Nash equilibrium in pure strategies Find all Nash equilibria in the games in Table 10.4, where Player I chooses between Up (U), (Middle (M)), and Down (D) and Player II chooses between Left (L), (Middle (M)), and Right (R). Table 10.4 Nash equilibrium exercises L R U 2,2 0,0 D 0,0 1,1

(a)

(b)

(c) Notice that in Exercise 10.5(a), there are two Nash equilibria in pure strategies, though one is clearly inferior to the other from the point of view of both play ers. In Exercise 10.5(b), kU, Ll and kD, Ll are not both Nash equilibria although they are “just as good” in the sense that they lead to the same payoffs. And in Exercise 10.5(c), there are outcomes that are better for both players than the Nash equilibrium. As these games illustrate, there is no straightforward connection between Nash equilibria and “best” outcomes for the players. As a result, it would be a mistake to try to identify the former by searching for the latter. An even more striking example of the general phenomenon is the prisoners’ dilemma (Figure 10.1).