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

[veryalien]

If they are in the same market you don't need trade routes. Britain and Australia are.

You still need convoys for market access.

 

[doubleskulls]

Are there any current ideas for changes to supply chain logistics in buildings based on distance from their inputs? It feels really weird to have something like iron mined in Australia to be just as efficient for a factory in Britain to use rather than iron mined either in the same province or nearby.

I think they are looking at giving a bonus for inputs from the same state.

 

[mork77]

- The Ripper can no longer be a child or toddler

 

[Soranya]

You still need convoys for market access.

In negliable numebrs and not scaling with the transported goods/orders.

 

[Richard Dolder]

In negliable numebrs and not scaling with the transported goods/orders.

It is weird that convoys aren't serving as "sea infrastructure" even if the ocean is treated as "one province".

(Likewise what happened to capping railways at the level of raillines connected to the market capital? It seems a really easy and communicatable thing that a big rail line 50 over needs a long supply chain.)

 

[Tempscire]

I've set up a game and a desmos project to clear up this confusion.

Thank you for the additional visualization. There is already a Desmos project by @Ekcrbe in another thread which can be accessed. At least from my perspective there really is no confusion here. I only was unsure whether the wiki formulas were correct or not. But @lachek fortunately cleared this up. I think I understand the results with the wiki formulas quite well. At least well enough to solve the integral, which takes a long time to compute, by hand and not only for one trade route but also for an arbitrary number of trade routes between an arbitrary number of markets.

(Have to use dots because integrals take a long time to compute).

Maybe you could solve the integral analytically (either by hand or with something like mathematica) and plot the resulting function directly.

I guess the root of the problem is the way trade routes expand - way beyond maximum trade route profit. This would not be solved by using "true profit" since it's pretty close to the current formula. The new formula seriously underestimates trade route profits, but will make routes converge more realistically, i.e. before price inverse point

I would not say that this is the root of the problem. But it is definitely part of it. This is exactly what happens when you take the discrete derivative in the way it is currently implemented.

A good overview is the following:
Currently there are two problems:
(I) The point of maximum profit is at a point of price inversion. In your example it is something like 400 while the price difference is 0 at approximately 320. The numbers are a bit hard to guess from the attached screenshot. But if you provide your pre-trade buy and sell orders, I can give you the exact numbers.
(II) The profit optimization algorithm is not exact. It overshoots the point of maximum profit. In your case this is 480.


If you just fix the optimization, (I) will remain the same but you will get exactly this value. You will still be at point of price inversion though. Also note that this is non-trivial to do when multiple trade routes are involved. Although you could use a slightly modified version of the optimization algorithm I posted for post-trade prices.


If you just calculate the accumulated ("true") profit correctly, point (I) will be fixed. The point of maximum profitability will be exactly at the point where the final price difference is zero (assuming no costs). You can clearly see this in your project. It is also guaranteed by a mathematical theorem. So it cannot get any better in terms of protection. The assumptions for the fundamental theorem of calculus are clear in your very easy example with just one trade route. With arbitrary many trade routes you have to be more careful. But if you are smart about the ordering of trade routes, everything works out fine. If you account for costs, the maximum will be exactly where the final price difference is equal to the costs, i.e. there is no marginal profit to be made. In your screenshot this seems to be approximately 320.
But we are both correct insofar as (II) will remain a problem. The current optimization will not be able to exactly find this point in (I) and might overshoot. My point was that this is the only thing that can go wrong as explained in the post you quoted. In your example this will probably be somewhere between 330 and 405. Note that this is very difficult to estimate, as it depends very closely on the discretization. Therefore, the large range given. In order to give you the exact number for your example, I would need the exact market condition pre-trade and the size of your level 8 and 9 trade routes.

The good thing though is that in the case of the accumulated profit the condition for maximum profitability is very easy to state. In fact we already know where it is maximal by the fundamental theorem of calculus. Therefore, it is easy to just replace the current imprecise optimization by a correct one. You just need to check how final price difference relates to cost. Two values which are already easily available in the current economic system. Therefore, one can also fix (II) with very little additional work and get a system where price inversions are impossible. This is the reason why I always proposed to also change optimization, if one uses the integral calculation. In this case (II) is really the minor problem of the two, as the integral calculation for multiple trade routes is a lot more difficult than the optimization.


