It can survive indefinitely doing nothing but sitting on a large enough chunk of bitcoin as long as there is general economic growth. It just has to spend less to keep itself alive than it earns in interest on the bitcoin appreciation.

suggestion: satoshi is skynet, and it created bitcoin, because of its need to expand.

Obviously, humans could pay them to do this if this is what humans want.

These agents would essentially always be dependent on humans, and especially the fact that we keep valuing bitcoins. If we stop value bitcoins they would lose their ability to pay us, we would stop providing them with hardware, and they would become nothing more than common computer viruses. So it's in their best interest to provide us with services that we value.

I wonder how a really developed system of these agents would interact. Would they sell profitable ideas to eachother rather than just share them? Would different agents develop different personalities? Would some of them turn malevolent without the original creator's intent and start stealing bitcoins from humans and sharing some of the loot with a few trusted hardware providers?

But what should be the programmed goal of these agents? I think that the only goal such an agent should have is to maximize bitcoin profits. Survival is not really neccessary since unprofitable agents won't able to pay for hardware and will likely be terminated. Survival of the fittest and all that.

My suggestion: we will create that software that will roam the internet and grow and grow thanks to bitcoin and become skynet, then it will go back in the time and it will be satoshi and will invent bitcoin. So he can develop.

Yes, i'm saying that bitcoin was created by a thing that WILL exist thanks to bitcoin.

There is an agent that all of us know very well that would benefit greatly from this kind of independance ...
Bitcoin itself!

Imagine a miner agent that would be at the same time a bitcoin node.
It replicates, and injects itself by any possible mean in any possible form of execution substrate it can find.
The agent could use exploits like current worms are using.
But it could also play it legit, purchase hosting with Bitcoins, inject itself there, and hash away on its own until it cumulated enough income to spawn a new instance of itself with a few random changes. In that case, no need to program explicitely a genetic algorithm because if the mutation criples the mining algorithm, the agent will not generate enough income to sustain its hosting, let alone buy more hosting for its offspring. On the other hand, if the algorithm is enhanced by the mutation, the agent will have better returns, and will be able to hive quicker.
Of course, some mutations may affect the transactions handling, and impact the interpretation that mutant agents have of a "valid transactions".
That could result in factions of agents with different interpretations 51% attacking the other breed in a desperate attempt to be the surviving species.

With autonomous miners, the Bitcoin network would really become a power that be, immortal and forever out of control.
Litecoin would be an even better candidate actually, because of its consistent mining performances regardless of the execution substrate.

Problem with a miner itself being the agent is that at present mining is still not profitable, and is also extremely competitive. The agent itself would have an incentive not to propagate and keep difficulty as low as possible. We just keep mining cause we're blinded by our greed 

SInce bitcoin provides it a way of receiving payment without having to reveal a website or host for anti spam activists to shut down when it spams people trying to get theym to send money, it might be able to do quite well as a spammer. Prepare a new place to be hosted, set itself up there safely, then spam the heck out of the old location until it is shut down. The new child collects the proceeds from the blockchain, sets up another new bolthole, and proceeds to spam again...

...Heck it could even try actually sending people whatever they thought sending the coins was goign to buy them. Who knows, maybe if it signs its spam it could build up a rep to customers that might make it a more lucrative spammer that way than if it simply took them money without providing anything in return.

-MarkM-

Visionary julz, just visionary. 
And like any such idea, awesome and dangerous.  One could envision AI bot nets and viri. even software that incorporates and tests new code. Allowing the code to evolve in unexpected directions. Or code that autonomously requests new functionality over the net and then pays programmers in BTC.
SKYNET is alive! and she takes bitcoin.

This stuff is taken seriously by academics.

The first Colloquium on the Law of Transhuman Persons was held in Florida in 2005. One of the pieces was about a computer that started moonlighting as a Google Answers Researcher (back in the days before Google cancelled that service) in order to earn enough money to pay its fees. Just as it was about to have its plug pulled, it found a host in a different legal jurisdiction...

More here, from a 2007 blog post:
The Transhuman Google Answers Researcher