CHAPTER 1 - Games in Extensive and Normal Forms

Abstract

This chapter reviews games in extensive and normal forms. There are many situations involving conflicts of interests in the real world. In a conflict situation, each participant designs his/her own strategy of behavior, that is, expenditures on advertising and new technology, business spying, etc., but the essential element is the conflict of interests, usually with incomplete information on which to base decisions. A convenient way of describing a conflict situation from a mathematical point of view, when the players have finite sets of options, is to use a tree graph. If the game is characterized by extensive form, the rules that describe the behaviors of the players are mathematically specified. In principle, the extensive form implies that every player would be able to state what he/she would do in each situation that might occur when the game is being played and would convey the decisions to his/her helper, who could play the game without the player's participation. Furthermore, in a finite game tree, the quantity of all pure strategies of every player is finite and strategies can be enumerated. The enumeration can be generalized to an n-person game.