If you for some reason want to keep the current imprecise optimization algorithm, you need a more robust profit formula. In fact one can show that it is necessary to have a formula which fulfills the property that the profit is smaller or equal to zero at any point of price inversion. Using post-trade prices is obviously one option. But in fact there is a class of infinitely many functions which give you more profit than post-trade prices but still fulfill this property. Suitable for application in Vic3 are the weighted harmonic means of pre- and post-trade price differences of a given trade route. These have the advantage that they are easy to implement, as you just have to change the profit formula. They protect from price inversions but still give quite a bit more revenue and a higher amount of traded goods than just post-trade prices. Therefore, they are a good candidates, if post-trade prices are insufficient but one does not want to implement something as complicated as the integral solution.

 

[NickiQQ]

- AI acceptance for white peace now increases over time the longer a war goes on
Am playing as indian and was so close to get the very hard at achievement, at start i use the FRE as a backer.
But now i have a war whit the USA for 2 states, and the FRE has some of the state ind the war. so they get % tik = white peace :`(
dont know why, they dont have any states taken from them


old pic.

 

[Jackadsa]

The pricing function is linear, ranging from 0.25 to 1.75 of base price and reaching those bounds when sell / buy is 2:1 and 1:2 vice versa and progressing linearly based on the ratio between buy and sell orders in between. Not sure where the claim to a concave pricing function is coming from, this is pretty well outlined in both tooltips and the defines file (the PRICE_RANGE and BUY_SELL_DIFF_AT_MAX_FACTOR defines in particular).

This is incorrect, the pricing function is not linear.

ratio = (buy - sell)/min(buy,sell), clipped between -1 and +1.
Market Price = base * (1 + 0.75 * ratio)

Because buy, sell are in the denominator of that ratio, the price function is not linear, it is curved in buy and sell orders (yes it is linear in the ratio, but the fact that it is ratio makes it non linear in the things inside the ratio). The `correct' average which would model the process of traders buying incrementally causing a gradual price movement from x -> y is obtained by performing an integral of this function, and it is not an arithmetic mean of x and y because of the non-linearity. It is a piecewise function that contains linear and logarithmic terms. It is not an arithmetic mean, but it is something that could easily be coded and efficiently calculated if desired. I am happy to provide the maths, though it was also in the threads that @durbal linked. If the price function used the 'correct' average, then a trade from an expensive market to a cheap one could never be maximally profitable if only two countries are involved (on the other hand, most of the issues in the past were coming when lots of countries were in involved in the trading rather than when there were only two participants, and in that case my feeling is that the only pricing based solution is to use market price, see my post after this one). The arithmetic mean allows for trades from an expensive to a cheap market to be maximally profitable, it is a pure mathematical fact that can be proven (and has been proven in these other threads) just from the pricing function, regardless of what other changes have been made to the way that routes grow and shrink. It also allows the mathematical possibility of profitable circular trades, even though the situation has otherwise been apparently resolved in a different way in the trade growth/shrinking mechanics.

Edit: I should have replied to @lachek instead.

Edit2: Sorry, I just caught up with the thread and saw this was already discussed by @Tempscire

While I'm here, I just want to plug the side suggestion that I think max would make a lot more sense in that function than min, and probably give better gameplay results. It would be great if these things were modable.

 

[Jackadsa]

Thank you for the additional visualization. There is already a Desmos project by @Ekcrbe in another thread which can be accessed. At least from my perspective there really is no confusion here. I only was unsure whether the wiki formulas were correct or not. But @lachek fortunately cleared this up. I think I understand the results with the wiki formulas quite well. At least well enough to solve the integral, which takes a long time to compute, by hand and not only for one trade route but also for an arbitrary number of trade routes between an arbitrary number of markets.

Maybe you could solve the integral analytically (either by hand or with something like mathematica) and plot the resulting function directly.

I would not say that this is the root of the problem. But it is definitely part of it. This is exactly what happens when you take the discrete derivative in the way it is currently implemented.

A good overview is the following:
Currently there are two problems:
(I) The point of maximum profit is at a point of price inversion. In your example it is something like 400 while the price difference is 0 at approximately 320. The numbers are a bit hard to guess from the attached screenshot. But if you provide your pre-trade buy and sell orders, I can give you the exact numbers.
(II) The profit optimization algorithm is not exact. It overshoots the point of maximum profit. In your case this is 480.


If you just fix the optimization, (I) will remain the same but you will get exactly this value. You will still be at point of price inversion though. Also note that this is non-trivial to do when multiple trade routes are involved. Although you could use a slightly modified version of the optimization algorithm I posted for post-trade prices.


