Implementation in Nash Equilibrium (II): Applications

In the previous chapter we presented a general mechanism that implements in Nash equilibrium any social choice correspondence satisfying monotonicity and no veto power. A general criticism of the Nash equilibrium approach to the theory of implementation is that, in the case where a correspondence is implemented, this kind of equilibrium requires a good deal of coordination among agents in order to select those strategies corresponding to a particular equilibrium.1 This problem is well-known in game theory: when playing, say, The Battle of the Sexes agents may, by means of strategies that are part of different Nash equilibria of the game, achieve outcomes that are not Nash equilibria. In our case, if the mechanism is run by a real person, she can suggest what strategy agents have to use (truth-telling). This is of course cheap talk, but it makes slightly more palatable the assumption that agents know the particular Nash equilibrium that is going to be played.