Are people presumed to be logical like Mr. Spock from Star Trek, or can they draw upon their emotions in decision making?

Are people presumed to be logical like Mr. Spock from Star Trek, or can they draw upon their emotions in decision making? While our analysis will be an exercise in logic, that does not preclude the possibility that people use emo- tions or “gut feelings” to arrive at a decision. In many cases, we will not be re- producing how people actually make decisions; rather, we will be describing what the end result of that process may be. A person may reach a decision through cold logic or on the basis of emotions rooted in past experiences.5

The more intriguing issue is whether we allow for variation in the skill of our players. Can we explore SpongeBob battling wits with Star Wars’ Senator Palpatine? Or have Mr. Bean and Voldemort exercise their “gray matter” in conflict? Although it would be exciting to explore such possibilities, they will not be considered here. A key assumption throughout this book is that people have comparable levels of skill. The strategic moves considered will take place on a level playing field. Although a player may have an advantage because she has more options or better information, no player will be able to “outsmart” an- other. (In principle, game theory can handle such possibilities, but that line of inquiry is largely undeveloped.)

1.5 Playing the Gender Pronoun Game BEFORE GOING ANY FURTHER in our quest to learn the logic of game theory, there is a sociopolitical–legal issue that my publisher, priest, and barista have urged me to raise with you: the use of gender pronouns. Any textbook that

FIGURE 1.2 A Range of Intellect

Dumb Smart

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C O

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14 CHAPTER 1: INTRODUCTION TO STRATEGIC REASONING

discusses people in the abstract—such as a book on game theory—must ex- plain how it intends to use gender pronouns and provide the rationale for that usage. While this matter is typically discussed in a book’s preface, peo- ple don’t tend to read the preface (apparently, “preface” means “ignore” in lots of languages), and every reader needs to know where I stand on this con- tentious issue.

To the chagrin of “stupid white men”—as filmmaker Michael Moore de- scribes them—the people who live in this book are not all males. If they were, where would the next generation of players come from for my second edition? Yes, women do live in the abstract world of game theory and will live along- side men. But allowing cohabitation between the covers of this book still leaves a decision of how to allocate men and women across our many exam- ples. I remember a scholarly piece on crime in which the male pronoun was used to refer to criminals (because most criminals are men) while judges, ju- rors, attorneys, witnesses, and victims were female. (To be accurate, most criminals who are caught are men; perhaps women are better about getting away with it.) Such an approach is disturbing. Might not an impressionable boy be led to believe that he should turn to a life of crime because that is what males do? And should we really convey the impression to a girl that crime is too risky for the female half of the species? Contrary to that approach, this book will allow both men and women to be deviants, sociopaths, and your run-of-the-mill perverts.

An alternative strategy is to deploy tactics utilized in the Gender Pronoun Game. This is the conversational game by which a person seeks to hide the gender of his partner. Instead of using “he” or “she” and “him” or “her”, one either avoids the use of pronouns or uses plural pronouns such as “they” and “them”. In the heterosexual world, a gay person might strive to avoid reveal- ing that her partner is of the same gender, and analogously, someone in the gay community (who is perhaps bisexual) might hide a heterosexual relation- ship. But these gender-neutral plural pronouns can become awkward (and drive my editor crazy), which leads me to another strategy: invent some gender-neutral pronouns. There is no shortage of worthy attempts, including “shis”, “shim”, “shey”, “shem”, “sheir”, “hisorher”, “herorhis”, and—my per- sonal favorite—“h’orsh’it” (a colorful blend of “he”, “she”, and “it”).

After long hours of monklike contemplation with my subconscious in sync with the Fox Network, I have decided to deal with this issue by mimicking real life. Just as our species is made up of both men and women, so will the play- ers occupying the pages of this book. If there is a two-player game, then one player will be male and the other female. More generally, I’ll just mix them up—a male here, a female there, a hermaphrodite when I’m getting bored. Admittedly, I have not counted their respective numbers to ensure an even gender balance. You the reader are welcome to do so, and once having been informed of your findings, I would be glad to replace an X chromosome with a Y or a Y with an X as is needed. In the meantime, I will do my best to be gender neutral and avoid stepping in h’orsh’it.

REFERENCES 1. John von Neumann and Oskar Morgenstern, Theory of Games and

Economic Behavior (Princeton: Princeton University Press, 1944), p. 6.

References 15

2. This discussion is based on Uri Zwick and Michael S. Patterson, The Memory Game (Coventry, U.K.: Mathematics Institute, University of Warwick, March 1991). It was reported in Ian Stewart, “Mathematical Recreations”, Scientific American, October 1991, pp. 126–28.

3. Nicholas Humphrey, The Inner Eye (Oxford, U.K.: Oxford University Press, 2003).

4. Winston S. Churchill, The World Crisis (New York: Charles Scribner’s Sons, 1923) vol II, p. 5.

5. On the role of emotions in social decision making, the interested reader is referred to Antonio R. Damasio, Descartes’ Error: Emotion, Reason, and the Human Brain (New York: Avon Books, 1994).

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If the human mind was simple enough to understand, we’d be too simple to understand it. —EMERSON PUGH

2.1 Introduction THEY SPEAK OF “DELIVERABLES” in the corporate world as the end product that is—well, delivered to a customer. So for those who are trying to understand social phenomena—such as economists, political scientists, and nosy neigh- bors—or those trying to determine how to behave—such as policymakers, business owners, and teenagers—game theory has two deliverables. First, it provides a framework for taking a complex social situation and boiling it down to a model that is manageable. Second, it provides methods for extract- ing insights from that model regarding how people do behave or how they should behave. This chapter focuses on using game theory to model a strate- gic situation; the next chapter begins our journey solving such models.

Human behavior typically occurs in an environment that is highly complex, and this complexity poses a challenge in modeling social phenomena. Deciding on what to put in a model is like trying to pack for college: there’s just no way to shove everything you want into that suitcase. In that light, it is useful to dis- tinguish between literal and metaphorical models. A literal model is a model that is descriptively accurate of the real-world setting it is intended to repre- sent. Other than for board games and a few other settings, a literal model of a social situation would be a bloody mess. In contrast, a metaphorical model is a vast simplification—a simplified analogy—of the real-world situation; it is not meant to be descriptively accurate. With a metaphorical model, we try to simulate the real world in essential ways, not replicate it. The “essential” ways are those factors thought to be critical to the problem of interest. Factors that are presumed to be secondary are willfully ignored. Most of the models in this book and most of the models constructed to understand social phenomena are metaphorical. Done right, a metaphorical model can yield insights into human behavior that are applicable to much richer and more realistic situations.

Whether literal or metaphorical, game theory offers a scaffolding around which a model can be constructed, and in this chapter we review the two pri- mary types of scaffolding. The extensive form is a description of the sequence of choices faced by those involved in a strategic situation, along with what they know when they choose. In Section 2.2, we consider extensive form games of perfect information, in which a person always knows what has thus far transpired in the game. Situations with imperfect information are de- scribed in Section 2.3, and these models allow a person to lack knowledge about what other people have chosen so far. The central concept of a strategy