Private property is a regulation. You can't even barter if the other guy has no concept of ownership, he'll just take it from you. Markets are invented by regulations.

I think at this point we're talking about laws, not regulations. You can come down off a mountain with a couple of stone tablets and that's enough to get going with barter, as barter is individuals deciding how much things are worth to them.

Conversely, the carbon market is invented: there is no natural value of the negative externality of pollution, so we invent one. And, as it's invented, it's riddled with holes.