You can participate in multi-person barter exchanges, without the need for any central authority.
Barter is a way of exchanging goods and services without the need for any money. Two people can simply trade with each other if they have mutually complementary needs. Trades involving larger numbers of people allow for more flexibility in finding people who can supply what other people want. Here's a way to carry out a multi-person trade by dividing it into multiple two-person trades, so that it isn't necessary for all the people to come into a room at the same time and shake hands to decide whether the trade is going ahead.
Suppose you've found a loop such that person A can give something to person B; B can give something to C; C can give to D, D can give to E, and E can give something to A. Here's a way to essentially divide up that multi-person trade into two-person agreements, so that each person doesn't have to worry about the details of the other people's parts of the trade.
Person A can start the process by creating a key with a password, perhaps using a website found by a web search for SHA generator. There are websites where you can just type in a password and receive a key which is a string of numbers and letters, although when large amounts of value are involved you may want to use a more secure method.
Person A keeps their password secret at first. A shows the key (not the password) to B and says, for example, "If you give me the password for this key by June 30, I'll give you one hour of guitar lessons." A knows that B can't provide the password because only A has it (provided A has used enough safeguards to keep it secret). B then gives the key to C and says, "If you give me the password to this key by June 23, I'll give you one hour of language lessons." B can make this promise because B knows that if C gives B the password, then B can use it to get a guitar lesson from A. C makes a similar declaration to D, and D to E, and finally E says to A, "If you give me the password for this key, I'll give you 5 kg of organic vegetables."
At that point, A finds it worthwhile to give the password to E. A doesn't need to know the details of the trades the other people are doing. A doesn't need to know or trust all the people involved, or to trust that nothing will go wrong with any of the trades in any way. All A needs to know is that A can get vegetables from E by providing the password. The password then gets passed around the circle, and A ends up providing guitar lessons to B; or A might just go ahead and provide the guitar lesson as soon as A decides to disclose the password.
This is similar to the use of money in that the specific trades A is involved in (with B and E) are separated from the other parts of the trade. When you spend money, you don't usually know or ask what the other person is going to use the money for.
The difference between barter and money is that there is never an overall shortage of ability to barter. When people are short of money, they might say "I'd really like to buy your product, but I don't have much money these days and I need to save it for the essentials." A bunch of people could all be saying this to each other and no money circulates, even if they each have some money and they could all benefit by trading with each other. With barter, people can use their own labour to buy from others. They're not agreeing to receive anything until they know exactly what work they're expected to provide to someone in return.
When people don't have easy access to computers to work out keys and passwords, there are other ways of doing it. There may be physical objects such as a stick of wood, an eggshell or some types of rock, that one can break into two pieces and easily see whether the two pieces fit together to prove they came from the same original object. Person A can break the stick, keep one half, and give the other half to B saying "If you give me the other half of this stick, I'll give you one hour of guitar lessons." That half of the stick gets passed around the circle, until A pulls the other half of the stick out of hiding and gives it to E, demonstrating that it fits, and the trade goes ahead.
Another way to do it is on paper. Person A can take a piece of paper and mark two boxes on it labelled "sample signature" and "final signature" (as on traveller's cheques), A signs a sample signature but leaves the final signature box blank. A writes "If I sign in the final signature box I'm agreeing to provide one hour of guitar lessons to the next person on the list." A or B can fill in B's name as the person receiving the guitar lessons. B then writes "If A signs in the final signature box I agree to provide one hour of language lessons to the next person on the list." and signs it. C, D and E each write "If A signs in the final signature box..." And so on, until E hands the page to A with an offer to provide 5 kg of organic vegetables. A then finds it worthwhile to sign in the final signature box in order to receive the vegetables. The paper gets passed around and the various goods and services are provided.
Person A is the only one who needs to provide both a sample signature and a final signature. The others simply sign it. The sample signature is because people who have never met A might be part of the trade, and they may want to verify that A's signature is real. Everyone is talking directly to the people they're giving to or receiving from, so they may have established a level of trust, or can watch the person sign or ask them whether that's their signature. They may not know A or may not be talking directly to A during this trade, but they're declaring "If A's signature gets filled in, I will do ..." so they need a way to be sure whether A's signature has genuinely been filled in.