A full characterization of nash implementation with strategy space reduction

Abstract

Noting that a full characterization of Nash-implementation is given using a canonical-mechanism and Maskin's theorem (Maskin, 1999) is shown using a mechanism with Saijo's type of strategy space reduction (Saijo, 1988), this paper fully characterizes the class of Nashimplementable social choice correspondences (SCCs) by mechanisms endowed with Saijo's message space specification -s-mechanisms. This class of SCCs is further shown to be equivalent to the class of Nashimplementable SCCs, though any further 'strategy space reduction' mechanism breaks this equivalent relationship down.JEL classification: C72; D71; D82.

Natural Implementation with Partially-Honest Agents

“…As informationally decentralized mechanisms, the authors take Saijo-type mechanisms (Saijo, 1988;Lombardi and Yoshihara, 2011b), where each agent must announce her own type and that of her neighbor, an alternative, and an integer (henceforth, s-mechanisms). One main …nding is that, in contrast to the case of Maskin-type mechanisms, a weaker variant of Maskin monotonicity is necessary to fully identify the class of implementable SCC s by s-mechanisms.…”

“…This stands in stark contrast with the standard literature on implementation, where it is well-known that this SCC is not implementable. 20 Lemma 2. Let n 3 and`= 2.…”

Nash implementation via simple stochastic mechanisms: strategy space reduction

“…Note that this result is in line with other well known results of Nash implementation. In particular, the reported equivalence result is analogous to the equivalence relationship between Nash implementation by s-mechanisms and Nash implementation in general social choice environments (Lombardi and Yoshihara 2010).…”

Natural Implementation with Partially Honest Agents in Economic Environments with Free-Disposal

“…11 Observe that our forthrightness condition di¤ers from that of Saijo et al (1999) because it applies only to e¢ ciency prices in F (x; u) rather than to those in (x; u). We shall make use of this di¤er-ence in the next sections, which will be relevant for the case where F is the Walrasian correspondence.…”

“…11 The reader should refer to Dutta et al (1995), Saijo et al (1996), and Lombardi and Yoshihara (2013a) for a more discussion on forthrightness. 8 …”