Notes on Burning MEV through block proposer auctions

auction off the “right to propose a block” on the consensus layer through a scottish auction (highest bidder at end of fixed time interval)
once a winner is selected, the execution block they propose will be one that provably burns at least as much ETH as their bid

Every slot, each validator has a small probability of being an eligible_proposer with some target number of max_elligible_proposers
slot_time_seconds increased to 16s, adding 4s at beginning for bidding
t = 0 , nodes (CL or EL) listen for all bids and propagate them to each other
t = 4 , eligible_proposers reveal their blocks and nodes keep track of the best_block which has the most MEV commited to being burned
t = 8 , slot's validator committee attest to what they know the best_block to be
t=12 , usual attestation aggregation period

proposers are incentivized to burn the most MEV (because then they win the burn auction and get the block reward)
builders are incentivized to bid max amount for their block to get included (not a clear reward here, its priority fees + some MEV withheld)
[question?] what is the equilibrium here? is there a dominant strategy?
an advantage of this approach is that it becomes harder for builders and proposers to vertically integrate. Because eligible proposers are random, a proposer can no longer accept blocks from relay/block builder they control/collude with

With MEV burn, proposers lose their monopoly over block proposal, so their goal is no longer about maximizing MEV bribes, it’s now about maximizing their chances to get the proposer reward

technically nothing should change for builders, they bid to win the auction to get included on chain nonetheless

theres various concerns around whether this introduces attestation based attack vectors
no way to restrict burning only MEV, proposers could also burn the block reward to win
this lowers the security budget (less payments to validators)
creates advantages for being the "best validator" and a goal of PBS is to make validators dumb

builders can coordinate upstream to not bid max profits.. and theres no incentive to burn more eth from the block builder. should be noted thus possibility already exists without burning MEV.
assumes proposers have different bids which incentivizes builder proposer coordination
adds 4 seconds at beginning of the block to bid but the best blocks are made at the end of the slot time period
this forces MEV on every validator
if no MEV for a block this incentivizes burning the block reward
bids are anounced by proposers which incentivizes coloaction i.e. Proposer will want to be as close as possible to builders to anounce bid faster