Tech buying - some details

[vulture]

Since I've just worked out some tech pricing info for the democracy game, I thought I'd post a summary of the info here; I couldn't find the info in the archives, so possibly some of it is new.

Firstly, how the cost of researching a tech varies with the number of civs you know who have that tech. If no-one else has the tech, you have to pay the full price in beakers to research the tech. If everyone one the planet has the tech, and you have contact with the, the research cost is halved. In between, the cost varies linearly with the number of civs you know who have the tech.

N is the number of AI civs in a game
M is the number of civs you have contact with that have a certain tech
C is the base cost of the tech (as worked out from the editor info and world size)
A is the adjusted cost - the actual number of beakers you need to research the tech

A = C * (1 - M / (2 * N))

The formula isn't exact, although it's fairly close. So, in an eight civ game (7 AI civs), each civ you know that has the tech knocks about 7% off the research cost for that tech.

Next, the cost of buying a tech from an AI civ. The basic cost in gold is 3/4 of the cost in beakers (yup, it's cheaper to buy than research). The exception is if only one civ you have contact with has the tech. In that case the swine will exploit its monopoly and charge twice as much (1.5 times the beaker cost of the tech). So if buying a tech that only one civ has will cost you 1000 gold, waiting until a second civ has it will drop the cost by more than a factor of two to something like 429 gold in an 8 civ game. So don't be in a hurry to buy techs.

Thirdly, what happens when you are taking 40 turns to research a tech? The cost of buying the tech depends on how many beakers you have left to research, not on how many turns. So say you set science to zero, and one citizen to be a scientist. You produce 1 beaker per turn. Assume the tech you are researching costs 600 beakers. You will of course research it in 40 turns (unless you've modded the number). After 30 turns of research, you have amassed 30 beakers. The cost to buy it from the AI will be the cost of 570 beakers - pretty much the full cost - and not 25% of the full cost (which you might have thought, given that you are 75% of the way to getting the tech).

This is the danger of using the 1 scientist trick to get a tech in 40 turns. If you suddenly need to get the tech in a hurry (due to needing to change building a wonder, or for some other reason) then you may find that you have to throw away a lot of money to get a tech that you would have finished researching in 3 turns anyway...

Some of this is pretty obvious I know, but other people seemed to think that something different was pretty obvious, so I did a few tests to see what was going on, and these were the results.


NOTE: I've only checked this under a limited range of conditions for ancient era techs. There is no guarantee that things work similarly in later eras, although no reason why they should be different.

[Ekanata]

Is this also apply to AI ? I mean, if player sold a tech to AI, will the same rule apply ? And how does difficulty level effects tech price ? (both to player and AI)

[alexman]

Vulture, great job, thanks!
As far as I know, nobody has done tests like this after 1.29f came out.

(Until 1.21f it worked the same way except that A = C * (1 - M / N), and the only civ to know a tech did not get the double price bonus).

Ekanata, I believe this is how it works: the same rules apply to the AI, with one catch: they modify your money by their production bonus (or penalty at lower levels). So if you're playing on Monarch, 10 of your gold are only worth 9 gold to them. As a result, they give you less for a tech than you would have to give them if they bought it from you.

[Ekanata]

When I'm leading tech-wise, I want to keep it while at the same time maximizing the gold I could get from selling tech. To achive it, I would wait until one civ almost finished its research before I sell the same tech to everyone else.
For example, I already discover Engineering (cost about 600 beaker), while Rome is still researching it. When it almost finished its research, I would sell engineering to everyone else, making Rome 'over-researching' engineering.

Unfortunately, I found it difficult to keep track the moment someone about to finish its research. Using the above example, when everytime I 'probe' Rome's research progress, I found that my engineering value is dropping about 30 gold every turn. When the value reach about 4 times of its drop rate, I thought I could sell engineering on next turn to maintain my tech-lead. Unfortunately, on the next turn Rome would already finished its research and therefore dropping market value of engineering. And its always happened with every tech and civ. I found it unlikely that an AI would temporarily raise its research capability (more road, budget, or pop) every time its about to discover something.

Therefore, I suspect that the tech price dropping at slower rate than resarch progress, which explain why Rome would still pay a lot although continuing research proved to be more effective. And I'm sure it's not about the 1 scientist trick, because the research is done in around 10 turn by Rome.

[planetfall]

How is the pricing adjusted by the opinion of the AI civ?

Is the pricing adjusted by your "score" in the game? Is pricing fixed or does a tech cost more if you are leading and less if you are in last place?