If you just calculate the accumulated ("true") profit correctly, point (I) will be fixed. The point of maximum profitability will be exactly at the point where the final price difference is zero (assuming no costs). You can clearly see this in your project. It is also guaranteed by a mathematical theorem. So it cannot get any better in terms of protection. The assumptions for the fundamental theorem of calculus are clear in your very easy example with just one trade route. With arbitrary many trade routes you have to be more careful. But if you are smart about the ordering of trade routes, everything works out fine. If you account for costs, the maximum will be exactly where the final price difference is equal to the costs, i.e. there is no marginal profit to be made. In your screenshot this seems to be approximately 320.
But we are both correct insofar as (II) will remain a problem. The current optimization will not be able to exactly find this point in (I) and might overshoot. My point was that this is the only thing that can go wrong as explained in the post you quoted. In your example this will probably be somewhere between 330 and 405. Note that this is very difficult to estimate, as it depends very closely on the discretization. Therefore, the large range given. In order to give you the exact number for your example, I would need the exact market condition pre-trade and the size of your level 8 and 9 trade routes.

The good thing though is that in the case of the accumulated profit the condition for maximum profitability is very easy to state. In fact we already know where it is maximal by the fundamental theorem of calculus. Therefore, it is easy to just replace the current imprecise optimization by a correct one. You just need to check how final price difference relates to cost. Two values which are already easily available in the current economic system. Therefore, one can also fix (II) with very little additional work and get a system where price inversions are impossible. This is the reason why I always proposed to also change optimization, if one uses the integral calculation. In this case (II) is really the minor problem of the two, as the integral calculation for multiple trade routes is a lot more difficult than the optimization.


If you for some reason want to keep the current imprecise optimization algorithm, you need a more robust profit formula. In fact one can show that it is necessary to have a formula which fulfills the property that the profit is smaller or equal to zero at any point of price inversion. Using post-trade prices is obviously one option. But in fact there is a class of infinitely many functions which give you more profit than post-trade prices but still fulfill this property. Suitable for application in Vic3 are the weighted harmonic means of pre- and post-trade price differences of a given trade route. These have the advantage that they are easy to implement, as you just have to change the profit formula. They protect from price inversions but still give quite a bit more revenue and a higher amount of traded goods than just post-trade prices. Therefore, they are a good candidates, if post-trade prices are insufficient but one does not want to implement something as complicated as the integral solution.

One issue that these analyses don't really cover is the case of multiple trade participants, rather than only two. And in practice, this is usually how the problems were emerging in my games, many countries are piling on. Are there any solutions other than using final market price that are robust under multiple importers? I don't imagine that there can be any such solution.

Consider country B imports from A, driving the price in A from 10 -> 30, with a buy price of 20 under the arithmetic mean, or say x under some other mean. Another country C with market price anywhere between x and 30 can come along and engage in a profitable trade from an expensive market to a cheap one. The only thing that would forbid this using a purely pricing mechanism is if x=30, no?


If the game excluded only one trade route at a time from the calculation of the pre-trade price, rather than all the exporting or all the importing ones, then the various other price-based solutions would be applicable. And to be honest, I imagine that change in of itself would in practice resolve a lot of the expensive -> cheap trade route issues that I am seeing even without pricing mechanism changes.

Also, I think it's worth commenting on this:

(I) The point of maximum profit is at a point of price inversion. In your example it is something like 400 while the price difference is 0 at approximately 320. The numbers are a bit hard to guess from the attached screenshot. But if you provide your pre-trade buy and sell orders, I can give you the exact numbers.

There is also the question on whether a route maximizing profit is the correct objective, or maximizing trade volume subject to the constraint of positive profit. The latter is the more realistic objective for a competitive market, but can only give a realistic outcome I think using post-trade prices. For a monopoly, the first makes sense, but then how are the competing interests of multiple countries to be taken into account?

It might be that using post trade prices but having routes grow to maximize volume subject to positive profit constraint might give gameplay results that the devs want. Currently it is a little closer to maximizing profits, but not quite. Routes grow until a further growth would cause more than a 10% drop in profit (among a couple of other requirements)

 

[KarlThorsten89]

I prefer the German Flag that has an eagle in the center and later an Iron Cross. Maybe a decision that allows us to change the flag would be nice, as long as it applies to the relevant country.

