The long-term solution to the peg being broken is fixing the DAI supply/demand balance. Nothing else will bring the DAI/USD back into the acceptable narrow band. In the face of the present Defi-mania this means increasing supply as much as possible.
That being said, I believe the Peg Stabilization Module (PSM) can be an important tool for helping the DAI markets function properly even with consistent high demand.
Basically you want to help the relevant markets, typically DAI/USD, to do this job themselves. Market makers keep the peg by buying Dai at for example 0.995 USD and selling it again for 1.005 USD. When enough market makers do this the peg is kept within bounds. The problem is that the consistent high demand for DAI prevents the buy orders from ever being filled. A market maker now has to sell USD and buy DAI at a loss in order to keep playing the game. It is a direct loss if you have to buy DAI at 1.02 to keep yourself in business. Needless to say market makers are highly hesistant to do this and as a result the defi surge is pushing DAI of the peg, despite the Maker community doing its best to add collateral. A PSM module could be set up to better manage peg fluctuations and help the markets function.
However, the existence of the PSM opens up the possibility for gaming the system, draining Maker of resources and possibly making the peg situation even worse. Below are some tips and tricks that can be used to avoid this.
PSM activation at random. If DAI/USD is going up and the market knows the PSM will kick in at 1.03, few traders will bother to sell at anything other than 1.0299. This is precisely the situation we want to avoid. By having the PSM activate at random, or possibly just by an increased chance of activation at higher peg deviance, you can avoid traders gaming the PSM to some extent.
PSM duration should be variable. Sometimes the activated PSM should do its work in the shortest possible amount of time to prevent traders adjusting. At other times the PSM should broadcast that it has been activated and will take unspecified action within 24hrs. At times the notification alone could be sufficient to scare the peg back in place.
PSM addresses should vary. Sometimes the PSM ethereum address should be public and the moves announced. At other times the PSM should act from previously unused addresses to avoid players detecting and trying to game any PSM action. This will add uncertainty and avoid giving some market makers the idea they can plan for PSM action.
PSM action should be variable. Sometimes the PSM is activated but does nothing. Sometimes it adjusts the peg by just 1% and then deactivates. At other times maximum effort is made to push the peg back to 1:1. Quite often even pushing it past the peg by a small amount can be used. The last serves to discipline market makers into never ever buy DAI at above the peg. Bought above the peg? You lose.