Wait did you say money?

Money doesn't exist in the situation you describe. Who is issuing the money? At best trading for good is the best possible.

Money is just a concept. Whether that's governement issued legal tender, gold, cigarettes or coffee beans doesn't really matter. Silver coins were in use long before governments started stamping them.

bitcoin does though

But without anyone to engage in fiscal or monetary policy to protect the value of BTC, it'd be vulnerable to huge swings in value.

Well, despite what anarcho-capitalists may say, in an anarchist society you would find it very hard to maintain capitalism as is familair to us today. This is because the State, and by extension its threat of violence, enforces private property rights. In a truly anarchist system where no other protection force evolves to reinstitute the government's role in protecting private property, you would have a very hard time building large amounts of capital. You may be able to control some small amounts of relatively private property (in addition to some personal property), but you absolutely could not maintain the current breadth of our global supply chain without the credible threat of violence from a large organization bent on maintaining private property rights.[0]

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[0]: Merely the threat of violence from a large organization, but not one with a goal of maintaining private property rights, is insufficient to maintain capitalist supply chains, because such an organization would naturally try to increase its own power through force. It would look more like a warlord, cartel, or small-time dictatorship with all of the corruption that implies than a smoothly working system of trade.

If you run a pub, either you're tougher than any challengers or you employ bouncers. Maybe you even have the local community on your side because they like how you run the pub.

The problem is if someone amasses enough capital to pay a gang of thugs to do his bidding. Then you can just take over properties, which earn you more money to pay more thugs. You can easily scale that to a global organisation. That's basically what drug cartels are. They run just fine, trade with other illegal organisations etc. It's just that the overhead of building infrastructure and providing security is enormous, so it only really works in extemely high margin industries like illegal drugs.

But according to anarchist theory, those thugs wouldn't do that because that would violate anarchy. This is the problem with most political theories. They assume near 100% compliance.