I am just absurdly interested in these "pegged" coins of all type, as you can tell from my own threads. I was wondering how you would handle the case when the coins were too plentiful and their prices too low, so I'm glad you described your plan.
If the price of the coins drops too low, then the mining reward will be dropped (not all the way to zero which would stop people from mining), and the transaction fee would be raised. The lower the price of the coins, the higher the transaction fee. All coins collected from transaction fees which are not given to miners are destroyed.
I am concerned that destroying coins in high transaction fees would lower interest in the coins, leading to lower prices for existing coins, which would force you to raise transaction fees, which would lower interest in the coins, leading to lower prices, . . . you get the picture. Basically, this could result in a divergence which never recovers.
I don't think we can know exactly what will happen with this setup without the actual stable coins in existence. My guess is, the higher transaction fees would cause people to hoard the coins. This will then remove more coins from existence than the higher transaction fees, and thus cause the price to rise.
Anyone desperate enough to sell below the fair value, would also likely be desperate enough to pay the transaction fee. Hoarders would then have an opportunity to make money through arbitrage, and coins would be destroyed at the same time.
In other words, I think the threat of higher fees or higher mining rewards would keep the price fairly stable without the actual higher fees or higher mining rewards going into effect that often.
Another concern I have is that you don't want to drive the price too forcefully, or you will limit the impact of goldcoin traders on real-life markets. As long as the prices converge over the long-term, short-term swings are not much concern, and they present arbitrage opportunities.
I agree. I would have to think carefully about how to set the fee structure. A little bit of price fluctuation is fine as long as it converges to a stable price over time. However, that does seem to go against the name "Stablecoin". Maybe, "Targetcoin" is a better name.
You might want to consider combining your feedback system with the one I came up with: charging variable transaction fees. If you have a distributed exchange, you can charge no transaction fee when trading at the external spot price for gold, and an increasing transaction fee the further you trade from that spot price. This continually nudges prices toward the external spot price, and helps you not rely so heavily on destroying coins.
The problem with a distributed exchange is, there is no central authority to enforce trading fees. Otherwise, it would be a good idea.