Resumen de Necessary and sufficient condition for two-player subgame perfect implementation

Hannu Vartiainen

• Implementation theory concerns the problem of designing mechanisms that decentralize decision power to the members of a society. Decentralization is necessary especially if information is dispersed among players. Moore-Repullo (1988) and Abreu-Sen (1990) study implementation of social choice correspondences (SCCs) by using subgame perfect Nash equilibrium (SPE) as the solution concept. They find that via an extensive form mechanism one is able to implement non-monotonic SCCs (see also Herrero and Srivastava 1992). Since Maskin (1977), monotonicity has been known to be a necessary condition for Nash implementation. Moore-Repullo and Abreu-Sen construct a necessary condition for SPE implementation which, together with no veto power (NVP), forms a sufficient condition for implementation in three or more players caser.

  The gap between necessary and sufficient conditions in the context of three or more players is closed by Vartiainen (1999).