Corporation costs, an in depth analysis!

[NaZdReG]

even with solver's patch I don't think they are overpowered. eventually you are paying large gpt.. my last game it was a net loss of 500gpt so I had to reduce the slider to keep up.


what it does is gives a cottage econ a way to leverage that money into production without just paying to rush things.


also I noticed in my game the ai switched to state property to avoid having to pay for my corporations effects in their cities.

unclejj's point is also valid.. while it helped me race to a dom victory the setup time was quite an effect. by the time I was fully ready the ai was almost at tech pairity. but it helped me hit critical mass and put my civ to a production point the ai could not match.

however since you cant have mining inc and creative constructions they are able to match your production benefits if the ai goes in that direction.

NaZ

 

[madscientist]

If I am not mistaken, you can have both mining Inc and creative inc, just not in the same city. Build both but spread only one into your cities, paying maintenance for the headquarters without Wall street is worth keeping it from the AI.

 

[Primogenitor]

Personally, I think corporations are good, but only for large civs. More cities means more benefit from every resource, and more cities means more land which means you have more resources in the first place. Its an exponential feedback cycle which just runs away with itself.

However, if I am going for a corporation game, I tend to try to found religions at the very start. Then that means Wall Street applies to both the religion and the corporation HQ, which helps.

 

[frob2900]

Its an exponential feedback cycle which just runs away with itself.

It's not exponential. The benefits (and costs) are roughly quadratic with the number of cities you have.

Back-of-the envelope-calculation:
(assuming a corporation consuming only one resource type, but the calculations can easily be modified to take several resources into account)

Total empire area, A = n S, where n=number of cities, S=average number of tiles uniquely covered by a city
Total resources, R = A D, where D=density of a given resource on the map
Total Benefit, B = n R b, where b is some conversion factor (e.g. 0.5 food per resource for Sids Sushi)

Therefore B=n R b = n A D b = n^2 S D b

B=n^2 S D b

So the total benefit scales roughly as n^2, where n is the number of cities. The multiplicative constants are the resource density, average city tile coverage (generally about the same as a BFC, taking into account overlap) and the resource-benefit conversion factor b.

Of course, this can be boosted by trading, but nevertheless, the amount of resources you have available for trade are also dependant on your empire area, so the general n^2 dependance still holds.

 

[r_rolo1]

^^ This means that there is a point where further expansion of corp in our lands will start to pay less compared with the maintenance ( this also aplies to Solvers patch ). Any idea how to calculate it?

 

[frob2900]

^^ This means that there is a point where further expansion of corp in our lands will start to pay less compared with the maintenance ( this also aplies to Solvers patch ).

As far as I see, it doesn't mean that.

Writing:
A=n*S (where n,S are as above)
R=A*D (as above)
B=m*R*b (R, b as above, m=number of cities running the corporation)
so B=m*b*n*S*D

C=m*(f + R)*j - I*m
Here j=corp. maintenance multiplier due to e.g. inflation (so j=1 with solvers patch)
f=is a base cost (see the OP), which is 7 if all your cities are size > 20, but in practice roughly around 6-6.5, though
R=number of resources consumed, as above
I=income per city with corp if you have corporate HQ, i.e. 0 if you dont, 5*(gold multiplier%) if you do. If you have all buildings in your H.Q. city then I=15)

So taking the benefit/cost ratio (assuming the resources the corporation produce are as valuable as gold per unit, so e.g. 1=1 for Sids Sushi etc.) you find:

B/C = (m*b*n*S*D)/(m*(f+R)*j-I*m) = b*n*S*D/(j*(f+n*D*S)-I)

so that the number of cities running the corporation vanishes from the expression. The total number of cities in general, however, still factors in, but both in the numerator and the denominator.

Obviously, taking the above ratio is based on assuming that it does cost you to expand to each city. Obviously, if you have zero resources of a given type and wall street in your HQ city, then you will (with solvers patch) be earning money for each expansion, so the above ratio becomes negative and thus useless. (For such situations it may be more beneficial to take the difference B-C).

 

[r_rolo1]

^^ So with B/C = n*Y ( Y= b*S*D/(j*(f+R)-I) a assumed constant), this means that bigger empires have bigger ratios.... Shouldn't we put normal maintenance in here ( you can't use SP and corps at the same time and even SP is maintenance free )?

 

[NaZdReG]

...wow beancounters

for the rest of us I have to sum it up like this.. the more territory I took over the stronger my production cities got which meant faster military production which equals more territory etc.

from the moment I founded the corp my power rating skyrocketed until I owned the entire continent.. then it was very straightforward to end it.

