This chapter looks at games which have a dynamic structure; that is, games in which one player makes a move after the other (rather than choosing strategies simultaneously). In these situations, game theory needs to specify the precise protocol of moves. Diagrammatically dynamic games resemble tree diagrams (recall section 2.2) which are known formally as the extensive form. So the extensive form representation is appropriate for a dynamic game, whereas the matrix representation (or, more formally, the normal form) which we have been using so far is suitable for interactions in which players choose simultaneously.
The next section begins with an illustration of the advantages of the extensive form as compared with the normal form for such games. It continues by showing that in some games the extensive form can help pinpoint a solution which proved elusive while the game was viewed in its matrix, or normal, form. In terms of the discussion of the previous chapter, the study of a game’s dynamic structure potentially helps by reducing the number of Nash equilibria.
The hallmark of the analysis of extensive form games is the use of a type of reasoning called backward induction. Section 3.3 focuses on a particular refinement of the Nash equilibrium which results from a marriage of the original idea behind the Nash equilibrium and backward induction: the famous (within game theoretical circles) subgame perfect Nash equilibrium. Section 3.4 is devoted to some (important) controversies which result from the application of the common knowledge of rationality (CKR) axiom in dynamic (i.e. extensive form) games.
Sections 3.5 and 3.6 sketch three other major refinements of the Nash equilibrium: sequential equilibria, proper equilibria and those which depend on the use of forward induction. The chapter concludes with a critical assessment of the Nash equilibrium concept as well the attempts to refine it.