It is not guaranteed. You should not treat is as FDIC insured funds.

But let's do a little game theory. Say the market starts losing faith in USDC and people start selling 1 USDC for, say, 0.98 USD.

Coinbase can either let this happen, or they can start using their cash and investments to buy back USDC at a 2% discount.

If Coinbase has every reason to believe that USDC is just fine, then they have a large financial incentive to start buying USDC back. This will raise the market price back to near $1 USD.

That is how they stabilize their stablecoin.

It is game theory and market mechanics and not a government that stabilize stablecoins. If you don't trust this, then you should not hold USDC.

That's the optimistic scenario. The pessimistic is USDC goes down to $0.98 and then people panic and sell and it goes down to $0.97, $0.96, ... Meanwhile Coinbase tries to borrow a whole lot of cash to try to prop up the currency. The amount they have to borrow keeps going up though and at some point they stop being able to cover the promise.

This scenario is not implausible. It literally happens every few years in the modern economy with different assets. Real assets that are backed by real things, not a completely synthetic currency.

The dollar assets backing USDC are the only thing that really secures it. Not "game theory". Sometimes you lose games.

I think you're describing stablecoins just right. If that's all of it though, why should anyone be interested in what reserves these stablebanks hold.

What they're doing is, creating a USD bank. It's not just about bank guarantees. Game theory describes the stable outcome, it doesn't predict it.