(1), (4), (5) and (6) imply that all miners are withholding all hash power until the total fee in mempool hits a desired threshold. I don't think that equilibrium can exists. Indeed any miner has the opportunity to orphan the last top to "steal" the transaction in that block while the network is waiting for the mempool to fill. Consequently any miner has to "defend" their block after finding a solution by mining on top of it, and will naturally add all fee paying transactions they can get on the way, forcing every other miner to commit at least some hashing power as soon as a new block is propagated.
I'd not considered the strategy of attempting to orphan existing blocks. Good point. I'll need to think about this.
Is this not a general problem with (4) and (5)? Ignoring Alice, is sweeping the mempool always economically unwise absent a block subsidy?
You could rework your example with the assumption that miners are throttling their hash rate based on total fees in the mempool but even that may not stand in view of this previous counter argument.
13. Suppose that these 10-satoshi-fee transactions are distributed uniformly with time.
(13) coupled with (6) will reduce the average time it takes for every miner to start committing hash power, not just Alice. Generally, it means (7) is true with or without Alice. It also means that Alice may never hit her expected fee density.
I imagine the global stock of mining hardware will remain fairly heterogeneous. I expect that some hardware will be more efficient than other hardware and so will be put to work sooner. Alice, being a very large miner, would likely have some very efficient miners as well as some more aged hardware which can only earn its electricity consumption as the mempool grows large.
I certainly don't expect a situation where all miners have equally efficient hardware worldwide and all this hardware is put to work in unison at some special threshold.
(13) coupled with (6) will indeed reduce the average time the moment (13) comes into play. By (1) I intend at each step to allow difficult to adjust appropriately to look for long-term stabilities.
In the Bitcoin network, block space suppliers compete for market share only by lowering prices, since the notion of quality does not apply to block bytes.
This is the simplification I'm challenging with my example.
You are speculating that Alice can exist in this market at a higher sell price only by waiting for demand to periodically outweigh supply. However (5) contradicts that strategy, as it suggest supply is infinite for intents and purposes.
Yes, I'm assuming infinite supply in this sense. However, while transaction creators demand the space, they also care about the time they must wait for the space. Alice can do nothing about the first but she can have a small effect on the second. For the lowest possible expected time to first confirmation of 10 minutes, a transaction creator needs every last miner willing to process their transactions.
As stated previously, other miners will not sit at this equilibrium.
I honestly haven't thought much about what other miners will do in this situation. I guess that the most they could do to undermine Alice's strategy is to simply continue with their own, sweeping up every transaction they can find.
Assume my counter argument does not stand and Alice can still build "fat" blocks periodically regardless of the implications of (5). If she chooses to stick to this strategy despite the current equilibrium, the rest of the network will have a double incentive to orphan her:
1) Because of the first counter argument, as other miners know she is withholding all hash power until the mempool is attractive enough (according to (12), tx emitters know of her strategy, so there is no reason to believe other miners won't)
2) Because her blocks have higher than average fee density.
Given (5), I wouldn't expect miners to care only about fee mass and pay no attention to fee density.
I admit it seems rational that miners would try to orphan Alice's blocks in this scenario. I'll need to think a bit harder about what might happen. However, at this point I expect that another miner, Bob say, would experience an even greater burden. Breaking one of Bob's blocks would give another miner access to all the transactions of the previous round, not just the 10-satoshi transactions. When trying to break one of Alice's blocks, a miner is forgoing the opportunity to try and grab the 1-satoshi transactions she left on the table.