Several users in this forum have addressed bitcoin and other cryptocurrencies as ponzi schemes. Bitcoins have several uses which could legitimate its value as a currency, but also have received massive investments in the last months, making it considered a highly speculative asset. Are there signs and information that proves that cryptocurrencies are being used as a (intentionally fraudulent) scheme, or should we consider it a speculative asset similar to other assets in economic bubbles that happened before?
In general, "Ponzi schemes" in the context of asset pricing refer to "rational bubbles", or a failure of the transversality condition you need when passing from a flow identity to a present value identity. They are not "fraudulent schemes". For instance, there can be a rational bubble on a "fundamentally" worthless asset in a perfect foresight world if its price grows at the real interest rate available in the broader economy. (This is actually what you're talking about, in case it's not clear to you - each investor assumes they can offload the asset at a higher price to another investor, and you push the problem of the "greatest fool" to infinity, which makes the assumption a rational one ex post.)
Is there any evidence for the existence of such rational bubbles? Cochrane (2002) points out that rational bubble theory does not account for the association of "bubbles" with high trading volume. In a rational bubble, it is rational to hold the asset in every period: there's no reason to observe high turnover along with high prices. They are also silent on the association of high prices with high volatility - in a rational bubble context, volatility (induced by shifting from one equilibrium to another) is always present, and the choice of equilibrium (the fact that we're on an explosive price path) does not produce more volatility than usual. Rational bubbles appear to be a poor explanation of events that people have historically described as "bubbles" (and of the price behavior of cryptocurrencies).
In contrast, the convenience yield theory outlined in Cochrane (2002) and also in this blog post seems to fit the data much better. If "overvaluation" is driven by a liquidity premium induced by shorting constraints and a short-term constraint on supply, then we would expect to see the standard prediction of monetary economics that high prices should be associated with high turnover. In that case, overvaluation relative to "fundamentals" should also require shorting constraints - in the case of dollars vs treasuries, for instance, it's illegal to print banknotes or close substitutes to money to finance a purchase of bonds, which is a kind of shorting constraint. Indeed, shorting constraints are what we see in the cryptocurrency market: BTC futures have only recently started trading on stock exchanges, and even then the "electronic paper" that you hold when you take the long side of a BTC futures contract is not the same thing as holding BTC directly, so what appears like a possibility to short BTC through these contracts is in fact not so. (It satisfies "speculative demand", so it's possible to "bet on cryptocurrencies" without having to hold any, but it's not possible to use these contracts in the place of cryptocurrencies in transactions.)
If you want to ask whether cryptocurrencies are a bubble, then you have to define what "bubble" means. If it is "overvaluation relative to fundamentals", then is USD a bubble? After all, it's trading at a premium relative to T-bills. If you include any convenience yield the asset may have in your definition of "bubble" so that USD is not one, then it's likely that cryptocurrencies are not "bubbles" either. It's very difficult to say anything about whether cryptocurrency valuations are "justified" or not by this explanation, since the convenience demand of cryptocurrencies, like of cash, has components which are not transparent. We're mostly in the dark, and I wouldn't try to outguess the market price of an asset in a circumstance where we know next to nothing about the factors which are driving the convenience demand for it.
I would say cryptocurrencies are in a speculative boom phase based on examples of Ethereum being 10 dollars in 2016 and jumping to 370 dollars the following year and Bitcoin going from 900 dollars to 10,000 dollars in those same years.
With that said, speculative boom phases are poor guides to future valuations and the maturation trajectory of a new sector.
So, to answer your question, yes they are in a speculative boom phase or as you put it in a bubble.
Many people decry the current speculative frenzy in cryptocurrencies, and others warn the whole thing is a Ponzi scheme, a fad, and a bubble in which the gullible sheep are being led to slaughter.
I think what non-experts or rather people who don't write software for cryptocurrencies should do is analyze these cryptocurrencies through the filters of scarcity and utility and come to your own conclusion on a case by case basis based on the application of those filters.
A Ponzi Scheme is a fraudulent investment operation where the operator generates returns for older investors through revenue paid by new investors, rather than from legitimate business activities or profit of financial trading.
Hence, cryptocurrencies are not Ponzi Schemes, since this would require some central authority falsifying records to mislead investors. Cryptocurrencies are specifically designed to make this type of fraudulent activity, which relies on information asymmetry and trust in a central authority, mathematically provably impossible. Nobody is buying shares in an investment scheme, investors are trading an asset among themselves in the most transparent way possible (Everyone has access to an immutable public ledger, the Blockchain, containing details about every transaction that has ever occurred).
So in some sense, cryptos are the exact opposite of a Ponzi Scheme. On the other hand, one could make a case that Fractional Reserve Banking and Social Security are Ponzi Schemes.
EDIT: Other answers have suggested that fraudulent activities are not a necessary condition for a Ponzi Scheme. Other objections to my answer include my use of a non reliable source. From a legal perspective, the last word on whether something is a Ponzi Scheme lies with the Securities and Exchange Commission, whose definition should therefore be considered:
A Ponzi scheme is an investment fraud that involves the payment of purported returns to existing investors from funds contributed by new investors. Ponzi scheme organizers often solicit new investors by promising to invest funds in opportunities claimed to generate high returns with little or no risk. In many Ponzi schemes, the fraudsters focus on attracting new money to make promised payments to earlier-stage investors to create the false appearance that investors are profiting from a legitimate business.
Furthermore, it has been suggested that a group of actors attempting to drive up the price of cryptocurrencies by engaging in leveraged buying, are effectively running a Ponzi Scheme, and therefore cryptocurrencies are a Ponzi Scheme. I strongly disagree with this claim. Apart from the fact that it does not meet the definition, it is also not a claim about cryptocurrencies but about rogue actors using crypos in an attempt to implement a Ponzi Scheme. Any arbitrary asset could be traded in this way - this is not a specific characteristic of cryptocurrencies. Such "strategy" qualifies as deliberately creating a bubble, (an ill-conveived undertaking, exposing the creator to ever increasing market risk), rather than running a Ponzi Scheme.