There are a set of games in which a major part of the game-play involves the ability of players to change the rules. Here we collect examples of these games that we can learn from, and propose new ones.
Nomic is a game created in 1982 by philosopher Peter Suber in which the rules of the game include mechanisms for the players to change those rules, usually beginning through a system of democratic voting - wikipedia 
Building Utopia for instance is a Governance Sandbox, that is it is a form of Legal Game akin to Nomic.
Nomic Card Games
The game of Bartok, also known by a number of other names, such as Wartoke, Warthog, Bartog, Bentok, Last One Standing or Bong 98, is a card game where the winner of each round invents a new rule which must be obeyed for the remainder of the game - wikipedia
Example card from 1000 White Cards game - wikipedia 
1000 Blank White Cards is a party game played with cards in which the deck is created as part of the game. Though it has been played by adults in organized groups worldwide, 1000 Blank White Cards is also described as well-suited for children in Hoyle's Rules of Games - wikipedia
Fluxx is a card game, played with a specially designed deck. It is different from most other card games, in that the rules and the conditions for winning are altered throughout the game, via cards played by the players - wikipedia
Dvorak is a customizable card game that begins with a deck of blank index cards. These index cards (or pieces of paper or cardboard) are written and drawn upon by players before or during the game - wikipedia