Imagine a day when virtual cash gives central banks a run for their money – literally.

Not so fast. A Bank of Canada working paper released this week says central banks are unlikely to cede their monopoly on issuing currency to a new generation of web industry giants, such as Facebook and Amazon.

That's because virtual currencies are prisoners of their basic function: Getting consumers to buy more stuff.

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As a result, these companies are unlikely to ever make their virtual currencies fully convertible into regular cash, according to the study, Some Economics of Private Digital Currency. And without full convertibility, the use of virtual money is limited to the virtual world.

"We find that it will not likely be profitable for such currencies to expand to become fully convertible to state-sponsored currencies," conclude the authors, Joshua Gans of the University of Toronto's Rotman School of Management and Bank of Canada economist Hanna Halaburda.

The authors make a distinction between true virtual money, such as Amazon Coins and the short-lived Facebook Credits, and other digital currencies whose main purpose is the "transfer and storage of money." Think PayPal or Bitcoin.

What Amazon and Facebook want is to encourage consumers to keep coming back to their sites. Amazon, for example, issues "Coins" that give consumers a discount they can use to buy apps.

"Coins is simply a subsidy to buyers to participate in the platform," according to the report.

"Introducing Amazon Coins is potentially more convenient than subsidizing via cash, since it insures that the subsidy is spent on the Amazon app platform, and not on other services on Amazon or outside."

The authors also reject the notion that these truly virtual currencies need special new regulation.

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The case of Bitcoin – a fully convertible, pure digital currency – is more problematic. Earlier this year, the U.S. Treasury department started requiring that all virtual transactions worth more than $10,000 (U.S.) be reported to authorities to prevent virtual currencies being used for money laundering and other illegal purposes.

The authors don't reach a firm conclusion on whether governments should crack down on virtual currencies, pointing out that regulation might stifle innovation. At the same time, they warn that "multiple competing platforms creates inefficiency" that will dissuade people from embracing them.