The mechanism is staking. People stake Eth 1.0 to get 2.0 later, along with a bridge to convert Eth 1.0 to 2.0. They can't unstake for a period of time but get decent automatic returns.
There won't really be much reason for people to use 1.0 to execute smart contracts*. There really isn't much for miners to do besides eventually cashing out and becoming a validator. Eventually when "the merge happens" Eth 1.0 will be automatically converted to 2.0. This won't be for a few years (but PoS will launch this year)
*The 1.0 network supposedly uses 1000x times the energy of the 2.0 one to execute a smart contract and would obviously be more expensive to work with, so people will probably avoid using 1.0 as soon as possible. Less use means lower gas fees means lower payouts for miners, who already had payouts reduced by EIP 1559, and will likely have payouts reduced once more. So miners will see a slow death.
There won't really be much reason for people to use 1.0 to execute smart contracts*. There really isn't much for miners to do besides eventually cashing out and becoming a validator. Eventually when "the merge happens" Eth 1.0 will be automatically converted to 2.0. This won't be for a few years (but PoS will launch this year)
*The 1.0 network supposedly uses 1000x times the energy of the 2.0 one to execute a smart contract and would obviously be more expensive to work with, so people will probably avoid using 1.0 as soon as possible. Less use means lower gas fees means lower payouts for miners, who already had payouts reduced by EIP 1559, and will likely have payouts reduced once more. So miners will see a slow death.
Someone please correct me if I'm mistaken.