Board game decomposition

I tried figuring out the elements of boardgames. Hopefully it will be useful in future design decisions.
Source of inspation: Decoupling Aspects in Board Games Modeling

Logic:
This is the core of the game.
Agents:
Users of the game. May be humans or computers.
Representation:
How the game is presented to the user. Possibly with figures cards and tokens. Usually expresses the game logic, making it reasonable for the user.

States:
The conditions of the game at each turn.
Behaviors:
Transitions from state to state.
Rules:
Static laws producing the behaviors in the game.

Administrive agents:
Upholder of the rules of a game. Like the bank in monopoly.
Players:
Players playing the game.