Note that it is common in statistics or mathematical modelling to just "assume" IID distributions even though it is clearly very hard to impossible to "verify" that this is fulfilled in your practical application (in particular independence of random variables is hard to ensure for a real world system). But in particular for this example I think the assumption of IID is especially poor, to be honest.
The revenue equivalence theorem can break down if some bidders are drawing values from X while other bidders draw values from Z. Really hard to establish whether this is happening empirically.
Yeah, I think you misunderstood me. As I see it,
"Note that it is common in statistics or mathematical modelling to just "assume" IID distributions even though it is clearly very hard to impossible to "verify" that this is fulfilled in your practical application (in particular independence of random variables is hard to ensure for a real world system)." = "Really hard to establish whether this is happening empirically."
But in particular for this example I think the assumption of IID is especially poor, to be honest.
Could be. Since there is no credible way of substantiating this empirically, I prefer not to speculate.
Note: The traditional auction format (winner pays his bid) doesn't generate accurate valuations if the revenue equivalence theorem breaks down either. The gold standard "theoretical" auction format for revealing true valuations is the second-price auction, where the winner pays the second highest bid instead of the highest bid. Here the Nash-Equilibrium is always bid your true valuation. The random process generating valuations becomes irrelevant for equilibrium analysis. Again, real people don't behave as game theory predicts. Give them a traditional auction, complex from a theoretical perspective, and they feel comfortable bidding. Give them a second-price auction, simple as anything from a theoretical perspective, and they get confused.
I actually hate auction theory.
a) limited relevance outside of a very narrow sphere of economic life
b) almost useless empirically (once you move outside of relatively simple situations)
c) a lot of complex math (facilitating the type of penis comparison contest adored in all male-dominated fields)