Civilization – Do other civilizations pay for roads you build in their territory

I recommend not "investing" in a city-state unless you can get some influence for free to start out. Killing Barbarians or doing another quest for them will get your foot in the door, and let the $250 you have to spend periodically give you a lot more value. For instance, that $250 will be keeping you above the "Allied" line instead of just barely making you friends with the city-state.

Likewise, as mentioned above, the Patronage tree will give you significant bonuses to your influence over city-states.

It seems that the design is such that in the early game you won't be able to guarantee a city-state ally without committing a lot of cash.

To elaborate (not 100% sure on all these numbers but the overall point is still valid):

If you spend $250 to become Friends with a city-state, starting from 0 influence, you'll get 35 influence, making you barely Friends (30 influence). This means you'll be friends for 5 turns, at which point you'll need to spend another $250 to be friends again. You probably don't have another $250 that soon, though, so the influence runs all the way down close to zero before you're able to spend another $250, which again only gives you a few turns of friendship. This is obviously unsustainable.

If instead you perform a mission for the city-state and get 30 or 40 influence to start with, every time you spend $250 you'll get to use all 35 points of that influence before needing to spend another $250.

Similarly, you'd be better off saving your money to start with $500 worth of influence than buying $250 and not being able to afford more right away.

Long story short: if you're already friends, you get more value for your money. Likewise, if you're already allies, you get even MORE value for money you spend to sustain at that level.

To directly answer the question, road maintenance is listed as "Tile Improvement Maintenance", when you mouse over your treasury/income in the top left. You can see a circled example in the screenshot below. As for the details:

Roads cost to maintain both inside and outside your borders

Because my conclusions are contrary to previous info we had about road maintenance in neutral territory... Pics Or It Didn't Happen!

Exibit 1: Prince Difficulty, some roads in, some out.

As you can see, I have 4 roads in my territory, and one outside, costing me a total of 5 maintenance. I have no other roads anywhere else. I wish I had taken a screenshot of the previous turn. The next time I find myself in this situation, I'll take a pair of screenshots and replace this single picture. Either way, remember you can always try it yourself to be sure. YaY Science!

Exibit 2: Settler Difficulty, all roads out.

Thanks to @DMA57361's questions, I checked a different difficulty and a different number of roads outside the borders, namely all of them. On Settler difficulty, building roads only outside of my borders, I still ended up with maintenance for the roads, so clearly they do cost.

Edited to account for difficulty, now that I've completed more extensive testing.

Roads cost the same to maintain in your own territory, and in neutral territory. How much varies by difficulty:

Road Maintenance /Road/Turn
Difficulty | Your Land | Neutral
-----------|-----------|--------
Settler    |    0.34g  |  0.34g
Chieftain  |    0.50g  |  0.50g
Warlord    |    0.75g  |  0.75g
Prince     |    1.00g  |  1.00g
5-7*       |    1.00g  |  1.00g
Deity      |    1.00g  |  1.00g

Road maintenance is only ever a whole number. In case of decimal remainder, always round down. For example, on Settler, 2 roads cost 0.68, which clearly got rounded down to 0.

To find each of these, I built roads either only inside, or only outside my borders at a time. This confirmed the same results for inside and out, but got me only close numbers. Then @Oak used his powers of XML scrying, and found the exact numbers for us.

Since so many difficulties are 1g, (and the ones that are not are the easier difficulties anyway,) and for our general happiness, I hereby declare "1g" an acceptable approximation for all further calculations relating to road maintenance. Hurray!

When next I can test, I'll re-test road's in another nation's borders, to clean up the next section! Same Bat-time. Same Bat-channel.

Roads DO NOT cost to maintain inside another nation's borders

Edit: This section is suspect until I complete further testing, since one road did not cause me maintenance. My mistake for not setting up a proper control. This still may be completely true, but I need to test on different difficulties and compare with similar numbers of roads in my borders and in neutral territory.

In the game these two pictures originated from, I had no roads, and built a road inside each another civilization's borders, and a city-state's borders. I can't verify that they were costing any gold to the land's owner (Rome's income was fluctuating quite a bit), but I can say for sure they were costing me nothing. This is likely what bwarner saw that caused the error.

There may be other effects that change which roads cost to maintain, but these seem to be the major ones. Anyone found anything not explained by these.

PS As with any screenshot heavy post, I do my best to crop/scale the images to reasonable sizes without losing the important parts, such as the circled text. They still end up crowding the page, for which I'm sorry.