Modeling competitive situations

Abstract

This chapter studies how competitive situations are conventionally modeled in noncooperative game theory. It uses two sorts or forms of models: the so-called extensive form game and the normal or strategic form game. An extensive form representation of a noncooperative game is composed of the following list of items: a list of players; a game tree; an assignment of decision nodes to players or to nature; lists of actions available at each decision node and a correspondence between immediate successors of each decision node and available actions; information sets; an assignment of payoffs for each player to terminal nodes; and probability assessments over the initial nodes and over the actions at any node that is assigned to nature. There is no single way to proceed in general from a normal form game to a corresponding extensive form game. In one obvious extensive form, the players all choose complete strategies simultaneously, but often other extensive forms could be constructed from a given normal form.