Implementation with extensive form games: One round of signaling is not enough

In situations of complete information, when a social choice function can be implemented using an extensive form game. it is always the case that there is an equilibrium which does not go beyond the first stage (that is, an eq uilibrium with "one round of signaling"). We show that this is not true in the incomplete information case. We provide: an example in which a social c hoice function cannot be implemented with an extensive form game if the mec hanism has an equilibrium with one round of signaling and we put some restr ictions on the way in which out of-equilibrium beliefs are formed. The soci al choice function can, however. be implemented using an extensive form mec hanism. but the equilibrium hits to reach the second stage. (C) 1999 Academ ic Press.