TEMPORAL LOGIC APPROACH TO EXTENSIVE GAMES

A mathematical n-players game model can be represented in a normal or extensive form. A normal form representation of games is ideal to represent situations where players make one choice and move simultaneously. An extensive form provides an explicit description of a strategic interaction by specifying a physical order of play, actions available to players each time they get to choose, and eventual payoffs for each player for any sequence of choices. For these reasons the extensive form provides a richer environment to study interesting questions such as rivalry, repeated interaction, etc. Obviously every normal form of the game can be represented in an extensive form, but it is more natural and simpler just to write the normal form. It is less obvious that every extensive form of the game can be written in a normal form. This translation is possible if we note that a strategy in an extensive form game is not just a move or sequence of moves, but rather is a complete contingency plan. A strategy for a player i must specify what the player will do at every node or what information set the player has.