The simple story about decision market liquidity is: such markets need an expectation of liquidity to induce traders to reveal info there, so that prices can usefully inform decisions.
Isn't this susceptible to silly trading strategies that are intended to extract the liquidity payment rather than genuinely trade?
For example, the delta^2 term might outweigh the value of the position itself and so selling for zero becomes beneficial. Preventing this puts a limit on the "liquidity" value, but I'm not sure there aren't still some silly outcomes possible.
What about selling back and forth between two cooperating traders?
It seems to me that you are suggesting traders should be paid to trade to encourage trading to occur and the prices to settle on the "true" market value. Is that not right?
If people are paid to trade, it is necessary to make sure the system can't be scammed, or the potential for scamming is limited. The particulars depends on how the market and payments work. Non-linear payments complicates the analysis.
I'm just asking the question. How exactly scamming could be done depends on the particulars of trading, and I don't see these specified in your description.
I'll give a possible example, which may or may not work depending on your market particulars. If two traders agree to send in a sequence of trades very closely timed so that they have a high chance of trading with each other, they could end up moving the price around, while leaving it the same in the end, but extract some payments for moving the price during the sequence.
A simple inventory based market maker makes bid and ask trade offers with price a monotonic function of their inventory. You can only profit by trading with those by moving the price toward its final resting place, i.e., by better informing that price.
The monotonic function is going to have steps. Two traders can sequence trades in the middle of the steps.
Also, no one knows the final resting place until the end. Are you saying traders get paid at the end based on their history of how much they moved the price towards the final resting place? Maybe you aren't, but maybe it's not such a bad way to do it either.
Anyway, I don't think most people (including me) can relate what you are saying to their own trading concepts. Maybe another article could help. It seems like quite an important topic.
Isn't this susceptible to silly trading strategies that are intended to extract the liquidity payment rather than genuinely trade?
For example, the delta^2 term might outweigh the value of the position itself and so selling for zero becomes beneficial. Preventing this puts a limit on the "liquidity" value, but I'm not sure there aren't still some silly outcomes possible.
What about selling back and forth between two cooperating traders?
I don't understand what trading strategies you think will extract value from automated market makers.
It seems to me that you are suggesting traders should be paid to trade to encourage trading to occur and the prices to settle on the "true" market value. Is that not right?
If people are paid to trade, it is necessary to make sure the system can't be scammed, or the potential for scamming is limited. The particulars depends on how the market and payments work. Non-linear payments complicates the analysis.
I'm just asking the question. How exactly scamming could be done depends on the particulars of trading, and I don't see these specified in your description.
I'll give a possible example, which may or may not work depending on your market particulars. If two traders agree to send in a sequence of trades very closely timed so that they have a high chance of trading with each other, they could end up moving the price around, while leaving it the same in the end, but extract some payments for moving the price during the sequence.
A simple inventory based market maker makes bid and ask trade offers with price a monotonic function of their inventory. You can only profit by trading with those by moving the price toward its final resting place, i.e., by better informing that price.
The monotonic function is going to have steps. Two traders can sequence trades in the middle of the steps.
Also, no one knows the final resting place until the end. Are you saying traders get paid at the end based on their history of how much they moved the price towards the final resting place? Maybe you aren't, but maybe it's not such a bad way to do it either.
Anyway, I don't think most people (including me) can relate what you are saying to their own trading concepts. Maybe another article could help. It seems like quite an important topic.
Why is profit proportional to liquidity * delta^2?
its the intregral Int_p0^p1 L(p) (p1-p) dp.