If you are interested in it, when it's done, I can send it to you too, along with Mark and Rodrigo. My personal opinion of course is that this document should come to surface in the website as soon as possible, but I don't know if the others agree.

Hey look! I'm a warlord now!

I guess I don't understand what you mean by "people's wages just magically" increasing over time. There is nothing magical about it in the system. Essentially increased wages come just as they do in the real world, from productivity increases. Productivity increases come from primarily investments in capital, and utilization of new technologies. Minimum wage laws and such, at least as far as I understand it, have relatively little to do with average wages, which is what the model handles. All minimum wage laws do is set a floor below which you can't go. But I think in general minimum wages are set at the low end of the wage distribution anyway, because if they are not they will tend to give a huge shock to the economy. Anyway, most of the points you raise are already being addressed, and just aren't written up yet as axi says.

Axi:

Mark&Axi: About releasing the govt model, I'm waiting for the social to model be "ready" (in a general sense). That's because the govt model is extremely connected with the social model. The govt model I made assumed Manurein's social model with the "agents" approach, which is not going to exist any more in the new social model by TK. If we release the govt model now, a lot of it will need to be change according to the new social model and I guess that's only going to confuse people. If at least I have a general idea of how the new social model is going to be, I can make those changes before posting anything and therefore the govt model will be better understood. I'm currently working with TK via e-mail to create a crude first version of the social model. I think we'll be ready in couple of weeks.

I have been working for some time on a revision of the basic production model for the economic system. After some good advice from Adam Smith from the Apolyton forums I decided to go with a production function similar to what is commonly used in real economic analyses. It has a lot of flexibility coupled with reasonably realistic behavior, for a fairly cheap price in terms of computation. My main worry about it is that it may be a little difficult to explain to players. But I think after people get used to it they will really like it. For one thing, it makes setting the economy on autopilot much easier for those who don't much care about the economy.

This approach to production is what we will be doing with in demo 5. There are a fair amount of mathematical details in this writeup. That is because it is meant as a first pass to let Laurent, our Econ coder, can get an idea of the way the system is going. However, if you're not interested in the mathematical details here are the few things that you need to know about this change...

The people of your civ will automatically do reasonably smart things with this approach. They will, without your guidance, take advantage of all the natural resources available to them.
This approach smoothly uses any new technologies available when you make investments to improve production facilities. You don't have to build "advanced farms", your farming sector just becomes better gradually as you build more farms or replace existing farms. You can simply alter the rate of existing farm investment to change the rate of adoption of the new technology.
There aren't arbitrary breakpoints on how many people can use existing facilities. If you put more people to work in your factories, output will always increase. However, output increases with diminishing returns.

Now, on to some more of the guts of the model...

The basic idea of a production function is that one uses the input of different types of resources (labor, natural resources like land or timber, and capital investments) to determine the final output for an economic sector like agriculture. Typically adding more of any one of these things, for instance labor, without changing the other inputs, gives diminishing returns. So, for instance, if you double the amount of laborers on your farms, the amount of food produced will generally increase, but not as large as a doubling. However, if you were to double All the inputs, any output would be simply double the previous output.

There is one other feature about the production function approach that I'm using that's very important for Clash. Included in it is a factor that represents the effects of production technology changes on production (A in the equation below). As the tech factor A increases, the same amount of investment can get you more production. The way I have it in the current model A increases as new investments of capital are made. For example, it's assumed that the people, when they replace their farm equipment, replace it with the highest technology equipment available. This results in, on average, an increase in the productivity of farms beyond what the simple investment in more equipment would give. I'll give more details later.

The equation below is what a production function looks like. The total amount produced (Y stands for yield) is given by multiplying together several factors. Each of labor, natural resources, and capital has its own exponent (a, b, and c) that describes how production increases when you change the amount of that particular input. Just to make things concrete on the resource part, if we were talking about agriculture R would represent land. Some things, like services, don't have an explicit natural resource input so sometimes the production function won't have R or b. For a particular sector A, a, b, and c will have specific values designed to give reasonable outputs for the level of technology and application of other inputs.

Produced Amount (Y) = A*L^a*R^b*K^c
A = tech factor (includes available hardware, infrastructure, and other details)
L = Labor
R = Resource
K = Kapital (its traditional to use the German spelling)
a, b, c < 1 a+b+c = 1

Now I'll use as a specific example the production function for agriculture that we're going to use in demo 5 along with particular selected values for L, R, and K. We will use the same equation as above with the following values...

Produced Amount (Y) = A*L^a*R^b*K^c
A = 5 (production technology near subsistence level)
L = 1 head (1000 people)
R = 1 farm site
K = 1 (representing farm tools)
a = 0.5, b = 0.3, c = 0.2, which satisfies a+b+c = 1

Now, because I used a bunch of really simple values you can probably see that the crop yield is 5. That isn't really very much food production, since our farmers will need to eat 4 units of food just to avoid starvation. So a yield of 5 gives them a little bit of potential excess to trade for services or produced goods, or pay to the Player in taxes!

