Another analysis, similar but a little off-tangent to yours, would be to consider miners as a breeding group with various strategies, and see which one is able to gain more utilons (with which it creates more miners) and outbreed the other miners.
This models the fact that miners can use their earnings to reinvest into their mining operations and increase their mining hashrate, and the amount they can reinvest is proportional to their earnings.
A miner that "gives birth" to a child miner with the same strategy is, in the so-called "real world", simply a miner that has earned enough and reinvested those earnings to double the hashrate of their business (which, logically speaking, would use the same strategy throughout the entire business).
Let us start with a population of 4 miners, 3 of which follow the non-myopic strategy, and the remaining following the myopic strategy.
Let us postulate that all miners have the same unit hashrate.
Thus, this starting population is 75% non-myopic, 25% myopic.
If there exists a timelocked bribe, then if non-myopic miner is chosen at a block, it will have to sacrifice the Alice fee minus whatever lesser transaction fee it can replace in its block.
If the Alice transaction is successfully delayed until the Bob transaction is valid, then the non-myopic miners can get the Bob transaction confirmed.
However, even in the case that the Alice transaction is delayed, the myopic miner still has its 25% chance --- equal to the 25% chance of the three non-myopic miners --- to confirm the Bob transaction and earn the increased bribe that Bob offers.
Thus, the non-myopic miners can end up sacrificing fee earnings, and in the end the myopic miner still has the 25% chance to get the Bob transaction fee later when it becomes valid.
So the non-myopic miners do not impose any loss on myopic miners.
On the other hand, if the non-myopic miners sacrificed their chances to include the Alice transaction in the hope of getting the later 25% chance to get the Bob higher-fee timelocked transaction, and then the myopic miner gets the next block, the myopic miner gets the Alice transaction confirmed and the 25% chance to get the Bob higher fee is lost by the non-myopic miners.
Thus, the myopic miner is able to impose costs on their non-myopic competitors.
So even if by chance for the entire locktime, only the non-myopic miners are selected, the myopic miner still retains its 25% chance of getting the block at locktime + 1 and confirming and earning the bigger Bob fee.
Thus, we expect that the myopic miner will earn more than 25% of subsidies and fees than the non-myopic miners, in such a mixed environment.
This is exactly our analysis, and is covered in section 2.5 of our paper. We formalize the ideas a bit more, and are able to relate the values of Alice-fee, Bob-bribe, timelock, and miner's hashpower percentage. We go a bit further into #reckless territory as well - reducing the timelock value to super low values. That's in Algorithm #1 of our paper, and is a bit more involved.
We can then consider that the myopic miner, being able to earn more, is able to increase its progeny (i.e. expand its mining business and inspire new miners to follow its strategy towards success) faster than the non-myopic miners.
We can thus conclude that the myopic miners will eventually dominate over the breeding population and drive the non-myopic miners to near-extinction.
This is an interesting direction that we chose to not look at. Like the MAD-HTLC authors, we assume a constant hash-rate distribution across time, which is obviously not a great assumption. It might work in the local context of an HTLC's timelock, but in our approach, we are also interested in *weak* miners, and finding them across 1000's of blocks might get tricky.
It is helpful to remember that rationality is about success *in the universe you exist in*.
While miners may step back and consider that, ***if*** all of them were to use non-myopic strategy, they would all earn more, the fact of the matter is that each miner works for themselves, and themselves alone, in a highly competitive environment.
Thus, even though they know *all of them* will benefit if they use the non-myopic strategy, they cannot be sure, unless they are all perfectly synchronized mind-clones of each other, that the other miners will rather be selfish and mine for themselves, even if in the end every miner earns less
The standard for success is to earn more *than your competitors*, not ensure that *every* miner earns more.
Fortunately, since miners are running a business, this competition leads to better services to the the customers of the mining business, a known phenomenon of the free market, yay free market greed is good.
The user Alice is a customer of the mining business.
Alice gets, as a side effect of this competitiveness of miners (which leads to miners adopting myopic strategies in order to gain an edge over non-myopic miners), improved security of their HTLCs without requiring slashable fidelity bonds or such-like that MAD-HTLC proposes.
Yes. And in the context of Lightning, both Alice and Bob need to have fidelity bonds, which triples the already bad channel-lockin cost.
Using this model, it seems to me that non-myopic miners can only maintain hold over the blockchain if all miners agree to use non-myopic strategy.
This is basically all miners forming a cartel / monopoly, which we know is detrimental to customers of the monopoly, and is the reason why we prefer decentralization.
If miners form a cartel and get to 51%, we are all doomed anyway.
Thanks for the detailed reply. And apologies for splitting my email into two parts.