Create an L2 ERC20 token for a game

Hi,

Trying to design a token that will be used as in-game currency for a game. The token is supposed to have real value and be tradable in a DEX. Something like MANA of Decentraland.

My first thought was an ERC20 token, but for every in-game transaction/move you would be paying high gas fees, and that does not make sense for the game. So I would like to create an L2 token that would ultimately be saved in Ethereum blockchain, such as Polygon, but I don't want to use Polygon as the token, I want to design my own token.

We are just prototyping, I have made a BSC token before. I just want to know the possibilities and the direction I should be going.

Any thoughts? Thanks