If instead our labor were allowed to work 2 farm sites the output would be 6.16. This production level of above 6 gives these farmers significantly larger surplus production than before. It could be used in different ways to grow the civilization. The increase in output that results from being able to work more land can be thought of in several different ways... with more land to pick from the people can take better farming sites on average, and leave the poorest land in the sites unused, or they can leave land fallow longer making it more productive, and there are several other possible explanations. It isn't really important which explanation makes more sense in which particular circumstance. The nice part about it for the player is that the people do sensible things without you needing to tell them "by hand" what to do.

How the tech factor A changes

So how exactly did the tech factor A get to be 5 in the example above? And how can be made to get better so are production becomes more efficient? I have come up with what I think is a reasonable way to have A reflect the fundamental technological realities of the civ in question. The amount that A increases depends on the amount of new investment, and how far A is from the current best available technology level, represented by the "ideal" tech factor T. The ideal tech factor represents what the tech factor A would be if all the investments had been made using the current best technology, infrastructure level, etc..

Change in A is governed by the following formula:
Anew = Aold + (Kbought/Kold)*(T-Aold)*I
Anew = new value of A after capacity improvements have been made
Aold = value at beginning of turn
Kbought = new capital investment made this turn
Kold = total amount of previous investment in the sector at beginning of the turn
T = ideal tech factor
I = innovativeness present in the economy ranges from 0 to 1

Anew = Aold + (Kbought/Kold)*(T-Aold)*I

I'm not going to go over this in detail, but hopefully you can see that the new value of A approaches T more rapidly as: a higher percentage of new capital investment is made, or the innovativeness becomes larger, or as the ideal tech factor increases. The latter factor comes in strongest when the people are replacing very old equipment (A much less than T) causing the rate of improvement in A to be relatively rapid.

The ideal tech factor T gets the most part of its value directly from the effectiveness as determined in the technology model. In addition T has buried in it "human capital" aspects such as education, infrastructure aspects such as roads, railroads, and power grids, and some "tweaking" factors to get the numbers to come out right when the desired amount of capital is invested. This is going to be a somewhat complicated subject all by itself, and I am just going to gloss over it here.

The level of innovativeness of the people (I) will be something like 0.2 for a completely traditional economy, 0.7 for a command economy, and 1 for a pure market economy. The character of an economy will be indicated by a certain percent of each of traditional, command, and market forces. The innovativeness will be figured by simply using a weighted average with the factors above.

That is the general idea of the new model. I am currently working up a spreadsheet with specifics that runs through a complete turn (from an economic perspective) for provinces at different stages of development. When the spreadsheet is reasonably complete I will release it for anyone who is interested in the details of how these things work.

I do have a couple minor concerns, however. They deal with minor details and should be easy to deal with; I am not critisizing the model as a whole. If I didn't mention something, I think it is good.

The main thing I want to stress is that we should not code the ideal tech factor T into the econ model. If we say that tech number 47 helps farm productivity a lot while tech number 82 helps mining output a little bit, then we will be creating a nightmare for mod makers. The impact that tech has on the T values for agriculture, mining, production, etc. should be coded into the technology model so any alteration of the tech tree can be easily turned into the proper alteration of the econ model.

Does this mean that the tech model just got a lot more complicated? No. If we do it right, a technology's impact on T values can be directly based on its interface tags. These tags, which are already a part of the tech model, can be one of the major links between tech system and other models.

To help the AI and serve as a way to navigate the tech tree, we had planned for each tech to be assigned one or more interface tags. Each tag would be the name of the civ activity that the tech helps, and a number representing how much that tech helps. For example, a tech might be tagged with Agriculture:7 and Mining:2, meaning that it helps agricultural production a lot and mining production a little. The AI and the players can sort technologies by their tags, investing research in what is needed most. For example, a player would click on the Agriculture button in the tech interface, and all techs with an agriculture tag would be listed in descending order of the tag number.

Rather than simply being a description, the interface tags can also have a direct impact on production using this new econ model. The ideal tech value T for some economic field can simply be a weighted average of the knowledge levels of all techs with that tag.

A lot of technologies will have interface tags with 1 or 2, meaning that they are not the things to research in an emergency, but thay do halp a little. Roads, for example, would have an Agriculture:2 tag, maning that better roads do help effective farm yields a little by making it easier to move the food to where it needs to go. As a general rule, every infrastructure or educational technology would have tags of 1 or 2 for almost every civ activity. This means that they should fit into the T calculation nicely.

Mark: Is the I value you mentioned the same one that will be used in the technology model to determine the rate of growth of technology? If so, I don't think it should be used here as well. If it has an impact in two different places, it will have a disproportionate effect on tech growth. It already changed the rate of knowledge acquisition, so why should it change the rate of application as well? I thought the tech model was supposed to include both aquisition and application.

