Is it reasonable to assume that people act only in their self-interest?
Does this assumption mean that people are selfish? Although rationality does mean pursuing your own interests, it places few restrictions on what those interests might be. It can encompass Ebenezer Scrooge either before Christmas Eve— when all he cares about is money—or after that momentous night—when he cares about his fellow human beings. Rationality is a church that welcomes all people, from the egotistical to the altruistic. To be rational means only to pursue your interests, however they are defined.
Initially, we will assume a particular implication of rationality: A player will not use a strategy (call it ) when there is another strategy (call it ) that al- ways produces a strictly higher payoff, regardless of what strategies are used by the other players. Thus, a strategy is never the right thing to do, as will always outperform . It would then be rather stupid to play (whether you’re Mother Teresa or Paris Hilton). We’ll go even further and assume that each player believes that other players avoid stupid strategies, that each player believes that other players believe that players avoid such strategies, and so forth. In other words, it is common knowledge among players that a player will not use a particular strategy when there is another strategy that is always strictly better.
In Appendix 3.5, we consider the concept of rationalizability, which is a stronger implication of rationality being common knowledge. Rationalizability is closer to the essence of what it means to be rational, although, because it is a rather subtle and complex concept, we make it optional here and leave it for the more adventuresome student (or the more exacting instructor).
3.2.1 Strict Dominance Let’s revisit Puccini’s opera Tosca, the strategic form game of which is repro- duced in FIGURE 3.2. Recall from Section 2.5 that Baron Scarpia, the chief of
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56 CHAPTER 3: ELIMINATING THE IMPOSSIBLE: SOLVING A GAME WHEN RATIONALITY IS COMMON KNOWLEDGE
3.2 Solving a Game when Players Are Rational 57
police, has condemned Floria Tosca’s lover Mario Cavaradossi to death. Scarpia tells Tosca that he’ll have the firing squad use blank cartridges in exchange for sexual favors from Tosca. Scarpia first tells the firing squad to use real or blank cartridges, and then he meets Tosca, at which point she must decide whether to consent to Scarpia’s demands or stab him. Soon thereafter, Cavaradossi is brought before the firing squad. Both Tosca and Scarpia move without knowing what the other has chosen. The payoffs reflect that Tosca cares foremost that her lover survives and secondarily that she not consent to Scarpia, and that Scarpia longs to have relations with Tosca and only secondarily desires to execute Cavaradossi.