Victoria 3 - Dev Diary #68 - Patch 1.1 Changelog (part 4)

[GM16]

How about countries not being able to trade with nearby markets which are separated from them just by thin strips of land (i.e. Paraguay and Uruguay can't trade because of Missiones salient)? There's got to be overland trade routes and overland trade agreements between countries along the routes.

 

[lachek]

If the wiki is correct, the pricing function is the following:

price = Base_price*(1+0,75((buy-sell)/min(Buy,Sell)))

Now lets says you have a market E with Buy_E=200 and Sell_E=300 and a market I with Buy_I=200 and Sell_I=100, a base price of 1 and a trade route exporting t goods from from E to I. Then the price difference is:

PD = price_I-price_E = 0,75((200-100-t)/(min(100+t,200)-(100-300+t)/min(200+t,300))=0,75((100-t)/(100+t)-(-100+t)/(200+t)) if 0=<t=<100.
This is definitely not linear in t!
In fact even in a single market the price is not linear in the traded volume for example in I we have
P_I(t) = 1+0,75((100-t)/(100+t))=1+0.75(-1+200/(100+t)) for 0=<t=<100. This is a constant plus a convex function in t, as 1/t is clearly a strictly convex function (on the positive half-axis).

So either the wiki is wrong or the price function is strictly convex in the trade volume for at least some volumes. In the above example the function gets linear for t>100. The min in the function is responsible for it being non-linear.


Regarding the second paragraph. If the function was really linear then averaging post-and pre-trade prices would give you exactly the area underneath the price difference function. I.e. the profit function as in Profit = (PD_PostTrade+PD_PreTrade)/2*Volume would be the antiderivative of the price difference function. This implies via the fundamental theorem of calculus that the price difference function is the derivative of the profit function. In particular the profit function can only be maximal, if the price difference is equal to zero. Therefore, you would not have a price inversion problem. Granted you do not differentiate continuously, but in a discrete way and currently do not search exactly for the optimum. Therefore, the volume would probably slightly overshoot the zero price difference mark. But this is not related to the function being strictly convex or linear.

Edit: Fixed a typo in the formula.

I think the wiki is wrong. I'll just copy/paste pseudocode here:

MaxPriceVariability = BasePrice * PRICE_RANGE
MaximumDifferenceFactor = BUY_SELL_DIFF_AT_MAX_FACTOR - 1
BuySellDifferenceRatio = Min( ( Max( Buy, Sell ) / Min( Buy, Sell ) ) - 1, MaximumDifferenceFactor )
PriceAdjustment = MaxPriceVariability * ( BuySellDifferenceRatio / MaximumDifferenceFactor )
FinalPrice = ( Buy > Sell ) ? BasePrice + PriceAdjustment : BasePrice - PriceAdjustment

It is true this makes it a piecewise linear function, and when the price in one market crosses the base price threshold that might make it the curve appear concave? It is likely also true that this means doing a straight average between pre- and post-trade prices could result in the wrong average based on volume traded no matter what, and doing some calculus might be necessary to find the true value. As a first pass we're going to attempt to use post-trade only prices for trade, since this is most likely to be correct anyhow.

 

[RELee]

I think the wiki is wrong. I'll just copy/paste pseudocode here:

EDIT: Wait! Pseudocode?! That's like 10 times better than real code, right?

 

[Fantasy295]

Should they though? Significant tuition payments seem to be a post-WW2 development, and then mostly in the Anglosphere. German universities, for example, still remain almost free, with only administrative and public transit fees paid.

Thanks for the explanation, this is new knowledge for me, I thought universities had tuition all the time

 

[Tempscire]

I am trying to say, as you observed now as well, that the wiki formula might not be correct an you can fit a piecewise linear function that solve for the conditions talked about in this thread

I dont know why @lachek would say its linear if its clearly not, and since the formula originally comes from a reddit thread afaik, it might not be taken from the code but someone might have fitted it to observed prices.

cant access the wiki right now, but if the example is sourced by ingame data and not just putting in the respective numbers, then it just is not linear at all, yes.

