I'm going to answer this with Ponzi Schemes. Which differ slightly but are similar in overall method. The scheme is named after Charles Ponzi who ran it in Boston in The Early 20's. I would go into greater detail but His autobiography is available online and is definitely worth reading. The writing isn't exceptional but the story is so good it easily makes up for it.

The idea was around before Charles Ponzi but he was the first very successful one I know of. The first recorded I think would actually be the fictional one described by Charles Dickens in Martin Chuzzlewit.

It would help if we defined the terms first because there are essential differences between a Pyramid Scheme, a Ponzi Scheme, and an Investment Bubble, although they do have the similarity that if they do not keep growing, they collapse, and they have a finite size, but I do not think that they answer the question.

In an Investment Bubble, like tulip mania, the South Seas bubble, the Railway bubble or the Dot.com boom, investors buy goods or shares, which initially usually have some “real” value, at above that value because they expect the value to rise and that they will be able to sell at a higher price. This raises the price of the goods or shares, fulfilling their expectations and other investors, also wanting to profit, buy at the higher price, expecting further price rises. A bubble is typified by a large pool of naïve investors entering the market and expecting sure profits. The bubble bursts when the prices rise so far that they cannot find new investors and prices fall back to, or below equilibrium with the later investors losing large amounts of money. While there may be some opportunistic fraud in the investment rush there is no inherent fraud in an Investment Bubble.

A Ponzi Scheme, occurs when a fraudster offers to receive monies for investment at a higher than normal rate of return to favoured insiders. The investment method may be secret or rely on some special opportunity, access, or skill to be provided by the fraudster. In practice the fraudster does not invest the capital received to get the claimed returns, but uses it partly to finance his/her own lifestyle and partly to initially pay out the advertised high investment returns while encouraging the investors to keep their capital in the scheme and recruit friends and associates to this special opportunity. The Ponzi scheme crashes either when it cannot recruit enough new members to fund the outsize returns, more investors want to withdraw their capital than can be funded by new members, or there is a competent audit of the investment program. Typically most funds have been expended by the original fraudster and the remainder mismanaged to keep up appearances so anyone with current investments at the time of the crash loses most of them.

A Pyramid Scheme works like a Chain Letter. In a classic chain letter you receive a letter with, for example, a list of ten names on it. You are told to send a reply to the name at the top of the list, remove that name from the list and add yours to the bottom. Then send the new list and the instructions to ten new people. When your name gets to the top of the list, you will receive 1,000,000,000 letters. In the U.S. they have been identified back to the early 1930s but are probably based on earlier ones. They tended to be visible to the postal authorities.

In a Pyramid Scheme you are asked to send a particular amount of money or something else of value with the letter to the name at the top of the list in the expectation that you will eventually receive a multiple of that amount when your name gets to the top. Note that you are not purchasing any goods or services, just the “authority” to forward the list. The scheme may be touted under different names and in meetings rather than by mail and victims may be encouraged to “buy into” multiple lists. There is no one particular fraudster. Essentially, everyone who takes part in it is promoting the scheme. They crash because the population size is never sufficient to meet their expansion. Most people lose all of the money they use to “buy in”. They are illegal in the U.S. and in Australia. (I don't know enough about other legal systems).