start up. The Progressive scalar changes through the course of the game (and seperatly for each empire) based on the what ever factors we can think of such as

Empire Raw Size
Empire Relative Size (% of all Stars Owned)
Empire Power level
Game Turn
Tec level
Relative Tec level

I once made an interersting Mod for SMAC inwhich I focused on reducing the late game tec explosion that common in SMAC, a strait out across the board tec slow down of 30% normal speed did a good job at cotroling the late game but initialy proved disasterous in the early game (your 3rd tec was taking 20 years). I found 2 interesting solutions to this. Firstly I gave every faction 2 free Tec points per turn per base (this is a un-used paramiter that can easily be inserted in the Faction text file). Second I gave each of the default "None" social Enginering Choices a +1 Research and several other nasty penalties so each faction starts the game with a -1 across the board except for a +4 in Research. Both these bonus helps in the early game but are either tiny or practical impossible to exploit in the mid/late game because of all the negatives. These 2 early bonuses cancel out the changes that were slowing the early game down so much. Something along the same lines could help FreeOrion.
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#21 Post by Daveybaby »

Or just take a leaf out of Moo3's book, have an exponential factor in there as well. This can be fine tuned to give the required scaling between early game and late game techs.
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#22 Post by skdiw »

Nice graph of S-curve; the s-curve would be ideal to use as modifier to many many of our game features. I suggested adding this function into FO repetouire of functions years ago, but I didn't see anybody really picked it up, :( at least not from programmers.
Why do you claim this won't vary at the start of the game? 2^20 is much different from 2^80, 1.05 ^ 20 is quite different from 1.05 ^ 80, etc... exponentials grow so fast that there's probably no useful middle region between no growth at x = 1 and hugely explosive growth.
You won't get a simple formula that exactly matches our needs without some approximations. Some sort of an expo formula is your best bet, since it gives you small change early relative to latter, which is exactly what we want. Granted, the beginning costs will still be higher than standard, but players won't argue a small amount of rp difference. With some rounding, you might just get the same costs in the early techs.

What you want is an increase in costs over time right? One that increases the costs that justify increases in production from bigger galaxy, while not change the early game because small and large galaxy behave similarly? Let keep it simple and say t, just for illustration (t is a big factor). Well, take the integral of t and you get the same sort of formula I said. I don't think you can find a better formula without being very complex, like a step function which I think you are eluding to (which I don't mind since it fits really well for my "eras" research ideas, but Aq said too complicated or unnecessary if I remember). Impaler's idea is also a step, which makes for rush for tech X kind of game. Not that I mind, but Aq might say unbalance of learning branch.

If you want a middle region, then use a power series by adding more terms. But usually games are decided by mid-game so it's not too bad if you just nix the latter half. If you wan't an even better approximation, well, then use the S-curve then. Of course, the better your fit, the more complex.
And IMO this would be a bad formula to use anyway, because assuming RP production grows roughly linearly with galaxy size, if tech costs grow exponentially with galaxy size, more expensive tech will get more expensive much faster than RP will grow with galaxy size, making expensive techs far too expensive in big galaxies.
Okay, I think here is the problem. I don't think rp gows linearly. Empire in bigger galaxy bascially starts in the early game with more stars, hence a bigger base for growth. It still grows exp like in smaller galaxy. I don't see how you conclude linear growth. Look at your plot.
I said 'a' can be approx by x^a because you were thinking that if I multiply a and x, the early game would be different. I'm saying do x^(a+b) or do x^(ab)

So a is a function of galaxy size, and x is base tech cost... but what's b?
Again, b is the base tech expo number assigned to individual techs or a whole branch, since we want techs to outpace pp.
We don't want 'a' be dependent on empire size, since each player style, enviornment, and empire advantages are all different.
You could vary a with the average empire size, rather than separately varying it for each empire... But I suspect a better correction that doesn't depend on empire sizes at all could be found.
Yeah, you were just looking at it, or what I'm trying to get to.