Ah, alright. Now I understand the confusion.

You should remember that the price is a function of 2 variables, Buy and Sell orders, i.e. P(B,S). Now it is clear that there is a function which is pl in one of these variables that fulfills the following properties:
(i) P(x,x/2)=1,75
(ii)P(x,x)=1
(iii)P(x,2x)=0,25
for any given x.

If we constrain ourselves to functions with only 2 linear pieces as desired, then the resulting functions are unique, as two linear segments connected in one point are uniquely defined by three distinct points.

The (affine) pl function in S must be: 1+0,75(B-S)/B for S>B, as for B=S this is 1 and for S=2B this is 0,25. For B>S we also have 1+1,5(B-S)/B, as for S=B/2 we have 1+0,75B/2/B=1,75.

The (affine) pl function in B must be in the same way 1+1,5(B-S)/S for S>B, as this is 1 for B=S and 0,25 for B=S/2 and 1+0,75(B-S)/S for B>S, as for B=2S we have 1,75.

The problem now is the following: If you have a trade route from E to I, the buy orders in E and the sell orders in I increase with the volume of the route. Therefore, in order for the price difference function (i.e. the price in I minus the price in E) to be pl, one needs to either have a price function which is (affine) pl in both B and S or two different price functions, one (affine) pl in S and one (affine) pl in B for the markets I and E.

But a function satisfying (i) to (iii) can not be pl in B and S, as then the unique functions above would need to coincide and this is not the case, if one allows values other than B=S.

And if one uses two different functions one definitely runs into problems when a market has imports and exports at the same time and afaik all markets use the same price function.

Note that this argument does not exclude functions which are pl with more than 2 linear pieces between S/2=<B=<2S. But I am unsure whether such functions could be used, as it is not even clear where to cut. And I am positive that the argument can be extended to a far larger class of affine pl functions.

I think the wiki is wrong. I'll just copy/paste pseudocode here:

MaxPriceVariability = BasePrice * PRICE_RANGE
MaximumDifferenceFactor = BUY_SELL_DIFF_AT_MAX_FACTOR - 1
BuySellDifferenceRatio = Min( ( Max( Buy, Sell ) / Min( Buy, Sell ) ) - 1, MaximumDifferenceFactor )
PriceAdjustment = MaxPriceVariability * ( BuySellDifferenceRatio / MaximumDifferenceFactor )
FinalPrice = ( Buy > Sell ) ? BasePrice + PriceAdjustment : BasePrice - PriceAdjustment

It is true this makes it a piecewise linear function, and when the price in one market crosses the base price threshold that might make it the curve appear concave. It is likely also true that this means doing a straight average between pre- and post-trade prices could result in the wrong average based on volume traded no matter what, and doing some calculus might be necessary to find the true value. As a first pass we're going to attempt to use post-trade only prices for trade, since this is most likely to be correct anyhow.

I think this is the same formula as in the wiki:

Assume that the MaximumDifferenceFactor does not play a role in the min of BuySellDifferenceRatio, this is not the part I quoted from the wiki, this is just the cutting function and that BUY_SELL_DIFF_AT_MAX_FACTOR=2 .

First if B>S we have ( Max( Buy, Sell ) / Min( Buy, Sell ) ) - 1=B/S-1=(B-S)/S and PriceAdjustment =BP*PRICE_RANGE*(B-S)/S.
Therefore, FinalPrice =BP(1+PRICE_RANGE*(B-S)/S)=BP(1+PRICE_RANGE*(B-S)/min(B,S)).

And if S>B we have ( Max( Buy, Sell ) / Min( Buy, Sell ) ) - 1=S/B-1=(S-B)/B and PriceAdjustment =BP*PRICE_RANGE*(S-B)/S.
Therefore, FinalPrice =BP(1-PRICE_RANGE*(S-B)/S)=BP(1+PRICE_RANGE*(B-S)/min(B,S)).

