Sequential Games: The second category of dynamic games considered in this chapter is the case of sequential games.  These games are different from the repeated games in the previous section because they do not necessarily involve the same decision or set of decisions being made multiple times.  They are, nonetheless, dynamic with decisions occurring at different points in time.  This dynamic nature opens the door to the possibility that choices early in the game may influence decisions later in the game.

 

As in the case of repeated games, the exact definition of what comprises a strategy differs in sequential games from their simultaneous choice counterparts in the previous chapter.  Contingencies come into play with each action at each stage being potentially dependent on earlier choices.  This means that strategies become much more complicated and potentially confusing.  It is a good idea to start with a simple example (perhaps something like Amazon / ePub game described in Q&A 13.1) to show that the number of strategies for the second mover is larger than one might think.  In this example, Amazon has two strategies and the Other Group has four (all combinations of ePub and AZW that follow each of Amazon’s choices).  Students often wonder why we need to specify something like ePub / AZW (meaning ePub at the top node and AZW at the bottom) as being different from AZW / AZW when the top node is not going to be part of equilibrium play.  The answer is that choices that happen away from the equilibrium path are still part of the equilibrium.  In fact, they are part of the reason that the choices in the equilibrium itself are made.

 

The key solution concept for sequential games is subgame perfection and the identification of a subgame-perfect Nash equilibrium.  This is easiest to describe by thinking about starting at the end of the game and working back towards the beginning.  Students typically catch on very quickly to this idea after a couple of simple examples.