Storybuilding vs. worldbuilding
As you read my answer you'll see me point out issues that are "storybuilding." Questions about storybuilding are off-topic. We'll help you build your world, but we won't help you write your story. Questions about law and other civilization-building questions are sometimes tricky because civilization worldbuilding is about structure and the moment the question isn't about structure it's storybuilding.
Thus, I hope not only to point out where you will have creative choices to make, but also the difference between structure questions and story questions.
It's important to know that I'm not going to tell you what specific regulations will exist. That's storybuilding and a violation of the Help Center's admonition against brainstorming. I'm going to identify worldbuilding issues that will guide you with your story and help you decide what regulations you want.
Let's begin.
The World's Most Concise Overview of Regulation
- You have the right to do anything you want until that action interferes with someone else's rights.
- Storybuilding: the author must establish what "rights" people have because there's no objective "correct" answer.
- You have the right to do anything you want unless you're consuming a resource the government (or a corporation/individual with enough influence to change laws) deems critical.
- Storybuilding: the author must choose what resources are "critical" because there's no objective "correct" answer.
- You have the right to do anything you want unless enough people complain about it.
- Storybuilding: the author must determine whether such people even exist and if they do, what they're complaining about because there's no objective "correct" answer.
- You have the right to do anything you want unless cultural morality has established social mores and/or taboos.
- Storybuilding: the author must identify cultural morality and how society reacts to violations of said morality because there's no objective "correct" answer.
The numbered items are worldbuilding, the establishment of structure. The bulleted items are (obviously) storybuilding because they represent an arbitrary choice made by the author, usually to address matters of narrative necessity.
Issues involving regulation
Jurisdiction: I wonder if it can be possible to colonize the solar system to the extent you describe and still have regional, nationalistic jurisdictions. But let's roll with it. The U.S. would have no jurisdiction concerning the space controlled by a (e.g.) Chinese colony and no nation would have arbitrary jurisdiction in any area of space deemed "international waters," which means you're dealing with international treaties. Oversimplifying something awful, activities in international waters are a free-for-all other than the basics: no stealing, first-come-first-served salvage, don't mess with somebody else's stuff, save the whales, etc. In a nutshell, what's mine is mine and what's yours is yours if there are arguments we'll make a treaty and so long as we all respect that you can do anything you want. But does that mean there's no regulation?
Heck no.
Maritime law is messy and complex. It's a LOT of regulation — and you're subject to your universe's intrastellar space version of it. Can I explain what aspects of maritime law might be involved with your universe? Nope — not only is that storytelling, but it's a violation of the Help Center's book rule. But it would be a good idea to do a little study about maritime law and what it means to, e.g., own or live on an island that isn't claimed by any nation... if there is such a thing anymore (and that's important to you, too...).
Activists: On the other hand, if there's a single person in the universe who can be offended by your gladiatorial fights, no matter how safe for the participants it may be, there will be someone with a sign protesting the violence. Laws and treaties change and they often change because someone's complaining about something. Activists are a convenient way to invoke change in a story. Wouldbuilding describes the rules of activism. Storybuilding is identifying an activist and how he/she acts. In other words, if you want regulation under the circumstances you've described, then you can use your universe's version of Greta Thunberg to rationalize those regulations.
Science Isn't Perfect: You're trading on the belief that a consciousness can be uploaded and/or moved around pretty much indefinitely without consequence. Science doesn't actually work that way. Nothing's perfect — especially when it comes to safety. In a world where moving consciousness around is a common-place thing there will already be regulations in place governing safe transfer, registered technicians (think "licensed contractor"), educational qualifications, certified equipment, and (worse) an entire body of law concerning the issue of duplicates (if you can move it, you can copy it) including legal rights of doppelgangers, legal disposal/control of doppelgangers, etc. All of this exists outside your sport, but acts to regulate your sport — and it will be can be voluminous and messy. If you want a real life example, look up the laws governing self-termination (Voluntary euthanasia) in U.S. states or countries that allow it.
From a story-based perspective, you can add flavor to your story with psychological studies into the effects of transferring consciousness too many times or the effects of copying said consciousness. This invites regulation in the same way that video games are labeled "mature audiences only." The greater the risk, the greater the regulation, which brings me to...
If it ain't real, it's not a sport: Unless your story wants this all to be dark-web, black-market, back-room cock fighting kind of stuff, then you'd have minimum-age-adult-consent and being-of-sound-mind regulations for two reasons:
While our world today is filled with people who have enormous fun playing video games wherein "people" die and plenty of red pixels are generated, half of the reason such games exist is that they're inexpensive. You'd find, I believe, far fewer participants in something as expensive as actual robot-on-robot action when there's no more emotional investment than what's found in a video game. Nobody actually dies in video games... but nobody feels actual pain, either. Add the pain and, worse, the agony of death and suddenly you have a massive psychological impact to the players. Consider the regulations surrounding boxing, ultimate fighting, or any other form of "blood sport." If you want a taste of this, consider watching Will Smith's movie Concussion, and pay attention to both the efforts to protect the players and the efforts of the U.S. football industry to avoid the regulation.
And if you had the "whole experience," (pain... death...) then what's the point of playing with a copied consciousness? Oh, you could "save yourself" by having a backup copy somewhere... but that copy never had the experience. Where's the fun in that? Where's the adrenaline rush (if you have a digital version of that)? Where's the risk? Where's the educational experience that makes one a better athlete? We're back to boring! I'm not saying NASCAR people are only in it for the risk and chance to see a magnificent crash... but I need only look at the number of spectators along U.S. highways to know that without all that risk of real pain and real death, you wouldn't have a profitable sport. And that means no consciousness backups — and that invites regulation to ensure the
idiotscontenders really arebored stiffprepared for the consequences. Thus, it would be helpful to review the safety regulations involving auto racing.
Money: Finally, where there's money, there's regulation. That's just a fact of life. If there are rules above worldbuilding that are immutable, one of them might be, "money changes everything."
Who cares if two rednecks head off to the middle of nowhere and beat the crap out of each other? With the possible exception of spouses and close friends, nobody.
Who cares if two rednecks regularly head off to the middle of nowhere to beat the crap out of each other? If it's a good fight: bookies, food sellers, T-shirt hawkers, spectators...
Who cares if two rednecks advertise that they'll be in the middle of nowhere beating the crap out of each other? All of the above plus the land owners, marketers, citizens-concerned-about-juvenile-diliquency...
Who cares if two rednecks hire managers to help them monetize the fact that people are interested in watching them beat the crap out of each other?
Governments.
And governments get involved notably when the industry is bad at self-regulation, such as not having consistent and well-enforced rules (aka "regulation," it just lacks governing sanction). If you want a humorous look at the development of government regulation in U.S. sports, watch the movie Leatherheads.