This argument is getting a bit technical, but this is what I said:
No, the company is still doing its 100% IPO. The underwriters essentially short sell on top of the 100% if there is huge demand. And when they buy back, they usually don't put up "walls" at the IPO price, they just buy back cheaper, otherwise they don't make money and have no incentive to do this. The greenshoe option is exercised by the underwriter to protect him from loss if the price actually rises.
No, the company is still doing its 100% IPO
The company can raise more than initially planned if the greenshoe option is exercised, i.e. if the post-IPO price is above the IPO price.
The underwriters essentially short sell on top of the 100% if there is huge demand.
It is very rare for the IPO to be under-subscribed, even if it is most likely over-allotment option will be present.
And when they buyback, they usually don't put up "walls" at the IPO price, they just buy back cheaper
There hasn't been much research on the exact execution of the buyback (because the data is private). It is true that the buyback happens at prices below the IPO price, on average at around 5-15% discount.
otherwise they don't make money and have no incentive to do this.
The underwriter is making money on the fees. By increasing the size of the IPO through over-allotment option, the underwriter is collecting more fees if the over-allotment option is exercised. By not exercising the option and doing the buyback the underwriter is making a trading profit, however there is reputation damage for underwriting unsuccessful IPO and this is not the desired outcome.
The greenshoe option is exercised by the underwriter to protect him from loss if the price actually rises.
The underwriter never has a trading loss on the IPO. If the post-IPO price is above the IPO price by exercising the over-allotment option the underwriter is covering the short position with no profit or loss. Don't forget the extra fees from the larger IPO.
Regardless of the actual mechanism, the over-allotment option is there to offer price support. If financial markets can offer this support, with all its regulation and due diligence we should at least demand the same from the crypto IPOs.