There are also tenders, which I don’t know much about.
And I have seen auctions where they set the reserve at a ridiculously high amount, and then negotiate with the highest bidder. A few years ago, one place I was underbidder at $280k (for something that I thought should go for about $250k), final bid was $290k, then vendor negotiated that bidder up to $350k! Another I was underbidder at $190k, final bidder was at $200k, then vendor negotiated them up to $250k.
The dirtiest trick that real estate agents do is to convince/pressure vendors to bring the date of sale forward. Sale goes through at a lower price, agent does less work and turns over their properties more quickly (which vastly enhances the agents yearly profits).
New Zealand restricted sales to foreign buyers in 2018, to prevent ballooning property prices for New Zealanders. Also rich foreigners buying large farms and prime coastal real estate was unpopular with most of the voting public?
Edit: when the real estate market was burning hot, lots of sales were deadline (blind). I think deadline sales mean that the winner often has bid their highest price (I certainly did for my home). In auctions you often pay just a little bit over the underbidder, even if your top dollar might have been potentially a lot higher. When selling you mostly care about that one person who really loves your place and that is willing to, and can afford to, pay well over market price for it. All other potential buyers are just wasting time.