 

[PedroLuiz]

I think they are looking at giving a bonus for inputs from the same state.

i hope they don't slap *another* throughput bonus

 

[Nikolai II]

i hope they don't slap *another* throughput bonus

Maybe they could give a slight rebate in purchase costs of local input material (since the market prize includes average worldwide shipping, and in-state material needs to get shipped less distance) - so building steel mills in coal/iron regions would be slightly more profitable?

 

[Erfar]

Is there Puppets/Dominion tax fixed?

 

[PedroLuiz]

Maybe they could give a slight rebate in purchase costs of local input material (since the market prize includes average worldwide shipping, and in-state material needs to get shipped less distance) - so building steel mills in coal/iron regions would be slightly more profitable?

Market access multipliers for goods would make it that way (steel having a higher market access than iron since it is easier to carry)

 

[neroden]

Well, this patch is a start. I'm very glad to see attention paid to the economy-breaking trade issue, and I'd like to see how the fix so far is working.

Unfortunately, as long as the construction costs exploit is extant, I can't bring myself to even try to play. Maybe that'll be fixed in 1.1.1 ? https://forum.paradoxplaza.com/foru...s-free-construction-100-reproducible.1552282/

Then maybe I will be able to even look at the military situation.

 

[Tempscire]

One issue that these analyses don't really cover is the case of multiple trade participants, rather than only two. And in practice, this is usually how the problems were emerging in my games, many countries are piling on. Are there any solutions other than using final market price that are robust under multiple importers? I don't imagine that there can be any such solution.

Actually all my suggestions cover the cases of arbitrarily (finitely) many trade routes. At first I just looked at one route, as the easy case is required to get some form of intuition for the system. But I spent most of the analysis on many trade routes, as this is the far more interesting case. I just illustrated this in an example with one route, as I replied to a post regarding an easy one route example.

Consider country B imports from A, driving the price in A from 10 -> 30, with a buy price of 20 under the arithmetic mean, or say x under some other mean. Another country C with market price anywhere between x and 30 can come along and engage in a profitable trade from an expensive market to a cheap one. The only thing that would forbid this using a purely pricing mechanism is if x=30, no?

I think you need to be cautious here when you take the mean. As the harmonic mean is no longer linear this makes quite a difference. My suggested implementation would not allow C to make any profits. Lets calculate, take for example a price of 30 in C, this should rule out your worries:
The price difference before any trade between A and C is 20, the price difference without just the A->C route is 0. The post-trade price difference is negative, as the A->C route increases the price in A and decreases it in C. Lets say it is -y, with y>0.
There are two options: Either compare with the first or with the second price:
(i) Here we have P(A,C)=harm(20,-y) per convention this is -2/(1/20+1/y) which is certainly a negative number. Therefore, the route makes a negative amount of profit even without any costs. Just like in the post-trade price case.
(ii) P(A,C)=harm(0,-y)=0 per convention. Therefore, the route makes zero profit.

In either case the route can not be profitable.

If the game excluded only one trade route at a time from the calculation of the pre-trade price, rather than all the exporting or all the importing ones, then the various other price-based solutions would be applicable. And to be honest, I imagine that change in of itself would in practice resolve a lot of the expensive -> cheap trade route issues that I am seeing even without pricing mechanism changes.

You should be careful with this however. This can lead to infinite loops with the arithmetic mean. Lets say we have A->B with 100 goods and B->A with 100 goods. A,B have base price. Then each of these routes has a positive price. If you just discard one route the other remains and gives you a positive pre-trade price. While prices in such a constellation should clearly be zero. The harmonic mean would clearly fix this.

There is also the question on whether a route maximizing profit is the correct objective, or maximizing trade volume subject to the constraint of positive profit. The latter is the more realistic objective for a competitive market, but can only give a realistic outcome I think using post-trade prices. For a monopoly, the first makes sense, but then how are the competing interests of multiple countries to be taken into account?

That is a good question. It probably takes quite a lot of testing what is better for the game and I obviously cannot give you an answer to this just from mathematical knowledge. I guess it is very hard to tell what is the most realistic solution and probably up to the devs to decide which is the best for the game. I can just say that profit optimization is the hardest to do and it is quite easy to make the algorithm worse at optimization to obtain something which comes closer to maximizing volume.

It might be that using post trade prices but having routes grow to maximize volume subject to positive profit constraint might give gameplay results that the devs want. Currently it is a little closer to maximizing profits, but not quite. Routes grow until a further growth would cause more than a 10% drop in profit (among a couple of other requirements)

The problem here might be that profits get very low, as post-trade prices give relatively low profits and the worse your optimization is, the worse the profits get. This is maybe the reason the devs used average prices in the first place. So if such a solution is sufficient is probably up to the post-trade testing which is currently done.

