I think many people assume AMD is trying to beat Nvidia, but I think both companies don't care, as they can produce the optimum amount of cards, with optimum market segmentation, at the 'optimum' price.
AMD still makes most of their money from selling CPUs. Logically, it's probably better to focus most of their investment there.
It's not really in their interests to out produce each other, unless they can scale the production at low cost. They seem to have 'just enough' capacity at the moment. I would guess that scaling up chip production is always a big risk, financially.
If we use Zen 4 CPUs on TSMC's 5nm EUV process tech as an example, these are priced higher than most seem comfortable with - Therefore I don't expect improved prices for an even more complex product, like RDNA3 GPUs + MCM dies.
Nvidia's CEO has stated that the production cost of their latest 4nm GPUs has increased significantly.
One positive thing, is that Nvidia is using 4nm for the next gen, AMD is using 5nm + 6nm. So, hopefully, they won't be competing much for capacity.