Moving from the Extensive Form and Strategic Form 41
in a cell is Galileo’s payoff, the second is the Inquisitor’s payoff, and the third is the Pope’s payoff. In filling out the matrix, consider, for example, the strategy profile (Refer, DNC/C, Do not torture). The ensuing path is that the Pope refers the case, Galileo does not confess, and the Inquisitor does not torture Galileo. The payoffs are (4,2,2), as shown in the figure. Note that if the Pope chooses not to refer the case, then the payoffs are (5,3,3), regardless of the strategies chosen by Galileo and the Inquisitor, since they don’t get a chance to act. Similarly, if the Pope refers and Galileo initially confesses (by choosing either strategy C/C or strategy C/DNC), then the payoffs are the same whether the Inquisitor intends to torture or not, because Galileo’s confession means that the Inquisitor doesn’t get the opportunity to move.