We don't want too many startng options either, since that would be too much. I have a good idea for the pace, but that's for me. Other ppl like different speed so the only option we really need is some scalar factor that adjust overall speed.
:mrgreen:

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#23 Post by Geoff the Medio »

skdiw wrote:
exponentials grow so fast that there's probably no useful middle region between no growth at x = 1 and hugely explosive growth.
You won't get a simple formula that exactly matches our needs without some approximations. Some sort of an expo formula is your best bet, since it gives you small change early relative to latter, which is exactly what we want. Granted, the beginning costs will still be higher than standard, but players won't argue a small amount of rp difference. With some rounding, you might just get the same costs in the early techs.
Yes, the change with exponential is more later than it is earlier, but it's so much more that the function is effectively useless. Exponentials are just about the fastest growing (for large n) commonly used type of function. As I said, there's no middle ground between hugely explosive growth and no growth... Unless you can give some realistic numbers as an example, I don't see how it could work.
What you want is an increase in costs over time right? One that increases the costs that justify increases in production from bigger galaxy, while not change the early game because small and large galaxy behave similarly?
I don't want to "justify" anything. I want the rate of tech progress to be roughly the same for large and small galaxies, throughout the whole game. Thus at turn n in a small galaxy, you'll have the same number of techs researched as at turn n in a large galaxy.
Let keep it simple and say t, just for illustration (t is a big factor). Well, take the integral of t and you get the same sort of formula I said.
Huh? What is t?
I don't think you can find a better formula without being very complex, like a step function which I think you are eluding to
I don't care if it's a step function or C-infinity continuous. That it works is what matters. If it has to be a step function, that's fine.
And IMO this would be a bad formula to use anyway, because assuming RP production grows roughly linearly with galaxy size, if tech costs grow exponentially with galaxy size, more expensive tech will get more expensive much faster than RP will grow with galaxy size, making expensive techs far too expensive in big galaxies.
Okay, I think here is the problem. I don't think rp gows linearly. Empire in bigger galaxy bascially starts in the early game with more stars, hence a bigger base for growth. It still grows exp like in smaller galaxy. I don't see how you conclude linear growth. Look at your plot.
I said "grows linearly with galaxy size", not "with time". I assume the RP production of an empire is roughly proportional to the area of the empire, which seems a reasonable approximation. The growth of RP production linearly with galaxy size refers to after all of the galaxy is colonized. In this situation, the average size of an empire is proportional to the size of the galaxy. On the graph above, this means that at the rightmost side of the graph, the height of the lines for a given game turn is proportional to galaxy size. The growth with time is roughly exponential, however, until you start running out of space to keep growing expoentially, which is represented on the graph by, the "S-curve" you refer to.
I said 'a' can be approx by x^a because you were thinking that if I multiply a and x, the early game would be different. I'm saying do x^(a+b) or do x^(ab)
So a is a function of galaxy size, and x is base tech cost... but what's b?
Again, b is the base tech expo number assigned to individual techs or a whole branch, since we want techs to outpace pp.
You seem to be sure this will work... can you give some reasonable example numbers using this formula? If it works, I'll accept your claims, but right now I don't see how it will.
We don't want too many startng options either, since that would be too much. I have a good idea for the pace, but that's for me. Other ppl like different speed so the only option we really need is some scalar factor that adjust overall speed.
The only player controlled starting setting that I'm suggesting / agreeing with is the single research speed control. This would act independently of the correction for galaxy size, which the player would not be able to control.

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#24 Post by Ablaze »

So let me get this straight, the idea here is that tech costs increase over time? Has anyone considered the effect this would have on gameplay stile? If I research lasers now they will cost 5 rp for 2 turns, but 50 turns later they now cost 8 rp for 2 turns. For mid-range techs this could be quite a significant factor.