BTW you should probably cross-post your comments to the current tech thread, since many of them are pretty important with respect to the evolution and refinement of the tech model.

On using the tags to get the ideal tech factor technology component, I agree completely. However, one thing I think you left out is that technologies should sometimes have a lineage where technology A is succeeded by technology B. Even though they both might have an agriculture tag, they could not be both used for the effectiveness. Just whichever one gives a better effectiveness should be used.

Another point is that you say that infrastructure or education technology should boost almost anything. I would prefer to use the economic infrastructure components in the econ model for this in most cases. That's because the greatest educational technology in the world does your civilization no good if there are no schools and no resources invested in education. Similarly, knowing how to build superhighways does your no good if all you have are dirt tracks. Doing it this way would also make the tags system much simpler since educational techniques would only need a tag pointing to educational infrastructure then. At any rate, we should probably continue this part of the discussion in the tech thread...

I agree that an Infrastructure tag would probably be a better way to go.

Mark: I don't understand all of your comments about the ecology. What did you mean by an agricultural site? I thought a site was one tile.

Of course it may be that in most of these cases the effectiveness you get from the older technology is so small compared to the new one, that the Total effectiveness is basically still that for the new one. In that case its not a big deal if we just add them together. Although our players might be amused to see their telegraphy number still increasing with year-2000 technology!

Obsolescence should be defined in the tech definition, and when something is gone it will be deleted from the tech tree calculations entirely. This would mean that there is no need to filter them out in the oither models.

The farm effeciency system, which I used in the ecology model, assumes that all of the tile's land is equal. The tile is given a farm productivity measure, which applies to any farm built on that site. Those farms return yields based on the productivity factor of the tile. Each tile can build the same maximum number of farms.

The farm sites system, which Mark uses in the econ model, assigns a certain number of farm sites to each tile. All farm sites are assumed to be equal, and the productivity of the terrain is determined only by the number of farm sites on the tile.

The problem with the farm efficiency model is that it assumes that all of the tile could be converted to farmland, and that all farmland on the tile is that same. This does not really make sense, and the system has not been integrated into the economic model.

The farm site model ignores all climate effects, assuming that the one farm site on bad terrain is just as good as the farm sites on excelent terrain. Given the same labor and capital investment, all farm sites produce the same amount of food. This means that a population that only needs one farm site is supported equally well on desert and grassland. Additionally, the ecology model is not designed for the farm sites plan.

A combination of these plans, a model that generates a number of sites and a productivity number for those sites, would probably take too much processor time. It would be accurate and flexible, but I can't think of a way to make it run quickly and smoothly.

quote: Originally posted by Richard Bruns on 05-24-2000 12:52 PM The farm site model ignores all climate effects, assuming that the one farm site on bad terrain is just as good as the farm sites on excelent terrain. Given the same labor and capital investment, all farm sites produce the same amount of food. This means that a population that only needs one farm site is supported equally well on desert and grassland. Additionally, the ecology model is not designed for the farm sites plan.

It doesn't ignore climate effects! It works on the principle that we can approximate agricultural productivity by putting arable land into packages (sites) of different acreage that are all of roughly the same agricultural value. Some of the most productive agricultural land per acre in the world is in deserts, its just that there isn't that much of it in a typical desert 'square'.

IMO you need to think more about your analysis. If 1 pop point is on grassland, there will be about 10 sites, and they will produce Much more food than the desert. If you insist that the people are crammed into just a little patch of grassland (1 site), then it is certainly possible that a whole 60x60mi square of desert could have as much arable land. The arable land will mostly be in stream basins and oases. Going further, if you are thinking of 1 site of complete desert with no surface or accessable subsurface water, then it would probably take 10 squares or more to have one site (So we may need fractional numbers of sites after all ).

One pop point (1000 people) can probably do just fine on many desert squares (3600 sq mi.) since you are in the range of nomadic population densities. They wouldn't even need farms, they probably could just forage and / or herd.

I don't really see any conflict between the models... Your acreage x effectivess = my sites. A desert square has v large acreage but very low effectiveness, multiplied together gives ~1. You seem to be assuming (I may have this wrong) that people will build farms everywhere in the desert, which stretches my credulity. The farms will be build only on the Best patches of desert land.

But clearly both are toy models, and we could take pot shots at both of them all day. I have just spent tens of hours working on the production functions for the new economic model, I really don't want to go back and do it all over again unless there's a Very good reason. So if you can possibly fit the Ecology model values so they are in terms of sites I'd really appreciate it.

I didn't know that the people would automatically farm every agricultural site in the square. This would solve a lot of the problems I brought up, but it seems to make the concept of farm sites useless. If people always farm the maximum number of sites in a square, why do we bother with counting the sites? It would be foolish to reduce the number of sites farmed, so the R^b term will never change and is essentially redundant. It can be more easily represented by a single variable P that represents the agricultural value of the tile.

