Prerequisites: Chapters 12, 14, 22, 24, and 27.

Coaches of team sports like soccer supervise the training of their teams, and they play in the sense that they select the players and the system their team will use. Besides trying to motivate their teams, coaches also have the important task of reacting to what they see by substituting players or changing the system.

In a Champion's League soccer game between Bolton Wanderers and Bayern Munich in November 2007, Munich was leading 2-1 when their coach Ottmar Hitzfeld substituted for two key players on his team, Frank Ribery and Bastian Schweinsteiger, taking them out. After that, the Bolton Wanderers tied the score at 2-2, and the game ended there. The substitution occasioned Rummenigge's indirect criticism of Hitzfeld's move, which prompted Hitzfeld's response.

In this section we will extend the simple static simultaneous soccer model discussed in Chapter 14 into a game with three parts, where in each part the coaches move simultaneously. We will see that there are too many pure strategies for the normal form approach, so we will try a variant of backward induction on subtrees.