Cross-domain auctions are so **** hard :(.

More thoughts on this: Making a truthful, credible and 2-welfare approximated cross-domain auction is reasonably easy by using DRA (https://arxiv.org/abs/2301.12532) on the bundle, when sellers (validators) do not have access to side-channel/separated auctions.

When there is no cost incurred by bidders that just win one of the blocks, separate auctions are close to efficient (see https://arxiv.org/pdf/1408.1211.pdf). I guess when there are costs, this is no longer true...

Note: I think that 2-approximation can be improved by changing the commitments and running a VCG auction. But this is not the problem. When validators can run side-channel auctions, the problem is how to compare the revenue of running two separate auctions to the VCG one.