The Mathematics of Tucker: A Sampler

Clearly, for each man the pure strategy "confess" dominates the pure strategy "not confess." Hence, there is a unique equilibrium point* given by the two pure strategies "confess." In contrast with this non-cooperative solution one sees that both men would profit if they could form a coalition binding each other to "not confess." The game becomes zero-sum three-person by introducing the State as a third player. The State exercises no choice (that is, has a single pure strategy) but receives payoffs as follows: