Suppose the hardware power and network bandwidth are unlimited
You still have latency. "Bandwidth" is the transmission rate … I mean how much data can be sent and received in a given period of time.
That says nothing about how much time a given piece of data needs to reach its destination. That is, latency.
Why should there be a bad latency? Because of the network. I'll let Grace Hopper explain you nanoseconds.
Due to the poor latency in a game, the server's response takes some time to reach the clients. A. k.a. Lag. Of course, this is not the only cause for delays. Regardless, network latency causes delays.
So you can have a magic server that has infinite storage space and executes commands in virtually zero time, and the game still has a delay.
That means that regardless of the magic of the servers, it still makes sense to distribute multiple servers geographically across the world. And of course, everyone would connect with the one closest to him.
Of course, you may have multiple Magic Servers and load balancing between them, preventing all uses from being aggregated into a single server. In this case, however, no load balancing is required magically …
… except, well …
If we have a hub where millions of characters are moving … your server may be magical, but the client may not. It is a good idea to logically separate entities, if not physically, so that the client does not have to render everything. Why? Because the client's hardware is another cause of delays.
Since you have a perfect magic server, you can decide exactly what each client should see, so that clients do not have to spend time deciding to draw …
… waiting …
(This may be an open question, I'm not sure if I should ask questions here, but there does not seem to be a better place to put them, and I hope I can be inspired by discussions.)
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In a world where servers are magical, the server can render for the clients.
is there a corresponding economic, sociological and ecological model behind this?
In this universe, the computing power is unlimited. That does not mean it's free. We did not say anything about the energy consumption.
I do not know if it applies in your fictitious universe, but in ours there is a maximum theoretical data density. This means that your magic servers take up an unlimited amount of physical space (I expect to grow as needed).
Likewise, we have a theoretical minimum time. The plank time. Since we can not really do anything in less than a plank time … to do more things in the same time, we need more CPUs.
In the game
If we have a conventional MMORPG, there is a chat window. Imagine the chat window with news in all the languages of the world passing by at ridiculous speeds. While not separated by physical servers, it's a good idea to be able to filter by language.
There is also the problem of the masses. It's a good idea to have fewer channels to separate people. Not only because of the customer's performance, but also because large crowds can adversely affect the gaming experience.
A server that can grow indefinitely will certainly attract the attention of the authorities. What if it grows from a jurisdiction? Will different laws apply to different parts of the server?
Back to energy consumption. We do not have a growing server that could eat ecosystems … we have to feed the beast, and power plants affect the environment.
I would actually have to do the calculations – I do not take that answer seriously – to find out if you need a Type I civilization to have these servers.
See also: Matrioshka brain.
Let's face it, you do not really have the problem of having magic servers. All you need to know is that the network has latency.