To return to our prisoners, we assume that they appreciate the well-being of the other and theirs, contrary to what we assume. In this case, this must be reflected in their utility functions and, therefore, in their payments. If their payment structures are changed so that they feel so bad, for example, to contribute to the inefficiency that they would rather spend extra years in prison than endure shame, then they will no longer be in one. But all this shows that not all possible situations are a PD; this does not show that selfishness is part of the hypothesis of game theory. It is the logic of the situation of the prisoners, not their psychology, that captures them in the ineffective result, and if that is really their situation, they are stuck in there (with the exception of other complications discussed below). Agents who wish to avoid ineffective results are best placed to prevent certain games; the advocate of the possibility of cantonal rationality really suggests that they try to dig themselves into such games by turning into different types of agents. Some other theorists understand differently the point of game theory. They see game theory as an explanatory presentation of the processes of real human strategic arguments. For this idea to be applicable, we must assume that agents do at least sometimes what they do in non-parametric attitudes, because game theory logic recommends certain actions as “rational”.
Such an understanding of game theory implies a normative aspect, because “rationality” is called a property that an agent wants at least in general. These two very general logics about the possible uses of game theory are compatible with the tautological interpretation of maximizing profits. But the philosophical difference is not inactive from the point of view of the work game theorist. As we will see in a later section, those who hope to use game theory to explain strategic thinking are opposed to purely strategic behavior, to some particular philosophical problems and practices. Reintroduce parametric factors, i.e. rocks falling on the #2 bridge and cobras on the #3 bridge. Assuming the fugitive is safe to cross #1 the bridge safely, he has a 90% chance of crossing the bridge #2 and 80% chance of crossing the bridge #3. We can solve this new game if we make certain assumptions about the usefulness functions of both players. Suppose Player 1, the fugitive, only deals with life or death (life prefers death), while the persecutor simply wishes to report that the fugitive is dead, preferring that he has to report that he got away with it.
(In other words, none of the players cares about how the fugitive lives or dies.) Let us also assume, for the moment, that none of the players have any advantage or no use in taking more or less risks. In this case, the fugitive simply takes his initial randomization formula and weights it according to the different degrees of parametric danger on the three decks. Each bridge should be considered a lottery on the possible results of the fugitive, in which each lottery has another expected payment regarding the objects in its use function. This example of a Cold War standoff, although famous and of considerable importance in the history of game theory and its popular reception, was then based on analyses that were not very subtle. Military theorists were almost certainly wrong to the point of modeling the Cold War as an impact. On the one hand, the nuclear compensation game has been involved in larger global power plays of great complexity. On the other hand, it is far from clear that for one of the two superpowers, the destruction of the other, while avoiding self-destruction, was in fact the highest result.