The result is that if we assume all sites are automatically farmed, the farm sites model reduces to the farm effectiveness model!

I suggest the following agricultural production function:

Produced Amount (Y) = A * P * L^a * K^c
A = Tech factor
P = Farm Productivity of tile
L = Labor
K = Kapital
a, c < 1 a+c = DR

This equation is basically the same as the one Mark created. The only differences are P and DR.

DR is a diminishing returns factor defined for every terrain type. It will always be less than one. Input of Labor and Capital is assumed to mean the creation of new farms, so this will make the first farms the best ones as the first people take the good land. Later farms will become less and less effective, so there is an upper limit on the number of productive farms.

I think that the ratio of a to c should change as technology improves. a should be high at first, but in modern times c should be much larger. When all farmwork was done by hand, making twice as many tools wouldn't have helped much. But today, adding more laborers to the farm sector would do almost nothing, as high technology has made farming much more capital-intensive.

The number of sites can change as land is cleared, drained, or otherwise made valuable for farming. That is why R ^ b can't be simply a constant. R will generally be fairly stable, but will clearly change by factors of several-fold in squares that start out forested, swampy, etc.

Frankly I don't see the difference between your new proposed equation and mine. You are just replacing R ^ b with P. I would prefer to keep it as it is just for consistency among the different production models. But it gives an obvious way to change your P into the number of agricultural sites... just let R = P ^ (1/b). If your model would have P change, then we can recompute R.

I specifically said that R^b, or P, would be a variable. It is obtained by the adjusted Soil, Water, and Climate as defined in the ecology model. If these conditions change naturally or due to human activity, the P value would also change.

I simply do not see the need to use "sites." Why do we need to take P from the ecology model, raise it to the power of 1/b to get the sites number, and plug that into the economy formula where it is raised to the power of b? It would be much more efficient to simply put P into the economy model.

Sorry if I sounded annoyed. I just have very limited amounts of time to spend in discussion right now, since I am running into endless unforeseen details that are slightly wrong in the economic model. I need to get the demo 5 version working as quickly as possible, and that is eating up most of my available time. BTW I'm working out the model as a spreadsheet to help Laurent in coding it. If you would be interested in checking it out when I'm done, I'd be happy to send it to you. You might be able to catch some problem that I'm not able to see because I'm too close to the system.

Actually, the distinction between the P and R ^ b expressions is not trivial. I believe that each square's P will need to be raised to the power of 1/b if we end up using P for a very important reason. It has to do with maintaining proportional returns to scale in the economics model. I don't really know how much you know about production functions, so if I'm saying stuff you already know, please don't be insulted. And if my explanation doesn't go far enough, if you look up Cobb-Douglas production functions in a web search you will probably get some useful stuff.

Proportional returns to scale is the property that if you multiply all economic inputs in the production function by the same constant, then the output is the previous output multiplied by that same constant. So, for instance, with a
Produced Amount (Y) == F(L,R,K) = L^a*R^b*K^c
and with a+b+c = 1,
if we take two identical provinces and put them together, and calculate the output for the new province,
we get
Y' = F(2L, 2R, 2K) = (2L) ^a*(2R) ^b*(2K) ^c
= 2 ^ (a+b+c)*L^a*R^b*K^c = 2 ^ 1 *Y = 2 Y.
So if you take two identical provinces with output Y and put them together, they produce the output 2 Y. seems pretty sensible, and it's a really good property for production functions to have.

If your P, that you propose sticking in there instead of R ^ b, doesn't satisfy that property, then we will get really bizarre results from the output as province sizes change. For instance, if you use the "sensible" rule that P for two equal provinces would add, then you would get for our previous example:
Y' = F(2L, 2P, 2K) = (2L) ^a*(2P) *(2K) ^c = 2 ^ (a+ 1+c)*L^a*P*K^c = 2 ^ (1+a+c) *Y > 2 Y.
This is an undesirable property in my opinion...

Furthermore, R, or alternatively P ^ 1/b, is what the player needs to be told is the fundamental agricultural measure IMO. Any other functional form would have agricultural sites or whatever we call them either not add arithmetically, or produce bizarre results from the production function.

Now I haven't seen your model for P. If you have foreseen all that, and included it in the model, then I guess it would be a wash whether we go with your formula or mine. But you need to take that extra exponent so that you can use it to inform the player about the agricultural potential of a square or province anyway, so I do not see any advantage to doing it your way. As before, I think your ecological model is basically good, and I have no problem deriving the number of sites from it.

P is the smallest adjusted Soil or Water value times a climate value. It represents the quality of the land, not the quantity of good land. So it is not meant to be additive.