[Theseus]

I don;t know about the effect of opinion on pricing... I think it may have more to do with willingness to trade.

The price of a tech declines proportionately to the number of known civs that know the tech. So yes, tech is cheaper to research or buy if you are last (and know all the civs that know it).

It's actually a brilliant mechanism for gameplay balance, and is a fairly good approximator of RL tech diffusion.

[jshelr]

You can see from the formula why this structure is a very powerful incentive to beeline along some branch where you can sell a "new" tech to AI civs for enough to buy bunches of "old" techs.

Is it my imagination (likely) or is it true that the AI will panic sometimes when you suddenly appear ahead of them with a key military tech and pay huge amounts. Does one standard formula always apply to both music theory and tanks??

[alexman]

I think so. Music Theory is not very expensive. The AI doesn't research it early because it's optional, but they pay for it according to the formula if you offer to sell it to them.

[XOR]

But sometimes, in the same turn, some Civs will give me a higher price and some a smaller price.

[vulture]

Originally posted by XOR
But sometimes, in the same turn, some Civs will give me a higher price and some a smaller price.

There is an attitude effect somewhere as well, although I haven't looked at how that worked. In my tests I was buying writing of the AI, with prices in the 100-200 gold range. The strongest depenedence was on the number of civs who knew the tech. But the polite civs all offered me slightly better deals than the annoyed ones (by 2 gold, in ever circumstance of this test). I imagine the spread between the extremes of attitude it quite a lot more, and obviously the difference increases as base the cost of the tech goes up.

There may be other factors at work as well, but I haven't looked at that at all.

[vulture]

My current game has thrown up a few interesting ideas about the tech pricing system. I am on a small island with Persia (I'm playing the Romans for the first time since my first ever game). Just when I was building warriors to upgrade to legions for the great legions vs immortals clash, I discovered that there was asbolutely no iron anywhere on our island. But that's not the point...

Having come off better in three wars against the Persians, I'm finding it devilishly hard to beat techs out of Xerxes. Maybe it's because this is my first game on emperor, and the AI is that much more reluctant to give you anything. But I suspect that it's the double-price due to being the only source of the tech thing. Since the AI seems to value peace at a certain number of gold (which can be made up of techs or luxuries of course), the fact that Persia is my only contact means that the prices are doubled and the number of techs I can get for peace is essentially halved. So my best bet is to wait to make contact with another civ before making peace with Persia, to double the tech benefit I can get.

Another issue is that of course I don't want to eliminate Persia entirely, since this would just create a monopoly for the next civ I meet (although hopefully they'll have some contacts to sell me as well). Keeping Persia alive, even if the other civ never meets them, improves my trading position by a factor of 2. And *then* I can finish my revenge on the evil Persians.

On a side note, I've gone from having no leaders for the whole of AU 105, and now I've had two from successive combats, and in the first 10 elite combats of the game. Randomness isn't fair.

[jshelr]

I agree that it "feels" harder to beat techs out of the AI at the higher level. You "seem" to have to do more damage, take more cities, really put the civ in danger of being taken out on Emperor. Curiously, however, lots of things you think are true about this game turn out to be a reflection of the difficulties encountered during recent games rather than unbiased info. On Deity, I'm still at the stage where the AI is doing the damage and threatening to take my civ out. So, I wouldn't know about beating techs out of them at that level. Vulture's idea that it was due to lack of contact might be right and is certainly interesting and differernces in tech valuation between levels might explain the whole thing.

[Hurricane]

Great thread, Vulture!

I was really surprised to see your claim that a tech will only devaluate to 50% of its original cost. On a 8 civ map, the last civ would only pay 1/8 of the beaker cost, but now you mean they pay 1/2 the beaker cost, right? This explains why the small civs have a much harder time keeping up with the tech pace.

Also, I have also the noticed the "double price for 1st tech". Since the AI always will buy a tech if it can afford it, it has the result that the first civ to buy the new tech will bleed themselves to bankruptcy. I have seen it very well in my current 16 civ huge map game, where the 4 largest AI civs alternate between having the tech and money lead. For example:

A) The greeks discover Nationalism, sells it to outrageous price to Persians. Persians are soon broke, Greeks are wealthy.
B) Romans discover Steam Engine. The wealthy Greeks buy it, but since their 20 turn deal with the Persians soon ends, they end up being forced to put everything on texes. The Romans no have the tech lead until the Persians discover their next tech, sell it to the Romans, and start this all over again.