Searcher Bidding Complexity Due To PBS

In thinking about how the auction for bundle inclusion will change under PBS the following problem came to mind.

There are effectively two auctions happening. One for bundle inclusion and one for block inclusion. Searchers know how to bid for bundle inclusion, however block inclusion is very different. One may be faced with a scenario in which the sum of the winning bids for bundle inclusion in a Flashbots block (flashblock?) is not sufficient to win the PBS auction, despite the block being the most valuable block produced. In order for the flashblock to make it on-chain, searchers must work together and bid more than they need for bundle inclusion to facilitate block inclusion.

Below is an example of such a scenario (it may be a little unrealistic, but the problem is more general than the example). The example shows two distinct MEV opportunities being bid on for inclusion in the Flashblock. For simplicity, both opportunities are only pursued by two searchers, the superior of which has a good inkling to what the other can extract/bid.

### This seems unrealistic
* Argument: No one will come close to creating blocks with a similar value to ours
* Response: This is a strong premise, we should have good reason to assume weak competition if we do
- Response: One can imagine something like Yuga requiring all NFT mints to go through a certain wallet.
- Argument: No way searchers have this much profit left after getting a bundle included
- Response: Long tail MEV
- Response: Exclusive order flow is a problem. For example, we recently spoke to Rook searchers who had no competition for block inclusion because of EOF (for which they didn’t have to pay that much).
- Response: PBS may end up being a game of inches
- Argument: This will be rare
- Response: Even if it is rare, there may be many such blocks in a row leading bad UX (e.g. if this arises from specific market conditions like a Coinbase wallet incentive)
- Response: With EOF it may not be.

### Why this is a problem

- Searchers face a lot of uncertainty. It is hard to know how much everyone else is willing to bid for block inclusion especially because of the following uncertainties:
- What other bundles will be included in the flashblock
- How highly other searchers value their bundles
- How high other searchers will bid to include their blocks

This provides incentive for searchers to **merge/form coalitions** to coordinate on total bid (centralisation)

- EOF of other block builder gains traction.

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#### Some discussion that already happened
On the point about searcher uncertainty: "and the argument is that this incurs a lot of overhead on searcher’s side, so the collective time they spent playing mind games because of the existence of 2 auctions instead of 1 is negative sum. So we should devise a better mechanism design?"

Response: "Yes negative sum bc of time wasted and revenue wasted on blocks that don’t make it because someone else is trying to game the system or on overbidding to compensate for potential slackers.
May also see searchers invest more time in auctions that see them more reliably included/with more “fair” UX for searchers."