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Hey, thanks for your interest! Good questions! I hinted at them a little bit with this in my journal:

To exit the position, users sign with the MM to receive an unencumbered VTXO at the new market price. After entering a position, you can still unilaterally exit the Ark, but not the DLC contract: The refund paths only become available after the oracle has had time to attest and the winners have had time to claim the DLC-VTXOs for themselves. MM liveness gates pricing and exit, but never custody.

But let me also reply to your quotes directly:

But the fundamental question of doing prediction markets in a non-custodial way is whether or not users have custody of their funds after a bet has been placed.

DLCs make it possible for you to always claim what you win if you win. They also make sure losers can withdraw if the oracle fails to attest. Trust moves from the market operator to correctly resolving a market and not running away with the funds to an ideally oblivious oracle.

If there's no "unilateral exit" where users can retrieve their funds and sell an event contract after it's been placed

Yes, the market maker gates prices, and thus whether you can exit at a better price, but DLCs guarantee contracts at the prices you bought them. If your prediction was correct, you can be sure you’ll get paid, but you can't expect to sell your shares before they go to 0 or buy more. It's a fine but important distinction IMO.

I'd be happy to chat.

Where?

If people buy conditional DLC-VTXOs, and still have some sats remaining in their wallet balance, then can they do unilateral exit with those sats? And people cannot exit the Ark once they've purchased some conditional VTXO at market price, but they can exit after claiming those DLC-VTXOs?

The reason why I thought DLCs wouldn't be feasible to enable LMSR-based cost function AMMs is due to the amount of liquidity that needs to be committed in advance. In a custodial environment, the LMSR efficiently prices event contracts from the pool of liquidity it already has, but if it's non-custodial, then every payout must be committed in advance.

For example, if someone purchases some contracts with a 100,000 sat payout, then those 100,000 sats need to be committed by the AMM into the DLC for it to be non-custodial. Under that kind of architecture, the volume of the prediction market is bounded by the liquidity available within the AMM to allocate to the DLC payouts. If the AMM runs out of liquidity for payouts, then how can new market participants buy event contracts from the AMM? If the balance of the AMM is 1m sats, then people can trade buy at most 1m sats worth of event contracts before liquidity runs dry.

Regardless of the liquidity, as long as you use an LMSR based mechanism, the AMM operating the prediction market will have bounded loss. It's just if the AMM is operating in a custodial environment, the liquidity can be utilized more efficiently. If it's operating in a non-custodial environment, every payout must be committed into a DLC, and thus AMM liquidity is a constraint.

Have you given any thought to this liquidity constraint under a DLC model? I have been wondering for some time if it's possible to do LMSR based prediction markets on Ark without a DLC type construct, due to this liquidity limitation.

Happy to chat here: https://calendly.com/james-birkeland/30min. Not available this week, but next week I have some time.

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If people buy conditional DLC-VTXOs and still have some sats remaining in their wallet balance, can they do a unilateral exit with those sats? And people cannot exit the Ark once they've purchased some conditional VTXO at market price, but they can exit after claiming those DLC-VTXOs?

You can always use Ark's unilateral exit for your VTXOs, locked with a DLC or not. You cannot exit the DLC contract. Does this make sense? This confused me too, but it's a very nice property.

Have you given any thought to this liquidity constraint under a DLC model? I have been wondering for some time if it's possible to do LMSR based prediction markets on Ark without a DLC type construct, due to this liquidity limitation.

I definitely see liquidity as a major problem here, but because of Ark, not because of DLCs. I haven't thought much about this yet, though. So maybe I will arrive at the same conclusion later.

Happy to chat here: https://calendly.com/james-birkeland/30min. Not available this week, but next week I have some time.

Don't have much time myself currently. Will get back to you! I'm also planning to post about this on Delving Bitcoin soon, but with some math and numbers regarding liquidity requirements.

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How is the DLC enforceable if anybody can do a unilateral exit from the VTXOs that are stored within the DLC? If it's LMSR based, then the AMM needs liquidity from the losing bets to pay off the winning ones. If people know they're on the losing side of a wager, then what's stopping them from exiting the Ark? Like would they exit the Ark but still be locked into the DLC on-chain somehow?

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Like would they exit the Ark but still be locked into the DLC on-chain somehow?

Yes! Unilateral exit means you broadcast the chain of presigned transactions, so your VTXO turns into a UTXO, but spending this UTXO still requires the correct unlock script. In the case of a 2-party DLC, there would be three ways to unlock it: one for each winner with the correct attestation, and a delayed refund for both. This means the Ark operator as the market operator is still part of the DLC, just onchain now instead of in a VTXO.

Did this help?

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