TABLE OF CONTENTS This chapter provides a general formulation and some background material for the class of infinite dynamic games to be studied in the remaining chapters of the book. In these games, the action sets of the players comprise an infinite number (in fact a continuum) of elements (alternatives), and the players gain some dynamic information throughout the decision process. Moreover, such games are defined either in discrete time, in which case there exists a finite (or at most a countable) number of levels of play, or in continuous time, which corresponds to a continuum of levels of play.
Quite analogous to finite dynamic games, infinite dynamic games can also be formulated in extensive form which, however, does not lead to a (finite) tree structure, firstly because the action sets of the players are not finite, and secondly because of existence of a continuum of levels of play if the game is defined in continuous time. Instead, the extensive form of an infinite dynamic game involves a difference (in discrete time) or a differential (in continuous time) equation which describes the evolution of the underlying decision process. In other words, possible paths of action are not determined by following the branches of a tree structure (as in the finite case) but by the solutions of these functional equations which we also call state equations . Furthermore, the information sets, in such an extensive formulation, are defined as subsets of some infinite sets on which some further structure is imposed (such as...