NaZ

 

[frob2900]

^^ So with B/C = n*Y ( Y= b*S*D/(j*(f+R)-I) a assumed constant), this means that bigger empires have bigger ratios.... Shouldn't we put normal maintenance in here ( you can't use SP and corps at the same time and even SP is maintenance free )?

Sorry, I was unclear (I just edited my post), but R is also a function of the number of cities n, since R=A*D=n*S*D, so y is not a constant.

As n goes to infinity (assuming a very, very large map, with huge amounts of resources) then B/C=b/j, which is just the resource->benefit conversion factor divided by the inflation factor. (of course, b is rather small on such a large map)

...wow beancounters

for the rest of us I have to sum it up like this.. the more territory I took over the stronger my production cities got which meant faster military production which equals more territory etc.

from the moment I founded the corp my power rating skyrocketed until I owned the entire continent.. then it was very straightforward to end it.
NaZ

Yup. But the point is that your corporation based production bonus goes roughly as your number of cities squared, and not exponentially, which is a completely different kind of growth.

 

[Sisiutil]

...wow beancounters

As ye sow, so shall ye reap...

 

[r_rolo1]

^^Ok, overlooked the n dependancy of R. But I wanted to expose my personal belief that with a assimptoic aproach of B/C to b/j , when you factor the non corp maitenance of the cities necessary, there is a maximum of corp eficiency versus number of cities of empire ( you can't have maintenance free cities in civ and AFAIK the maitenance formula is something like M = z*e^(w*n ) with e being the Napier number and z and w unspecified constants and quadratic / exponential always has a maximum ( may not have relevance in our context, like if it exists with n<0)

 

[Validator]

even with solver's patch I don't think they are overpowered. eventually you are paying large gpt.. my last game it was a net loss of 500gpt so I had to reduce the slider to keep up.

from the moment I founded the corp my power rating skyrocketed until I owned the entire continent.. then it was very straightforward to end it.

Is it just me or are these two statements somewhat contradictory?


Running a large deficit isn't in itself an indication that corporations are costly to your empire. You have to consider how many you're getting for that gold. If you were getting 1000 for 500 I think most people would say you were getting quite a bargain.

This failure to take into account the value of the , , etc. that you get from the corporation is the main flaw I see in UncleJJ's analysis of the corporation issue. Once the items you get from the corporation are added to the equation corps become profitable even without using Solver's patch. When the inflation cost is removed from the equation they just become overpowered.

 

[popejubal]

Yup. But the point is that your corporation based production bonus goes roughly as your number of cities squared, and not exponentially, which is a completely different kind of growth.

It is certainly true that the production bonus goes up in proportion to the number of cities squared, but that production bonus can be used to increase the number of cities.

Given that my empire has X number of cities in it today, if I can take over Y number of cities in N turns with the resources I have now, I will be able to take over (X + Y)/X cities after I have assimilated those cities into my empire. As my empire continues to grow (even leaving out corporations), I will accelerate my rate of conquest. When my rate of growth is based on my current size, that's when you see an exponential growth.

The fact that the corporations increase your rate of conquest by the square of your size just makes it even more exponential-er.


If anyone here is wondering why we can't just automatically win every game of Civ if our empires are all growing exponentially, remember that the AI civs are also growing exponentially. That's why you need to grow more exponentially-er.

(Someday my grammar will be more gooder, but until then, I'll make do with the words that I gots.)

 

[frob2900]

The fact that the corporations increase your rate of conquest by the square of your size just makes it even more exponential-er.

Yup. That's exactly true. Assuming that conquering a city roughly takes a fixed number of (of course, this isn't true, since like you said, the AI is also growing), then the rate of conquest (i.e. the rate at which new cities are added) is:

dn/dt = (a*n+b*n^2)/w
Here "a" is the average number of non-corporation hammers per city, "b" is the corporate production benefit from above, "n" is the number of cities and "w" is some average hammer cost for conquering one city.
The time scale is some average number of turns between each conquest.

The solutions to this differential equation completely blow up due to the n^2 term. Here's a comparison of two growth rates, one with corporations (assuming the production and food benefits of the corporation are as large as a sizeable fraction of those from the city tiles + specialists..which is unrealistic, but even changing this, the general shapes hold), one without:

Red line is with corporations (tangent-like growth, the line becomes totally vertical at some point)
Green line is without (exponential growth)
The horizontal axis is some average time between each city conquered.
The vertical axis is number of cities acquired since the hypothetical "borg-like" war where you conquer an enemy city, put Mining Inc. and Sids Sushi in it, put in a factory+barracks and then start pumping out armies to get further cities .

Of course, at some point you hit the ceiling and get a a conquest victory!


