Chapter 2 Games in extensive and strategic forms This chapterdiscusses formal definitions as well as a few illustrative examples for the following notions: games in extensive form games in strategic form pure and mixed strategies and equilibrium points. Two classes of games that are of interest are presented: games of perfect information which always possess equilibria in pure strategies and games with perfect recall where mixed strategies may be replaced by behavior strategies. A first basic way of describing a game called the extensive form is presented. As the name suggests this is a most detailed description of a game. It tells exactly which player should move when what are the choices the outcomes the information of the players at every stage and so on. A second basic way of describing a game is called the strategic form (also known as normal form or matrix form). There are many situations in which a players best behavior is to randomize when making his choice. This leads to the concept of a mixed strategy. A pure strategy of a player is a complete plan for his or her choices in all possible contingencies in the game. A mixed strategy means that the player chooses before the beginning of the game one such comprehensive plan at random (according to a certain probability distribution). An alternative method of randomization for the player is to make an independent random choice at each one of his or her information sets. These randomization procedures are called behavior strategies. But when a player has what is called perfect recall the converse also holds: every mixed strategy is fully equivalent to a behavior strategy.