Vassal states are an important feature of pre-modern civilisation and should be modelled.
Also called: client state, satellite state, associated state, puppet state, neo-colony, protectorate or tributary state.
The controlling state is called a suzerain, surrogate or hegemon.
List of dominant sovereign states and their servient territories
The more powerful civilization demands that the less powerful civilization accepts its suzerainty. As part of the demand, a tribute is set.
The less powerful civilization accepts as becomes the vassal, whilst the more powerful civilization becomes the suzerain.
Does the vassal retain diplomatic relations with other civilizations? ?
Does the vassal control its military units? Yes
Does the vassal control domestic expenditure (e.g. military/research/infrastructure)? Yes
Perhaps model via alliance and relationship score.