I seem to have caused yet another misunderstanding. I assumed that you would be calculating the squares individually, then adding them up. The equations I proposed were based on this assumption, so of course they do not work when the inputs are added before the calculation. I never meant for the values to be added up and put into one function, and I didn't know that was what you meant. I thought you wanted to do something like this:

F(L,R,K) = L^a*R^b*K^c where R=P^(1/b)

Province production
= L1^a*(P1^(1/b))^b*K1^c + L2^a*(P2^(1/b))^b*K2^c + . . .

It does make more sense to add up all of the inputs and then run the equation. I should have realized you were doing that, even though you never said that was what you were doing. Now that I see what is going on, I understand it better and see that your math is good and reasonable.

However, I am also better able to see and explain the problem with the farm sites system. By treating all sites equally, it creates unrealistic scenarios and odd incentives. Consider the following example:

Province A has two squares. One of them is good farming land, with ten farm sites. The other is barren wasteland, with only one farm site. Currently the good square is populated, and there is one unit of labor and one unit of capital working on that square.

Now assume that one more unit of capital and labor become available. Should these be assigned to the good land or the wasteland? The reasonable and historical thing to do is to put them on the good land. However, the farm sites model results in greater total farm output if they are assigned to the wasteland. In either case, there are two units of labor and capital. If they are all put on the good land, there are ten total farming sites. But if they are split between good land and rotten land, there are eleven total farming sites, resulting in greater farm output.

The result of this would be to encourage players to keep the minimum number of farmers on every square. Expansion would always be more profitable than staying on a small number of good squares. Any extra farmers on a square would be wasted if it is possible for them to move to any other unoccupied square.

The idea of the farm efficiency system is to multiply the effort put into a square by some factor that determines how good the farming is on thet square. This means that more effort will be put into good farmland rather than wastelands. However, the farm efficiency model requires that the output of every square be calculated individually, and then added to get the total province farming yields.

I first thought that farm efficiencies P1 through Pn could be averaged to get the total province efficiency, but then I found that this does not work if the province has terrain with dissimilar P values. There were also problems with diminishing returns when I tried to make a formula that calculated all of the province at once.

There is a possible solution, but I have a couple reservations about it and I'm sure others will also. We seem to agree that provinces should be geographically as well as socially and politically similar. Would it be too much of a stretch to make ecological provinces and standard provinces the same thing? Most social groups arose in areas that had the same climate and geography. Such areas also make natural political units and will ususally have similar infrastructure. So, can we define a province as an area that has similar culture, infrastructure, geography, and ecological features?

I will have to change the ecology model to fit this new definition. I would have to eliminate the idea of border shifting, and have ecological changes apply to the province as a whole. There could also be some other changes needed; I will have to recheck the model. But I think it would be worth it. Each province would then have the same P value for all tiles, so labor and capital inputs could be summed and put into one farm yield calculation for the province. Infrastructure and technology (A) and farm productivity would be easier to deal with. The question of which value irrigation improves would be rendered academic. Additionally, calculations for the ecology model should also get easier and faster if economic and ecological provinces are the same.

quote: However, I am also better able to see and explain the problem with the farm sites system. By treating all sites equally, it creates unrealistic scenarios and odd incentives. Consider the following example: Province A has two squares. One of them is good farming land, with ten farm sites. The other is barren wasteland, with only one farm site. Currently the good square is populated, and there is one unit of labor and one unit of capital working on that square. Now assume that one more unit of capital and labor become available. Should these be assigned to the good land or the wasteland? The reasonable and historical thing to do is to put them on the good land. However, the farm sites model results in greater total farm output if they are assigned to the wasteland. In either case, there are two units of labor and capital. If they are all put on the good land, there are ten total farming sites. But if they are split between good land and rotten land, there are eleven total farming sites, resulting in greater farm output.

Well, I never published how I was going to handle this, so I can see where you might be concerned. Actually, I get around this problem by assuming that usually the people working in the sector are distributed evenly on the sites. So in your example when you put another point of labor into the farm sector of the province, the new population of 2 in the farm sector will have 10/11 of the population in the good square, and 1/11 of the population in the lousy square. Again, this method is much more streamlined than handling things on a per-square basis. There is of course going to be some loss in overall efficiency because it can take squares awhile to achieve their "usual" values when you add or remove squares from a province. I don't know exactly how I'm going to handle this yet, but it will probably involve some trade-offs between doing it perfectly correctly and the cost in clock cycles.

I don't know if I've explain this issue adequately to you, but trust me that none of the problems that you raise actually occur in the system as I have it now.

"We seem to agree that provinces should be geographically as well as socially and politically similar. "
I don't recall ever agreeing with that sentiment. I'd characterize it as fairly frequent that provinces like this will occur. However, I think it will be almost equally as likely that any particular province will have mixed geography, and/or multiple ethnicities. I realize that you have your own vision of how Clash should play out. But I think, especially in the early game, dynamic provinces that aren't tied down by arbitrary restrictions will be the best way for the players to minimize micromanagement burdens.

