The weirdest game theory incentive for BIP110 is that the more people want to dump BIP110 coins, the more transactions they'll add to the BIP110-chain which presumably will have much lower hash rate. Eventually, the large backlog of transactions will cause higher fees and with it, more incentive for miners to mine that chain. Depending on the price ratio, this still requires a huge amount of fees to motivate miners to switch. For example, if the price ratio is 10:1, then fees will have to take up 28.125 BTC (28.125 + 3.125~31.25) on the BIP110 chain for similar profits. Which is 28125 sats/vbyte average for the block, which is really, really high, but that's what it'll cost to dump coins at that ratio. Higher ratios require even more fees and lower ratios require less. tl;dr The more people dump BIP110 coins the more miners are incentivized to mine the BIP110 chain.

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I don't see a static price assumption, just some market price for miners to get coins. The key question for me is whether there's a market for exchange of a 110 coin to other cryptocurrencies including stablecoins
Where would this buying/selling happen? On exchanges like coinbase? Idk I think they will just freeze withdrawals in this scenario till it's sorted out. If not on a large regulated exchange then maybe on a smaller exchange that wants to participate in allowing replay attacks? Maybe but I can't name one. Is there somewhere else outside of the regulated ecosystem that would have enough liquidity?
How would they dump them? You'll have to wait for core to fork the chain first
your question is my key question. mining difficulty adjustment and market price is part of the math
Without replay protection, only a Bitcoin Wizard will be able to safely split their 110 coins. And yet, even having done that, they will be unable to find a venue in which to sell them. The game you envision simply does not exist.
This requires some way to dump them. I have yet to see a single BIP-110 advocate willing to trade their BIP-110 coin for Bitcoin at any exchange rate. As @npub17u5d...t4tp mentioned, splitting coins is also going to be tough. If I thought there was going to be a sustained split I'd consider cranking (or clanking) out some software for splitting, but I just don't see it happening.
28.125 BTC over a 1M vbyte block is 2,812.5 sat/vB, not 28,125. Still high but you're off by 10x
BIP110-compliant transactions are also Core-v30 compliant, so, unless an input UTXO is dependent on minority chain's transaction order (very few initially) a miner on the majority chain will snarf up those fat fees. A miner gets nothing from mining the minority chain, no matter how fat the fee, unless the chain is heaviest when presented to the exchange 100 blocks later. Nakamoto consensus at work. Unless, of course, BIP100 precipitates a BCH-like fork in the *market*. In that case we did see miners opportunistically switch chains for a while, but even there, the BCH market eventually thinned out (and BTC hashpower grew) until any significant shift of hashpower over to BCH would crash its market, making such tergiversation unprofitable. Of course, the mere presence of a high-fee transaction creates the "goose egg" problem, where miners will want to fork the chain and re-mine the big egg instead of building on the heaviest chain. First described in 2016, we haven't seen it happen yet, but ever-declining coin emission takes us further into untested waters. A disruptive event that creates a large number of high-fee transactions could tip us over into a new, pathological Nash equilibrium. https://blog.citp.princeton.edu/2016/10/21/bitcoin-is-unstable-without-the-block-reward/
You’re also assuming people will mine bip110 out of pure financial interest. Some will mine it in a revenge mode, not carrying what the price is at all. Especially the ones who consider the non-bip110 chain worthless anyway (due to being the spam/VC/captured chain). Remember about the “dying on this hill” meme? This is how it would look in practice.
You need 100 blocks confirmed on the bip110 chain to sell the coins mined in the first block after the split. Assuming no emergency difficulty adjustment is made, which is a hard fork. 100 blocks may take few months to be mined. So at least from freshly mined blocks, there won’t be any sell pressure.
I cannot wait to see the receipts when give away your worthless coins.
What the pro-spammers don't realize is that if there is a chainsplit, myself and probably thousands of others will patiently wait, run nodes, and mine on the true chain as long as it takes. Eventually the pro spam chain will become so centralized it fails like every other alt coin. Im willing to wait decades. Rug the spammers.
The more people dump BIP110 coins the lower the price of BIP110 coins will be and thus less incentive to mine the BIP110 chain. (This assumes there’s even a way and place to dump them in the first place.)
selling "bip110 coins" might be the dumbest thing you can do. since its a softfork and it will wipe everything you have on the chain where you put everything.