Skidoo, you've been harping about your s-curve for so long that I feel like you deserve a bit of help here. Calculating an s-curve does not take calculus, if it did you would be preaching a lost cause. About half way down this page is an algorithm for CQuadraticTimeInterpolator. All it would take to build an s-curve algorithm would be to put two quadratics on top of each other.
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#25 Post by skdiw »

Okay, lets make up some numbers:

refrence galaxy: t=time on line 1, then number of tech costs at line 2
1 10 20 30 ... 100
1 25 66 117 ... 631
here, I used tech cost=t^1.4 For example, at turn 10 researching level 10 techs, the research cost is 25 rp.

Now for large galaxy:
1 10 20 30 ... 100
1 32 90 164 ... 1000
the formula here is cost=t^1.5
Since larger galaxy produces more exponentially, the tech cost will be more, also exponentially to reflect the growth pattern.

The numbers looks fine to me.
Skidoo, you've been harping about your s-curve for so long that I feel like you deserve a bit of help here. Calculating an s-curve does not take calculus, if it did you would be preaching a lost cause. About half way down this page is an algorithm for CQuadraticTimeInterpolator. All it would take to build an s-curve algorithm would be to put two quadratics on top of each other.
That's not a true natural S. Thats an approximation. If you want another approx. you can use a simple sin wave, which can be found standard in just about every software library.

If you want to help, then solve the problem at hand. I don't see how you are helping me, or helping at all for that matter.
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#26 Post by Geoff the Medio »

skdiw wrote:Okay, lets make up some numbers:

refrence galaxy: t=time on line 1, then number of tech costs at line 2
1 10 20 30 ... 100
1 25 66 117 ... 631
here, I used tech cost=t^1.4 For example, at turn 10 researching level 10 techs, the research cost is 25 rp.

Now for large galaxy:
1 10 20 30 ... 100
1 32 90 164 ... 1000
the formula here is cost=t^1.5
Since larger galaxy produces more exponentially, the tech cost will be more, also exponentially to reflect the growth pattern.

The numbers looks fine to me.
Yeah, they do look fine... Except they're not what you were suggesting before.

Firstly, that's fractional power growth with time, not exponential growth. That is, you have:

adjusted_cost = game_turn^A

where A = 1.4 or 1.5.

But "expoential" growth with time would be something like:

adjusted_cost = A^game_turn

where A > 1.

This is not just semantics... your formulas from before were actually expoentials, not powers, as well.

Secondly, ignoring the expoential / power thing, how does this relate to your previous formula? :

adjusted_cost = base_cost^( galaxy_size + base_expo_number )

There's no time in the old formula, and there's no galaxy size in your last example...?

Also, what was the purpose of having "base cost" x and "base tech expo number" b in the old formula...? What's the difference, aside from where they are in the formula?

And for the new example, what do you mean
by "researching level 10 techs" ?

If you actually meant / mean to suggest a power function, then my objection to exponentials does not apply... However using a power function has its own flaws, in that it just keeps growing with time, whereas the tech production starts to level off, as illustrated with the s-curve graph...

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#27 Post by Geoff the Medio »

Ablaze wrote:If I research lasers now they will cost 5 rp for 2 turns, but 50 turns later they now cost 8 rp for 2 turns.
I thought of that... It is a problem with our system of set costs for techs.

SMAC avoids the issue by having all techs be effectively the same, and just using a function to determine the cost of researching the nth tech, which increases if you reasearch another tech first... but you don't notice since the techs don't have clearly indicated costs.

If we use a gamestate-varying adjustment (such as a function of turn number, or something like percentage of the galaxy that is colonized), a possible, though unsatisfying, solution is to:

a) fix a tech's cost on the turn it becomes available to be researched. After that it would never increase, no matter what adjustment (time or empire(s) size) we use.

and optionally:

b) limit the increase factor from a tech and the techs that are unlocked by it

(a) means that once a tech's cost is established, it never changes. Whether (b) is necessary or not is debatable, as without (and perhaps even with it to a lesser degree), issues arise about unlocking certain later techs ASAP so as to "lock-in" the low initial cost for them...