This leads into your idea of insisting upon a coincidence between economic provinces and ecological ones...

In addition to my points in the paragraph above that we need fairly flexible provinces, IMO your idea could lead to an increased number of contorted, ugly, provinces, and a great deal of player frustration. Provinces already serve a dual role in organization of economic and governmental activities. I think we need to keep the economic and ecological provinces distinct. I guess after both the economic and ecological models are reasonably well established, we could then look at the level of coincidence between the economic/political and ecological provinces and see what overlap there is. But I'm skeptical about the combination of the two concepts. For instance, what if my civ annexes a single square of some different ecological type adjacent to my existing province. According to your definition I would need to generate a whole new province for this lousy square. I consider it much more reasonable to be able to just make that square part of the existing province.

quote: Originally posted by Richard Bruns on 05-26-2000 01:54 PM There is a possible solution, but I have a couple reservations about it and I'm sure others will also.

Mark: I was not insisting on anything. Why do you assume that everything I write is meant to be set in stone? I was just tossing out an idea to see what the response would be. My hope is that if I explain an idea and point out its advantages, someone else can improve on it or take one of its good points.

By the way, when I wrote that idea I was assuming that provinces changed hands as a whole. I had forgotten that the current Clash plan calls for nickel-and-dime conquests that require micromanagement of lots of little units on the map.

Well, your suggestion is basically what I had in the old economic model. I stand by my analysis that with 20k squares we should not model every square with great precision. The production function model still has a "poor man's" version of this sort of dependence in that if you stick a single head in a square with 10 farm sites, its productivity is about double that of a square with one farm site. So the production function approach in essence has embedded within it an assumed distribution of good to average sites in highly-endowed provinces, and average to poor sites in the poorer provinces. But backing away from the details, my main point is that most players are not even going to Look at single squares and how many sites there are. Players are going to focus at the province level and higher. Any large amount of effort we spend in detail the modeling at the square level is, I believe, essentially wasted resources.

Richard:

Obviously we view presentation of ideas differently...
You closed with: "I think that using farm efficiency and making provinces have the same land values would be the best way of calculating farm productivity. It should run quickly and give accurate game dynamics." That sounded pretty definitive to me... and that's why I interpreted your statement as a firm indication of which direction you thought we should head in. Anyway, I'm sorry it turns out that I came out arguing disproportionately strongly against something you were just throwing out as an idea. I'll try to tone it down a bit. I guess I will also start assuming that the things you're proposing are just meant to be directions that we might head in unless you use special phrases like "I think it's vital that" or similar.

On the issue of whether things are done primarily on a whole-province basis, or was more stuff happening at the square level, I have to agree in general that the more stuff that's done by province the better. For all I know, you're right about the military issue. At this point my take is that we can get away with doing some military stuff on a square level. However, if playtesting shows that to be impractical then we will obviously have to go more toward your vision. This could happen because of either excessive clock usage or micromanagement (this would be the case if we can't make the AI good enough).

It seems to me that allowing players to adjust province size would invite excessive micromanagement. My rule of thumb is that the players will be smater than I am, and they will figure out how to tweak things to their advantage if they are given the chance. If players are given the chance to adjust province sizes, they will find a way to do so in such a manner as to give themselves more production.

For this reason, I oppose player alteration of province sizes. If given the chance to change the inputs of production functions by changing province sizes, players will find a way to gain an advantage by doing so. This will make the game last longer, and players who do not micromanage will not be able to compete.

To allow players to manage provinces easier, similar provinces can be combined into administrative regions. This does not change the production functions; it simply gives the same orders to all of the provinces and displays all of their outputs in one window.

I also think it is reasonable to conquer all of the province at once. If players order campaigns rather than battles, this lump sum conquest makes more sense. Caesar conquered the equivalent of a province of Gauls in one year. It took a lot of little battles, but the effect was the same; a patch of land with similar society and terrain was conquered and became a province under the Roman Empire rather than a province of tribesmen.

Basically I am thinking of a Risk type conquest/combat system.

I personally don't like the risk type battle system. In most cases it isn't realistic for an all or nothing campaign. Most of the time even if large areas are overrun and "conquered" that doesn't mean everything is. Also it wouldn't be able to handle something like the Byzantine Empire which had to be slowly wittled away at (in clash sys it would be square by square) for a few centuries until only Constantinople was left. The captial was the last thing to fall and that was long long time after a campaign started and areas were counquered. In clash terms, much of that area would be in use by the enermy before then, but not all.

Also just because you "conquered" someplace doesn't mean you rule it, atleast in a practicle sense. Also this doesn't allow for things like Occupied terriory like Isreal has or the deviding of nations for small conquered regions like what happened after WWII with everything Russia conquered that didn't completely conquer a whole country.

I've read over the description of the economic model, the suggested changes and I think most of the comments that have been made in this thread. I'll try not to repeat anything that's already been said, but...