The graph assumes that the AI is a complete pushover and is not increasing his production power at the same scale as the player. With actual AI resistance the graphs will, of course not blow up like that

 

[NaZdReG]

well.. yeah corporations are very powerful. but they do use up a great person.. so you have to compare that to the great person's strengths and difficulty in obtaining. mining inc and creative constructions both require an engineer.. and while you get a merchant on your way to sid's sushi you don't get a free engineer so its more difficult.

compared to rush buying it is more powerful but requires quite a lot of investment in both hammers and time to spread the corporation.

I failed to mention that one of the AI on the other continent had founded mining inc and had spread it to all of his cities. but being a vassal it was too late for him to catch up to my power rating.

of cource you could end up resource screwed limiting its effects.. but the more you expand the more effect it has.

however since the AI doesn't reliably cottage spam.. you'll be in a downward spiral of econ.. that is until you get courthouses and econ buildings up to speed in those new cities.

I think if they impliment solver's patch then they might want to reduce the hammer conversion to something like sid's sushi where it is 1/2 food per resource.. effectively cutting the effects of the corporation in half.. or something like .75 to make it fair and balanced.

of cource the other tradeoff is the innability to run state property.. but now state property is a fixed 10% increase in production in all of your cities... not quite as powerful as running mining or CC but still able to compete a bit.

where I found CC to be somewhat potentially broken is combining it with aluminum inc. if you have 3 resources of coal then each city with it has access to 3 sets of aluminum.. which is a CC resource. and yes it does count to increasing the production effects.

even still.. the ai is capable of founding the corporations themselves and spreading them to you.. putting you in a reverse situation where you MUST attack them or suffer dire consequences to your econ. (or switch to mercantilism or state property)

@sisutil LOL
@frob if you look at the screenshot of my power graph it matches your curve pretty good considering. it started a small snowball at my capitol and just grew from there. each opponent fell quicker than the one before it. definately great for dom victories

but if you are going for space race.. then std ethanol might be better because research is what slows you down.. so you lose out on extra food.. hmm. extra production is useful regardless though.

sorry for it being a bit of a ramble but thanks for contributions, keep the thread alive it will be of strategic use to everyone

NaZ

 

[frob2900]

@frob if you look at the screenshot of my power graph it matches your curve pretty good considering. it started a small snowball at my capitol and just grew from there. each opponent fell quicker than the one before it. definately great for dom victories

And that was with deploying the corporation immediately upon conquest and then spamming troops? I so, yes, it does seem like the snowball effect works, although it would be interesting to compare with a game where someone is attempting to snowball without corporations.

The quadratic dependance of the corporation + boost also relies on the assumption that you are conquering more and more resources as you go along (roughly an average amount per city conquered, which of course isn't exactly true if you are conquering a bunch of jungle/grasslands and running Mining Inc. or an inland region while running Sid's Sushi).

The production growth prediction for a corporate warmonger is extremely dramatic, even compared to the standard exponential one (for a classical "Land is Power" strategy), so it would be interesting to see if this does indeed happen in games. If so, then corporation spam warmongering could be a very powerful strategy, given a roughly homogeneous distribution of resources on the map (of course, one needs to keep an eye on spending at the same time, unless running Solver's patch )

 

[NaZdReG]

I had set 2 of my lowest production cities to producing executives. sid's sushi was spread in advance of my DOW.. and creative constructions had 3 executives in my war stack. new cities were brought under corporate control before they came out of revolt.

their first build if they didnt have 1 was a courthouse then granary to start recuperating pop.

the effect magnified yes because of increased resources. also dilligent trades with the AI on the other continent while I was busy smacking everyone around.. little did they realize they were next.

and about costs.. I was forced to reduce my slider to 40% at one point until my new piles of workers got farms paved over with cottages under emancepation. I did take a hit to my econ but it was worth it.

one thing that made it easier was spreading sid's sushi to the other continent. at first I profited but it forced the ai to head for communism to run state property. the moment they turned the corp off they were willing to trade me surplus metals and fish which magnified the power as well.

trading for the resources also lets you fine tune how much you want to pay to have the corporation running. if it gets a little too much just cancel older deals for those resources and it can sometimes knock 100gpt or more off your costs

NaZ

 

[Indiansmoke]

I play without solver's patch, and I think that corporations are good the way they are. If the next official patch will lower the upkeep, corporations will be overpowered.

I fully agree, there are plenty of ways to use corporations at the momment, they are far from broken.

 

[Pikkis]

I noticed that your attachment shows Supermarket giving +20% gold. Only Mall gives that benefit. So "Add Supermarket = 16 GPT" should be removed, and UB comment should be add 10-20%, not 10-15%, if corporation payments follow the normal way.

 

[NaZdReG]

I had meant the american UB when I put that up. there was a note below it about america, mali, english UB's effects. sorry I should have made that clearer.

NaZ