That is, to be precise, reserve banking is not intrinsically a Ponzi scheme ... provided the credit contract created by the bank is sound, the credit money is sound.
What is required to prepare reserve banking for the post-peak loss of ongoing extensive growth, to be replaced at best by periodic waves of technology driven intensive growth, is a return to low and stable cash rates and regulation of banking operations to require prudent behavior.
Or, in other words, all those prudential regulatory schemes instituted in financial centers after the Great Depression, which have been progressively stripped away since the 60's. I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.
A Ponzi scheme (or Ponzi financing, as in Minsky's theory) is a scam initiated by an entrepreneur seeking investment. Mr Ponzi himself did this that way: he promised and initially gave high return for investment, which attracted much more investment, so that for a while he was able to give high returns from the investment growth alone. But of course, he had top cut and hide at some time.
Ponzi financing may occur not only as a designed scam, but from enterpriser's desperation as well. I call the Russian GKO scheme because the initiative came from the Russian government (for whatever reason), not from investors.
The situation of "too much money chasing too few assets" has different flavor. Here the initiative comes from eager investors. The mild term for this run is "asset inflation". I would avoid to use "Ponzi" or "pyramid" terminology here. I do not actually know how to call this stronger.
In a narrow sense, a pyramid scheme is a scam with a defined structure (mathematically, an exponentially growing tree graph) of cash contributions and flow. Here there is no formal distinction between investors and enterprisers - everyone plays the same role if only the game can continue indefinitely. Ironically, the current situation with all investors borrowing and all entrepreneurs investing is very analogous in this respect.
More generally, to incorporate the cases like CDO (presumably) a pyramid scheme can be defined as any designed or emergent financial structure with something organized within an unsustainable pyramid "geometry", as Liu describes. That would be the general idea.
The first paragraph should end: But of course, he had to cut and hide at some time.
The last paragraph should better by typed as More generally, to incorporate the cases like (presumably) CDO, a pyramid scheme can be defined as any designed or emergent financial structure with...
And the stronger characterizations of "asset inflation" can probably be "bubble" or "overheating".
Prudential finance involves debt that can be serviced by the income from the financed activity even if income flows from the funded project fall short of projections ... how prudent is a matter of how bad things can turn and still service the finance.
The trap that CDO are heir too is, rather, a debt-farming shell game. If the top tranche of a CDO is considered an investment grade asset, and so allows participation in non-investment grade activity by those limited to holding investment grade assets, and the low risk premium = high price of the investment grade tranche(s) more than compensate sofr the high risk premium = low price of the junk grade tranche(s) ... then instead of the classical small town bank looking on the interest on mortgages (and small business loans) as its bread and butter, mortgages become a way to generate ongoing commissions on origination, selling the mortgages on in order to be able to originate more.
Of course, market pressure will invariably push the finance sector into non-prudential behavior until a series of events realises the systematic risk that has been lying dormant ... unless a regulatory authority imposes a market penalty for engaging in non-prudential behavior. And it is the reaching for those short term gains (ignoring their attendant long term pains) that has driven the ongoing stripping of prudential regulation from financial systems around the world. I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.