Sample pooled schemes include private and public pensions, annuities, tontines, and the TIAA-CREF "traditional" scheme, or (a French example) a viager. ..

Just a side note on the latter. Very obscure if you're not French, but it could conceivably be of interest for retirement for some non-French people.

A "viager" contract in France is a very old, and surprisingly popular tradition that an elderly person sells their property (house or apartment) in such a way that they get to use the place for life, but the buyer gets it when they die. This is accompanied by (usually) a lump sum payment to the seller at the start, and (almost always but optional) a monthly payment to the seller for the seller's life thereafter.

This raises an interesting alternative, based on two observations: the seller of the place does not have to be a resident or citizen of France, and the monthly payments are often adjusted for inflation. The French government publishes an index for this.

Thus, one way to get a fully inflation-adjusted income for life (admittedly in Euros): buy one or a few places in France. Apartments in Paris and houses on the cote d'azur are particularly popular. Immediately turn around and sell it/them as a viager against your own lifespan, for income only. The catch is that typically you have to be actually living in the property (a "viager occupé"), and if you're not living there and the buyer gets use right away it's a "viager libre". The "viager libre" exists, but I think it's a bit more rare, so I'm not sure if that means it's harder to sell or easier. I dunno.

A random example: A French male age 68 selling a property with normal market value 500k as a "viager libre" (they don't get to live in the place) might get just under 8%/year income for life, as a percentage of the normal market value of the property. That might drop to 6.36%/year if the deal included a 100k initial payment ("bouquet" in the jargon).

Jim