So suppose a million custom erc20 tokens are created/pre-mined and sent to an address on the ethereum network. The coins have a starting worth of 0 eth. The coins are then somehow distributed to a bunch of people who have some sort of arbitrary use for the tokens. What makes the tokens gain some eth value? What makes this value go up and down? Is there an algorythm in place that rates the token value based on how decentralized the token is, transfer frequency, etc? What other factors can cause the stated value of the coin on the block chain to go up and down?
The value of the custom created token, is tied to the price of Ethereum, because this is your base currency.
Say you list your token on a DEX. I put in 2000 MyToken and 1 ETH. Now MyToken is effectively worth, 1/2000 ETH.
If the price of ETH is trading at $2000, then MyToken is effectively work $1.
Tomorrow ETH is trading at $3000. If somebody wants to buy MyToken, they will still pay 1/2000 ETH, which is effectively worth $1.50.
After the public has MyToken, and they start trading it, the price becomes set by what the next buyer is willing to pay.
If the next buyer is willing to pay more, then the price will go up.
If the next buyer is willing to pay less, then the price will go down.
Whatever people are willing to pay for something is what gives everything its value. The only reason Ether has any value is because people attribute value to it. The value you see listed for a token is the price that it has recently been sold/bought at from person to person. This price fluctuates as people decide it's worth more or less to them.