Some research suggesting that yes, people who know better really do compete to be the Greatest Fool:
Even people who understood exactly how much the asset was worth were overwhelmingly likely to pay, say, 60 yen for a share of the asset (the experiment was run in Japan), even when the most dividend income they could possibly get for it was only 40 yen. They gave up certain gains.
I remember talking to my friends back during the NASDAQ bubble and the housing bubble, and I already figured that was the case. But apparently some Very Smart People are very attached to the idea that Very Smart People are smarter than that. Which just goes to show how dangerously stupid Very Smart People are.