SITUATION: GALILEO GALILEI AND THE INQUISITION, II
Referring back to Figure 2.3, we see that Galileo has two information sets: one as- sociated with Pope Urban VIII’s referring the case to the Inquisitor and the other for the situation when it is referred, Galileo does not confess, and the Inquisitor tortures Galileo. A strategy for Galileo is, then, a pair of actions. We’ll let C/DNC (Confess/Do Not Confess) denote the strategy for Galileo in which he confesses at the first information set and does not confess at the second. The other three strate- gies—C/C, DNC/C, and DNC/DNC—are defined analogously. The Inquisitor has one information set—when the Pope refers the case and Galileo does not con- fess—and two actions, all of which gives him two strategies: torture and do not tor- ture. Urban VIII also has one information set, which is the initial node, and as he can either refer the case or not, he has two strategies: refer and do not refer.
As shown in the payoff matrix in FIGURE 2.14, Galileo chooses a row, the Inquisitor chooses a column, and the Pope chooses a matrix. The first number