However I think we should be able to make up a function in terms of base tech cost and galaxy size and number of empires that does the job without any parameters that depend on the gamestate (turn, empire(s) size). This would eliminate any need to worry about locking in early low-costs for techs or oddness about individual techs' costs changing over time in undesirable ways. It wouldn't matter what turn you research something; it would have the same cost throughout the game. (But its cost would vary between games with different sized galaxies.)

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#28 Post by skdiw »

Yeah, they do look fine... Except they're not what you were suggesting before.

This is not just semantics... your formulas from before were actually expoentials, not powers, as well..
Nature grows expo, but I said we can approx the pattern with power because most games use powers for growth so I assume we gonna use a similar formula. But really, it doesn't really matter because both will work--you just have to tweak the constants to several decimal places. The two functions are interchangable for our purposes. There is nothing special about fractions, they are still constants.
Secondly, ignoring the expoential / power thing, how does this relate to your previous formula? :

adjusted_cost = base_cost^( galaxy_size + base_expo_number )

There's no time in the old formula, and there's no galaxy size in your last example...?
t=x. x is like tech lvls 1, 2, 3... and is proportional to t, since as you progress the game, you research 1 -> 2 -> 3... so base cost for a given tech lvl is similar to time.

In the number example I gave, the reference is t^1.4. so t^a, where a=1.4. A "large" galaxy may have an inherent code value of b=0.1 so when you do calculation, you go t^(a+b) or t^(1.4+.1) or t^1.5. So a "yo mama" size galaxy might have b=0.2 for example. I thought this coding would be very simple and still get us what we want, which was the whole point.
Also, what was the purpose of having "base cost" x and "base tech expo number" b in the old formula...? What's the difference, aside from where they are in the formula?
base cost is cost of tech for given lvl. The expo number is how much the tech increases for every lvl so the higher the tech, the more it costs. The advantages of doing cost using formulas is 1. makes balance easier, since you don't have to change every tech individually, rather than a whole branch 2. makes modding easier 3. smaller learning curve
And for the new example, what do you mean
by "researching level 10 techs" ?
The functions are continuous. Obviously there are infinite points, so I have to chop off points here and there for illustration. You can think of it 10 turns down the line when the empire researched 10 techs.
If you actually meant / mean to suggest a power function, then my objection to exponentials does not apply... However using a power function has its own flaws, in that it just keeps growing with time, whereas the tech production starts to level off, as illustrated with the s-curve graph...
This is a discussion I raised already in seperate thread where I asked how research should complement the econ and the macro growth of the game. I don't see it as a problem because:

First off, most game ends way before saturation(tail flat end part of S-curve). You can't say that once you conqurer all the land, the saturation begins, because that's when players start teching and really that's when pp sky rockets. I have never played a game where the game saturated. That's why I said a expo or power function will do just fine because we don't need to bother with saturation if we never get there.

Secondly, the growth nature of expo creates less monotonous games because it creates shifts in the game. In the early game, each empire have access to all the essential techs necessary to get them started because techs are cheap. Mid-game, players have to plan a bit and pick their strategy to victory (whole point of 4X). By late game if the game doesn't end yet, each of the transcendent techs drastically changes the face of the game depending on the branch the player wants to specialize. I can't imagine an empire can easily research every transcendent tech unless he is just playing in a non-competitive game. Don't know about you, but I think this makes a better game than your normal 4X. I see the phenomonon as a good thing.

However, if you would like similar number techs researched at any point of the game, I called that recurssive tech tree or "eras." Here, there is no saturation and there are other advantages as well. You can read about that in other threads. In summary, basically you have the same set of techs, but once you hit the end, the same set of techs repeats itself from the beginning, except the cost and benefits are both raised. I posted details about that somewhere. This also makes a good game, imo.
:mrgreen:

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#29 Post by Black_Dawn »

Here's another way to control research speeds by galaxy size: implement an accross-the-board Beaurocracy cost (or Heavy Foot of Government cost, as MOO3 put it). HFOG/Beaurocracy would be related DIRECTLY to the size of your empire, perhaps through the simple formula of BASE HFOG (%)= # of planets controlled. e.g. if you control 33 planets, your BASE HFOG is equal to 33%.