Here B=Buy, S=Sell, BP=BasePrice. This seems exactly as in the wiki.

I think the real problem is that the price function can not be affine pl in both buy and sell orders, if it fulfills the desired properties (see above) and for the price difference to be affine pl one needs affine pl in both, as sell and buy orders grow in the respective markets. Therefore, the price difference would be non-pl even when the price is affine pl in one variable.

 

[SmokeyMcSubpoena]

Could you introduce a game rule to disable the Ripper, "they shall not have dyed in vain" and other silly events? Abraham Lincoln turning out to be Jack the Ripper may be funny to some, but for a lot of players it's incredibly immersion-breaking.

The dye event was jarring to me, but maybe it's my age. Both my wife and I are huge CK fans because of all the horrible jokes you can make, so it wasn't an issue of "oh they went too far", it was a "holy crap, did a 14 year old write this event? This is a game about the Victorian age from Paradox, not Tropico.". Tropico is ALL satire, that's the big difference. Some of them are fart jokes, others are puns, but the entire wonderful tone of that game is silly satire.

I assume that event was intentionally added to do a little market research about the player base...but the quality of the writing in this game is all over the place, and in general, it's leaning towards modern syntax more and more, which, to be fair, is an honestly debatable decision. There's a reason this game is drawing more new fans, and there's a reason why the second drew such rabid fans. It SOUNDED Victorian, to anyone who knows 19th cent lit.

 

[luanmameili]

​

- Fixed font atlas not notifying the map system when textures where recycled, leading to garbled map names especially frequent in Chinese, Japanese, and Korean languages

Acutually, such issue also exists in CK3 and Imperator:Rome.

 

[Sovetskysoyuz]

/edit: And for something on topic: No comment on the teleporting generals issue from the dev team (fixing the workaround without fixing the bug)? Or did I accidently skip it?

It’s been asked at least five times (including my question on the first page of this thread) and there have been no dev responses yet. I’m pretty concerned about this one; if the teleport workaround is patched out but the situations where it was needed to fix bugs or flawed mechanics remain, I’ll probably be skipping this patch as losing wars due to bugs or arbitrary restrictions is very frustrating.

(By ‘arbitrary restrictions’ I mean things like only being able to assign a single general to a naval invasion, even if it’s somewhere like Panama where you *know* it’ll create two fronts, and needing fifty days to send a second general after the invasion)

 

[durbal]

Spoiler

Ah, alright. Now I understand the confusion.

You should remember that the price is a function of 2 variables, Buy and Sell orders, i.e. P(B,S). Now it is clear that there is a function which is pl in one of these variables that fulfills the following properties:
(i) P(x,x/2)=1,75
(ii)P(x,x)=1
(iii)P(x,2x)=0,25
for any given x.

If we constrain ourselves to functions with only 2 linear pieces as desired, then the resulting functions are unique, as two linear segments connected in one point are uniquely defined by three distinct points.

The (affine) pl function in S must be: 1+0,75(B-S)/B for S>B, as for B=S this is 1 and for S=2B this is 0,25. For B>S we also have 1+1,5(B-S)/B, as for S=B/2 we have 1+0,75B/2/B=1,75.

The (affine) pl function in B must be in the same way 1+1,5(B-S)/S for S>B, as this is 1 for B=S and 0,25 for B=S/2 and 1+0,75(B-S)/S for B>A, as for B=2S we have 1,75.

The problem now is the following: If you have a trade route from E to I, the buy orders in E and the sell orders in I increase with the volume of the route. Therefore, in order for the price difference function (i.e. the price in I minus the price in E) to be pl, one needs to either have a price function which is (affine) pl in both B and S or two different price functions, one (affine) pl in S and one (affine) pl in B for the markets I and E.

But a function satisfying (i) to (iii) can not be pl in B and S, as then the unique functions above would need to coincide and this is not the case, if one allows values other than B=S.

And if one uses two different functions one definitely runs into problems when a market has imports and exports at the same time and afaik all markets use the same price function.

