Chapter 2: Representing Games
The first step in any application of game theory, whether to public policy or for any other purpose, is to represent the real-world phenomenon of interest as a problem of interactive decision, that is, a “game.” This chapter will set out some forms for representation of games that will be important for the remainder of the book. Some will be familiar, even pedestrian, to the reader who is well grounded in game theory. Nevertheless some topics may be important for the game theorist, if only for differences of stress. Contingent strategies are well known, but this book will often make them more explicit and formal than they sometimes are in the game theory literature. Nested games may be a novel topic to the game theorist, as the concept comes from applications in political science, and are crucial to the distinction of a private from a public sector. “Imperfect recall” is very little mentioned in recent game theory, and needs to be discussed in the context of cooperative game theory. Finally, the partition function approach in cooperative games, and its importance for the concept of externality, may be novel to some game theorists. These are important concepts for public policy. Nevertheless, the chapter is expository, with nothing new to the literature except specific examples, some terminology, emphasis, and expression. 2.1 GENERAL CONSIDERATIONS Game theory is a (mathematically) formal study, with deep roots in mathematical set theory. The language of set theory is designed for generality even at the expense of intuition...
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