HFOG would reduce yields accross the board, by an amount equal to its value; i.e. an HFOG rating of 20% would reduce production, agriculture, and RESEARCH yields by 20%. Small empires, therefore, would build and research things faster than large empires, making them more agile.

This scheme has 2 advantages: The early game would procede at much the same rate whether the player was in a small or Huge galaxy, and only later in the game would research significantly slow down for larger empires. Secondly, there are no complex maths or programming involved. All production on every planet would be reduced by the same amount. In the case of research, the mechanism is even simpler, because RP is put into a "pool" before being spread amoungst the various research projects, the programmers would simply have to reduce the RP pool by the value of HFOG.

After figuring out how difficult it is to program the local effects of HFOG versus the empire-wide effects, we could come up with technologies that would reduce its effects; either locally (individual planets who build a structure) or accross the entire empire. This would not upset the small-versus-large balance, as it would take large empires longer to research and build such technologies, and would still leave them with larger HFOG costs.

I think this idea kills two birds with one stone: it gives small empires a speed advantage over large empires, and makes research in small galaxies faster than research in large galaxies without having to create complex formulas for RP costs/production. What do you guys think?
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#30 Post by Geoff the Medio »

Black_Dawn wrote:...an HFOG rating of 20% would reduce production, agriculture, and RESEARCH yields by 20%.
This suggestion is good in that it reduces RP production, rather than increasing the RP per turn cost of techs. This eliminates an annoying and player-objectionable situation where the cost of individual techs can increase over time. RP production of an empire is always changing anyway, so the player won't find another modification to be so odd.

However the formula,

deduction% = #systems_in_empire

is too simple.

(I define "too simple" as simplicity to a degree that causes significant problems that could be corrected with a more complicated formula.)

A problem is that as you get more and more planets, the % incremental loss to production grows. ie. if I have 50 planets, adding one more loses me about 2% of my total production: (50% - 49%) / (50%) = 0.02 = 2%. If I have 90 planets though, adding one more loses me 10% of my total production: (10% - 9%) / (10%) = 0.01 = 10%. (both cases assume the new planet adds no additional production, which is a reasonable approximation for new a new colony).

This effectively establishes a hard limit of 99 planets in an empire, as at 100 planets, you produce nothing.

To me, a hard limit like this is not desirable.

Instead, I would suggest an smaller and smaller % of current production loss for each additional planet as the number of planets grows. There are various possibilities...

deduction% = 4*sqrt(#planets) is a bit better, as it ends up with about 90% deduction at 500 planets (the current max).

That said, the exact exponent (sqrt(x) = x^0.5) and constant out front could be changed by governments / tech / etc., as you sort of mentioned, potentially making the limit on empire size not quite so hard as I claim above...

However, such a system would also interfere with the implementation of more interesting and enjoyable sorts of HFOG systems. See the relevant thread:

viewtopic.php?t=974

Some of the systems proposed (inc. that by me) in that thread are much better for general HFOG penalty purposes, IMO.

Consequently, for this thread, and for the tech-progress with turn number issue specifically, I think we should have a specifically tailored adjustments for that purpose alone, that acts independently of HFOG-type penalties.

If we have only one adjustment for empire size for all sorts of production, while somewhat simpler, it becomes more difficult to balance things, since the one factor influences so many otherwise separate game systems. We'd have fewer independent factors to tweak, which would make adjusting one (eg. production) without screwing up the already ok otehr one (eg. research) almost impossible.
Small empires, therefore, would build and research things faster than large empires, making them more agile.
Please define "agile" and explain why it is desirable?
All production on every planet would be reduced by the same amount. In the case of research, the mechanism is even simpler, because RP is put into a "pool" before being spread amoungst the various research projects, the programmers would simply have to reduce the RP pool by the value of HFOG.
PP production will also be pooled empire-wide.

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