Note that this argument does not exclude functions which are pl with more than 2 linear pieces between S/2=<B=<2S. But I am unsure whether such functions could be used, as it is not even clear where to cut. And I am positive that the argument can be extended to a far larger class of affine pl functions.



I think this is the same formula as in the wiki:

Assume that the MaximumDifferenceFactor does not play a role in the min of BuySellDifferenceRatio, this is not the part I quoted from the wiki, this is just the cutting function and that BUY_SELL_DIFF_AT_MAX_FACTOR=2 .

First if B>S we have ( Max( Buy, Sell ) / Min( Buy, Sell ) ) - 1=B/S-1=(B-S)/S and PriceAdjustment =BP*PRICE_RANGE*(B-S)/S.
Therefore, FinalPrice =BP(1+PRICE_RANGE*(B-S)/S)=BP(1+PRICE_RANGE*(B-S)/min(B,S)).

And if S>B we have ( Max( Buy, Sell ) / Min( Buy, Sell ) ) - 1=S/B-1=(S-B)/B and PriceAdjustment =BP*PRICE_RANGE*(S-B)/S.
Therefore, FinalPrice =BP(1-PRICE_RANGE*(S-B)/S)=BP(1+PRICE_RANGE*(B-S)/min(B,S)).

Here B=Buy, S=Sell, BP=BasePrice. This seems exactly as in the wiki.

I think the real problem is that the price function can not be affine pl in both buy and sell orders, if it fulfills the desired properties (see above) and for the price difference to be affine pl one needs affine pl in both, as sell and buy orders grow in the respective markets. Therefore, the price difference would be non-pl even when the price is affine pl in one variable.

And the outcome of all of this and potential options to have trade not only be more profitable than simply using post-trade prices but also fix the price inversion problem are detailed again by @Tempscire here:

Are devs ignoring community concerns about Trade/GDP?

I am really disappointed in the focus of the new dev diary... It seems they are focusing on minor balance issues rather than low-hanging major fixes to the game... Will the devs implement the suggested fixes for trade/GDP? I am concerned these...

forum.paradoxplaza.com

Basically, you can have the best of both worlds: no price inversions and traders maximizing profit by using a mean value rather than simply post-trade prices. The problem is that the mean value you're using right now (arithmetic mean) is the wrong mean since the price function isn't linear.

All in all, I like the decision to use a mean value since it represents traders buying some goods at a low price and importing them to a market with a higher price piecemeal until eventually they reach the maximum to remain profitable rather than assuming the goods are all bought at the same price (more or less) as the final one -- we'd just need to use the correct mean though.

 

[Republic of Mercury]

The dye event was jarring to me, but maybe it's my age. Both my wife and I are huge CK fans because of all the horrible jokes you can make, so it wasn't an issue of "oh they went too far", it was a "holy crap, did a 14 year old write this event? This is a game about the Victorian age from Paradox, not Tropico.". Tropico is ALL satire, that's the big difference. Some of them are fart jokes, others are puns, but the entire wonderful tone of that game is silly satire.

I assume that event was intentionally added to do a little market research about the player base...but the quality of the writing in this game is all over the place, and in general, it's leaning towards modern syntax more and more, which, to be fair, is an honestly debatable decision. There's a reason this game is drawing more new fans, and there's a reason why the second drew such rabid fans. It SOUNDED Victorian, to anyone who knows 19th cent lit.

I think the dye event was copied from Victoria 2.

 

[SmokeyMcSubpoena]

I think the dye event was copied from Victoria 2.

That's even an weirder decision on their part if that's the case, because they should've also copied the good events.....

I haven't played that one enough to get it, but it would be a little less lonely there, cause "oh great" when the chartist rallies show up isn't exactly mature either...but it's not a bad pun...

If it's in 2, shame on them still, but 2 also has a totally different overall tone. There are no other events in 3 where both choices ridicule the subject matter of the event to the point of having a different tone, imo....