Independent Investment: The idea of having the provinces grow of their own accord, albeit affected by your actions is good. However, I think that the system of how they improve might be better if it could be controlled more.

For example, take a frontier town. Chances are, they're going to want to improve everything in sight to make things more comfortable for them, starting with making sure food supply is good, then maybe specialising in different trades such as carpentry or smelting, then wanting a better road connection than the existing dust-track to the next town...

All fine...however, aren't the prices of all these improvements fixed? Or have I misread the table? Surely the prices of the improvements will be affected by supply in the local region, which will change as the town makes use of it.

Let's say that this town wants more houses. That's great, there's a small wood nearby. However, if they decide they also want wood to trade with and to improve with and they don't actively replant that forest (and not all settlers would think that far ahead), they'll soon find that they don't have enough trees.

They then have the choice. Do they wait 6yrs or so to grow the forest again, or do they buy wood from elsewhere at greater cost to improve now? I'm not sure if this factor is taken into account, but my guess is that early colonists will be inclined to use what is there for the present with no thought to the future - the "survivalist" strategy. A prudent micro-managing emperor might order them not to do this, but with the obvious restriction to immediate growth.

Also along the lines of over-production is in agriculture and fishing. How many disputes are there now about fishing zones and quotas to prevent this? Or about needing to use chemical fertilisers to replenish soils so they can continue to grow crops year after year after year without needing to be "fallow"? Perhaps this should be taken into account...

Also, I have something with regard to the merchant idea. Is "building" merchants right? Originally, farmers sold their produce themselves. Once the area became bigger and they were growing more, it made sense for them to give to a local friend who would journey to the next town on behalf of all the farmers and sell their crops, taking a cut for himself. These were the earliest merchants - not built by the people, but arising as a profession due to increasing population.

I agree that merchants could be commissioned, but I also think they should spontaneously occur as the province/town grows. Also, perhaps commissioned merchants could initially be ordered on trade routes, then working on their own initiative until the govt. steps in and tells them otherwise? This would allow some govt. control, but there should be no control over the spontaneously generated merchants...private interests can't really be ordered about in that way.

Going back to the trade-route argument, I like the idea of defined routes, but this depends on the size of the game map. The smaller each individual "square", the better it will be to have actually generated routes rather than just the trade "links" as seen in Alpha Centauri and Civ 2. Piracy, etc. was always a problem and required constant military watching to check it. I would suggest that a military unit in a square will eliminate piracy in that square (you don't steal from under a policeman's nose) and reduce the chance of it occuring in surrouding squares by, lets say, 75% in adjacent ones and 25% in those of a 2 sq. radius.

That way, you can "define" main trade routes by defending from piracy and also give an interesting problem to the player in times of war...do you move these guarding units to the front lines and risk greater piracy?

My mind turns to the Carribbean example...true piracy, if you like, where pirates were hired by colonial powers to attack the trading of others. There you have an area trading in rich materials and with ships and cities holding vast wealth but with relatively little military power. If you want a piracy "equation", it would be something along the lines of

frequency of piracy = value of trade in square and surrounding squares / local military power.

I don't want to give figures in that yet. Also, with piracy comes a new investment for either people or govt.: pirate hunters (sea), bounty hunters and vigilantes. Benefits are that they reduce piracy more effectively than military units and don't require military units to be stationed in the area - costs are that they work on commission and are therefore expensive to run and can't be decommissioned easily (say a 10 turn notice...)

Also, vigilantes could be a policing system in frontier colonies with poor policing. They do their job, but cause terror and inefficiency (killing wrong people, etc.). Perhaps reduce crime or corruption, whatever the game will use but then decrease productivity?

One suggestion... for the things that you think we might have put in the models, but haven't come across yet, try using the search feature. For instance, in your merchant comments you mention about merchants having actual routes. They do, and we discuss that in a thread specifically dedicated to the merchant model. With luck, a forum search using merchant and route as the keywords would have turned it up.

The people generally don't specialize in specific trades like carpentry in the model. I thought that was just too detailed. The only way we have to do that in a crude fashion is by using Specials to represent important subcomponents of the economy.

You seem to think prices are static. Prices vary with the local market. So if you start cutting down all the trees (ecology model) the amount of resources will decrease, and the price of resources will then go up, making the people build fewer houses... However, because the price of resources has gone up, if there is a cheap way to get resources into the province, merchants will seize that opportunity to make a profit. It really works about as close to the real world as I think we can get in a game. Anyway, prices of both the fundamental things like food and goods, and more complex things like infrastructure change with the local market.

Currently, the merchant model only handles long-distance trade. We could change that so that merchants could also make money with intra-province trade. There is a whole thread on merchants that you should find, and please put these comments there, because they're likely to get lost in this thread. In case you don't figure it out yourself you could edit your post above, and while in edit mode just copy all the text on merchants, and then start a new post in the merchant thread with it. Currently the plan is that merchants that come from the people do their own thing, whereas if the government commissions merchants, the player gets to tell them what to do. But we have to make this streamlined, or it will be a micromanagement nightmare.

