I've been trying to understand Proof Of Stake cryptocurrency systems, but I don't see how new coins are made using the Proof Of Stake system.
My current understanding of Proof Of Stake
People put up a certain amount of cryptocurrency they already hold for a chance to be the entity that creates the next block. This is the Stake.
Whoever is chosen to write the next block verifies the transactions and as a reward gets to keep all the transaction fees. If you're not chosen, you get your Stake back.
The Stake of the new block writer is held in escrow (i.e. not allowed to be spent) until several new blocks are added.
If they are found to be cheating they loose their Stake.
I don't see where new coins are being added. It seems like the coin supply is set and it just moves around as people pay transaction fees.
In Bitcoin, and other Proof Of Work systems, I would buy a computer and become a miner. I'd keep solving hash problems until I mined a coin, then I could spend the coin. I do not need to have Bitcoin to mine it. With Proof of Stake it appears I have to have currency to get more - it's a chicken and egg problem.
In a Proof Of Stake system, how do I go from 0 coins to 1 coin? For example, I invent a Proof Of Stake cryptocurrency. How do people besides me get coins to spend?