_____________

PS: yea, wild. Just fired it up, event 12710 or something like that. A thoroughly weird choice to spend the time copypasting that one, instead of literally any of the actual historical popups, with less like....slapstick humor. Same conceptual criticism applies for 2 then, but that's about as useful as cussing out a grave.

Thanks a bunch for pointing that out though!

 

[Less2]

- Fixed a bug where making a general return to a previous location during travel would sometimes apply

If the front management AI isn't very significantly improves then this will probably kill all interest in the game for me. It's THAT bad. If teleporting generals is too gamey then at least knock general travel time down by -75%, or give some kind of grace period to re-assign generals within a week after any instance where the fronts change, or something.

 

[grommile]

It SOUNDED Victorian, to anyone who knows 19th cent lit.

The grammar of Victoria 2's narrative events was not nearly so floridly, nay, voluptuously verbose as one might expect of material referencing that strange and fearsome period when – lest we forget, dear reader – the likes of Bulwer-Lytton pushed the very limits of sentence construction far beyond what any person might reasonably expect the English language, flexible and versatile though it assuredly is, to endure without some manner of protest.

(The sentence I have written above should be taken out and shot.)

(Also, whenever people complain about Vicky 3 content, I remind myself that Howard Philips Lovecraft's "At The Mountains of Madness" has a finite chance of being a fictionalized account of historical events on the counter-Earth of your Vicky 2 campaign.)

 

[TripleAgent]

Love most of the patch notes except the "fix" for the general movement glitch. Normally I'd be fine with this fix, but this bug has inadvertently become one of the only ways we can effectively play with the broken war/fronts system. Lol we're probably going to need someone to make a mod to bring back a bug until 1.2.

 

[Searry]

So you fix teleports but you don't fix the front system where generals are sent home when it doesn't make sense?

 

[Soranya]

Yeah, they pay for good and services just like everyone else, not through the university. Public transit (at a discount) is often handled through the university though (or more precisely, through the student associations, but the university takes in the money along with admin fees), but not everywhere, and only for travel locally near the university. Some Länder don't do this and students have to buy normal, non-discounted public transit ticket if they need them.

Good thing the 49 Euro ticket is coming - soon - possible - or not - federalism sometimes is not that funny...
Which leads us back to V3 -> more federalist mechanics would be intersting for politics.

 

[franz612]

It would be lovely to have the state that produce raw material having an edge on producing industrial good, e.g. states with coal and iron should produce cheaper steel since the shipping cost is minimised.
The current system didnt simulate the comparative advantage of different states, the productivity is the same among all states as long as you have 100% market access. It does not make sense that two steel mills produce goods at the same price when a steel mill can get raw material next door and the other one needs to transport coal and iron from far away. And for miltary as well, the further your army had been sent from its HQ, more costly it should be. After all logistic and distance should have a bigger impact in game. I wont expect this to be fixed soon but would love to see this feature implemented.

 

[SmokeyMcSubpoena]

The grammar of Victoria 2's narrative events was not nearly so floridly, nay, voluptuously verbose as one might expect of material referencing that strange and fearsome period....
_____________

(The sentence I have written above should be taken out and shot.)

Both of those can be true at the same time rofl, but like, I dunno, something something fearful symmetry....(+50 years, I don't like Romantic poetry and I THINK the Tyger was about factories maybe lol)

although hat's off to that sentence, I had a beef with a prof 10 years ago who told me I wasn't allowed to use stream of consciousness in his class because I wasn't famous enough, so I made grading every one of my papers a living hell for that man

Still, clinically (imo) modern syntax and verbiage in history games aren't a great thing. Vic 2 wasn't blameless either.

 

[Soranya]

As a first pass we're going to attempt to use post-trade only prices for trade, since this is most likely to be correct anyhow.

Yes plz and thy!
Keep us posted on the results!

 

[grommile]

I dunno, something something fearful symmetry....

"The Tyger" is (a) poetry, not prose (b) while certainly not laconic, still quite economical with its use of words (c) from the 18th century