All:

In the very first section on calculating production, you included the calculations for marginal production increase on the far right. I was altering the technology levels slightly when I noticed that there's a slight paradox.

I've probably got this totally wrong, but I was assuming that T(ideal f) was not the upper bound of the A(tech f) function. If I'm wrong, ignore what I'm about to say right now.

Anyway, since you said at the top that 5 was the level for a low tech province, I raised the farm A(tech f) level to 8.00. In doing this, I noticed that for adding an extra unit of capital, a negative figure was given for production increase.

In other words, buying another hoe actually made you produce less. That goes against all economic thinking that I know of. I assume we're dealing with increasing/decreasing returns to scale, in which case for an extra unit of capital in a huge production line, maybe only a 0.02 production increase would be seen (ie, 200 capital units needed to increase production by 1), but I'm unaware of any circumstance that adding factors of production causes less to be produced overall.

Yep, you found a Bad thing in the model! First let me say that in Most cases T is supposed to be the upper bound of A. However in times of tech decline, or reductions in infrastructure, T can get 'behind' A. The problem comes from my simple formula:
Anew = Aold + (Kbought/(2Kold))*(T-Aold) [I changed it in the spreadsheet from what's in the thread above]
The basic idea is that when you buy new capacity you do it at the best technology available...
I think this quickie formula is ok when A is below T, the usual case. However when they switch over, then you drag down productivity of existing capacity too much. At a quick guess we need a different formula when T is below A. I Do want A to decline when T isn't adequate to support existing production techniques, but the effect should not be as dramatic as what the current formula gives.

I need to think about either a better formula that works for the whole range, or at a minimum something that avoids this embarassment by using a different formula for the T below A case that doesn't work! If you'd like to make suggestions, you're welcome to. But please think carefully about them first because there are a lot of ways to go wrong with something like this... As I've amply demonstrated

Thanks for pointing it out

Mark

Actually, this Is the new tech model. The one that is the old tech model is the one that's in demo 4. We can use all of the discussion of This one that we can get

This is a very common misconception about short-term increases to factors of production of a great scale. Let's take Mark's example of digging a ditch...

We have a ditch that needs to be dug. Only 3 men can work on the ditch at any one time. Assume that capital (spades) is fixed at 3.

If we have one man and three spades working on the ditch (1 labour, 3 capital), he'll get there in the end. However, 2 spades are going unused and, assuming they're well made and won't break, having them as spares is useless.
If we then have two men or three men working on the ditch, it'll be made a lot faster. If we then have 6 men, it will still me made faster, as the men can take rests, etc. If we have 12 men, the ditch will still be made faster:

At no point does the speed of production slow down. The more labour you add, the quicker it will be - always. Capital isn't quite the same (spades can't work themselves), except in terms of robotics.

The issue then is not speed, but as Mark phrased it "productivity" (time/labour). What we see is that the marginal productivity increase for adding 1 extra unit of labour gets smaller and smaller. When you use 3 men instead of 2, the marginal productivity will be quite high. However, by the time you get to adding the 60th man on, the decrease in time will be almost insignificant...although it will not increase.

However, there is a reason why we don't use a 60 man workforce - cost. There comes a time on the production schedule when the cost of employing the extra man outweighs the decrease in time that he gives. Exactly where that point lies can be calculated.

We have a ditch that needs to be dug. Only 3 men can work on the ditch at any one time. Assume that capital (spades) is fixed at 3.

If we have one man and three spades working on the ditch (1 labour, 3 capital), he'll get there in the end. However, 2 spades are going unused and, assuming they're well made and won't break, having them as spares is useless.
If we then have two men or three men working on the ditch, it'll be made a lot faster. If we then have 6 men, it will still me made faster, as the men can take rests, etc. If we have 12 men, the ditch will still be made faster:

At no point does the speed of production slow down. The more labour you add, the quicker it will be - always. Capital isn't quite the same (spades can't work themselves), except in terms of robotics.

The issue then is not speed, but as Mark phrased it "productivity" (time/labour). What we see is that the marginal productivity increase for adding 1 extra unit of labour gets smaller and smaller. When you use 3 men instead of 2, the marginal productivity will be quite high. However, by the time you get to adding the 60th man on, the decrease in time will be almost insignificant...although it will not increase.

Eventually, you'd reach the stage when the time taken for a quicker switch over would exactly equal the time lost if you didn't switch over. At that point you are operating at your maximum possible speed, given current constraints. No further speed increase is possible, therefore extra labour simply adds to costs without increasing speed.

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That's exactly what I said. Once you reach this stage, or go slightly over it - it will be pretty obvious. A manager/foreman or whatever would then advise against employing any more labour and may look at increasing another factor of production if speed needed to be increased further.