To avoid “phantom traders,” people who sign onto barter platforms and get goods or services without returning them in kind, Mr. Mouroulis requires users to provide identification and financial guarantees. A social activist who says he is driven by an ethos of solidarity for Greece, he has been meeting with other barter club founders to strategize over whether his model can help.

With just 85 members, Free Economy is hardly a parallel economic universe. But for some, the system has become a lifeline.

Jorgos Kazianis, 59, an experienced electrician who worked on projects like the Athens metro, had not found steady work since 2010 until he heard about Mr. Mouroulis’s network. He wired Mr. Mouroulis’s garage in exchange for alternate currency, which he used to procure olive oil, food and motorcycle parts. Other people began contacting him through the barter platform and now, one out of every five projects is a barter deal.

“It makes a difference,” Mr. Kazianis said. “I have virtual money in my barter account, and the best part is, there are no capital controls.” He does not trust the banks, and has €400, about $445, in his regular bank account, but €600 worth of virtual currency in his Free Economy account.

While some view bartering as a step backward, Mr. Kazianis said he saw it as a natural progression to relieve some of the misery that money — and the country’s membership in the euro currency — has brought to Greek society.

“Since ancient times, when there was no money, transactions happened through bartering,” he said. “I have no faith in money the way it has evolved today. This crisis is the byproduct of what money has become, where there’s a lot of it in the hands of the few, and a deficit of it for most other people.”