This discusses theatre games (aka improvisational theatre) in the context of how they approach defined-character role-playing. Theatre games were originally developed to stretch the ability of an actor. Many resemble word games: such as improvising a conversation where each successive line starts with the next letter of the alphabet.
This page is concerned with improvisational games where each actor has a pre-defined character that they attempt to act out. Playing these out often involves a director who gives structure to the scenes which are played out. There are a category of games in Australia known as "free-forms" which can resemble this.
The basic technique is to have a set of actors, each of whom has a defined character. Some sort of scene is set up, and they begin to improvise what their character would do. The rules vary wildly from group to group, and from game to game. However, below I will give examples of some common rules that are used to structure this sort of game: