One potential issue is that, since ε_n may be negative (a proposer may subsidise a proposal), it is possible for a proposer to censor transactions on a shard for arbitrary lengths of time.
I am not convinced that this is an issue. Consider that in the current system, it is possible to simply send 8 million gas transactions with a high gasprice, which seems like it would have a similar effect.
The non-full shard
Agree that in these cases state is not required for self-proposals.
for example, using the order in which transactions appeared in the shard’s transaction pool.
This is actually an interesting hidden insight: you can use nodes in the network to filter out non-fee-paying transactions for you for free, and use this as a source of transaction data. Though this technique is likely to be quite imperfect.
In Phase 1 sharding, there is no concept of a “spam” or invalid transaction
To clarify, there is never a concept of an invalid transaction at the collation finalization layer.
This model degenerates either to there being only one super-efficient (or malicious) proposer per shard
Not necessarily. I would argue that if there is only one proposer, then that proposer gets the incentive to start rent-seeking (increasing \epsilon), and that by itself creates the incentive for more proposers to undercut. It seems like the Nash equilibrium is that there is always some nonzero probability for the dominant proposer to lose any particular bidding round, which means multiple proposers. Also, there is the possibility of proposers that represent specific applications, as well as the possibility of proposers that acquire specialized domain knowledge about fee payment in specific applications (eg. accepting fees in E-DOGE).
It’s additionally worth pointing out that if the dominant proposer tries censoring, then that by itself confers an economic advantage to all of the other proposers.
I would be interested to hear what you think about the proposal/notarization separation model that I outline in the newer post I linked (A general framework of overhead and finality time in sharding, and a proposal).