Chapter 6: Non-cooperative Sequential Games and Public Policy
In Chapters 4 and 5, our focus was on non-cooperative games in strategic normal form. While (as von Neumann and Morgenstern showed) all games in extensive form can be represented in strategic normal form, to do so in general we may have to be careful to specify strategies as contingency plans. Thus, the strategic normal form will apply most naturally and with the best intuition to games in which simultaneous choices of behavior strategies must be made, such as the Prisoner’s Dilemma. Conversely, when some decisions must in fact be made before other decisions are made, so that subsequent decisions are made with knowledge of the earlier decisions, the game represented in extensive form may be more natural and intuitive. Such games are said to be sequential. In this chapter we focus on sequential games and on the game represented in extensive form. 6.1 SUBGAME PERFECTION AND TREMBLING HANDS Recall Game 2.2, Figure 2.1 in Chapter 2. We should notice that the decision by Firm A, to accommodate or retaliate, is a subgame in this game. Accordingly, we can define a behavior strategy locally at this decision point. The behavior strategy is just to accommodate or to retaliate, without specifying any conditions as to what previous decisions might be made. (Such conditions would be trivial in this case anyway.) In the spirit of Nash equilibrium theory, we might suppose that Firm A will choose the behavior strategy that leaves it with the larger payoff. This is “accommodate” for a payoff...
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