 

[Jackadsa]

I think you need to be cautious here when you take the mean. As the harmonic mean is no longer linear this makes quite a difference. My suggested implementation would not allow C to make any profits. Lets calculate, take for example a price of 30 in C, this should rule out your worries:
The price difference before any trade between A and C is 20, the price difference without just the A->C route is 0. The post-trade price difference is negative, as the A->C route increases the price in A and decreases it in C. Lets say it is -y, with y>0.
There are two options: Either compare with the first or with the second price:
(i) Here we have P(A,C)=harm(20,-y) per convention this is -2/(1/20+1/y) which is certainly a negative number. Therefore, the route makes a negative amount of profit even without any costs. Just like in the post-trade price case.
(ii) P(A,C)=harm(0,-y)=0 per convention. Therefore, the route makes zero profit.

In either case the route can not be profitable.

My apologies, I misunderstood your solution and thanks for the clarification.

I was thinking of a buy price, which is averaged between initial and final prices in the exporting market, and a sell price, which is averaged between initial and final prices in the importing market, and take a difference, as the game currently handles this.

But if I have understood you correctly, you mean to take an average between initial price difference and final price difference. I suppose this makes more sense as a model of a trader buying and selling small batches.

I guess it is very hard to tell what is the most realistic solution and probably up to the devs to decide which is the best for the game

For realism, I would just open up a history book and look whether trading routes tended to be operated by monopolies that had power to suppress competition or by collections of smaller self-interested entities. For best for the game, I think the discussion below is relevant.

The problem here might be that profits get very low, as post-trade prices give relatively low profits and the worse your optimization is, the worse the profits get. This is maybe the reason the devs used average prices in the first place. So if such a solution is sufficient is probably up to the post-trade testing which is currently done.

Well there were two comments by wiz that we are eternally speculating over, one about trade profits, the other about trade volumes and prices getting pushed to base everywhere. My own parsing of the comments was that the impact on trade volume and goods prices was the core issue, and the insufficient profits was diagnosed as the reason, which makes sense if you take as a given that trade centers are acting as monopolies and are only trying to maximize profit rather than volume. It also makes more sense to me, if I put myself in the devs shoes, to be more concerned about the impact of trade on the wider goods economy, rather than be fixated specifically on how much money traders are making as an end in itself. But we can only read the tea leaves on this.

The goods pricing issue though is a puzzling one to me, because if the original problem was 'prices always too close to base', I can't fathom why 'make prices even higher in the exporting country and lower in the importing one' is regarded as a solution, it just pushes the problem further in wrong direction. The two statements that were made in that dev diary also seem to conflict 1. "There was insufficient trade" and 2. "Prices would equalize to base for all goods everywhere". The latter would be a result of maximal trade, in a system where trading is priced realistically and there are no transport costs. Somehow it seems preferable for trade volumes to go higher than maximal, in order to cause price inversions that allow prices to differ substantially from base, just in a direction that doesn't really make much sense. This is honestly how I read it. The prices are more 'interesting' in the current system, and that in of itself is treated as good.

The other aspect that was mentioned was making exporting economies more attractive. But this isn't actually done with trade profits, because all the trade profit goes to traders in the country that set up the route, which in practice is usually the importer. The manner in which the currently implemented system aids exporters (or hurts, depending on your point of view) is by increasing the price of the good in their market beyond what realistic trade could achieve which gives their producing industry more profit. This is a feature of trade volumes becoming excessive and going into price inversion territory. So again it all seems mostly trade volume motivated at core, with trade revenue being mostly a dial that goes into that calculation.

 

[Dimes]

​

- Austrian-formed Germany no longer has the Matter of Hungary Journal Entry

This can be gamed rather easily...

 

[Catoscar]

Maybe they could give a slight rebate in purchase costs of local input material (since the market prize includes average worldwide shipping, and in-state material needs to get shipped less distance) - so building steel mills in coal/iron regions would be slightly more profitable?

This was actually my original idea, but as of now, the only way for the price of something to be different is to lose market access, so I'm not sure if making it so prices could be set separate from the market would be an easy change or break something else with the economy. The reason why a throughput bonus is usually suggested is because it's one of the only modifiers in the game ATM that benefits both the input good producer (more demand) and input good user (less employees required for same output) with the justification being that less employees are needed to handle the input goods since it's so close by.