Wouldn't someone want the money though? What if they got paid whether the game was completed or not in a given time frame? That's how a lot of government contracts work

Game developers are passionate about their craft. They want to make a good product and they want to see the product marketed well and succeed in the marketplace.
Another thing: Game developers do not want to spend the majority of their time teaching the client about the industry.

And it is usually the game development studio that pitches their game idea with prototype to a publisher to get the cash not the other way round.

Not true. Many times, the publisher approaches the developer and says, "we have a game we want developed." I know of no studies that could provide percentages of developer-concept projects compared to publisher-requested projects, so I don't think you could say either one is more "usual" than the other.

The fine folks in the Business and Law forum on the site are typically more experienced at that sort of thing. This is the For Beginner's forum.

Not any more it isn't. Now this is in Business and Law, where it belongs.

Can anyone point me in the right direction as to where I could find such information if I gave more detail.....?

Right here. What is the platform, genre, and monetization method of your concept?

Can anyone point me in the right direction as to where I could find such information if I gave more detail.....?

No one will be able to answer the question in general, because the working out even ball-park timeframes would depend on giving a specific team all of the precise details, and having them draw up a schedule. Different teams and different details will come up with completely different schedules/budgets for the same project. You can't really take a quote from one team and give it to another team and expect it to still apply.

Maybe if you can compare it to another project, you'd be able to get info about whether that other project was in the $1k/10k/100k/1M/10M/100M range...

Basically, you'll need to approach a work-for-hire game developer (usually: ones that aren't owned directly by a publisher, but make games for publishers), and tell them that you're in the market of having a game made. You'll tell them the kind of money you want to spend and give them your design, and they'll pitch you back a plan (or laugh and curse you, because you've given them a $10M idea with a $10k budget). If you like the pitch, your lawyers will then draw up the contact including all the milestones, and you're in business.

I would like to make sure that I have covered all avenues, so to speak, before I give more details (hope you undertsand), But as soon as it is done I will be in touch.

The only details we need to give you a vague ballpark number is platform, genre, and monetization method. We don't need a title or a story or anything else. And please don't PM me or email me asking for a number -- that would be an entirely different matter from your original question:

timescales etc etc.

an anyone point me in the right direction as to where I could find such information

We can give you a rough idea of timescale and moneyscale right now, and we don't need a lot of information from you. You say it's "an online game." So does it run in a browser or is it to be downloaded? Is it multiplayer realtime? And are you planning to sell it to a publisher (that's one "monetization method") or are you going to self-publish and make money by ads or microtransactions or subscription? We don't need to know much more than that to tell you how long such a game typically takes and typically costs.

For me, my game development is just a hobby, and has cost me nothing other than the power bill.

If you do all the code and art yourself, the project will be fairly cheap.

Your only expense may be web hosting to get the project out there and perhaps a few hundred dollars for a small online advertising campaign.

If you are not doing all the work yourself:

Outsourcing your artwork is not too difficult.

Outsourcing code is something else. You may need to pay someone full/part time and most people with the experience to do so will probably prefer to work for a larger company or pursue their own projects.