Subgame Perfect Implementation

Subgame Perfect Implementation and the Walrasian Correspondence

“…We …rst show that the Walrasian correspondence de…ned over this class of exchange economies is not implementable in subgame perfect equilibrium. Indeed, the assumption of di¤erentiability cannot be relaxed unless one imposes parametric restrictions on the environment, like assumption EE.3 in Moore-Repullo (1988).…”

“…In their seminal papers, Moore-Repullo (1988) (MR in the sequel) and Abreu-Sen (1990) (henceforth, AS) show that monotonicity is no longer necessary for implementation in subgame perfect equilibrium. Suppose that we have two states of the world and , and that outcome a is in the social choice correspondence under but not under .…”

“…Monotonicity (Maskin (1999)), a necessary condition for Nash implementation, is violated for allocations at the boundary of the feasible set. However, we know since the seminal work of Moore-Repullo (1988) and Abreu-Sen (1990) that monotonicity is no longer necessary for subgame perfect implementation. We …rst show that the Walrasian correspondence de…ned over this class of exchange economies is not implementable in subgame perfect equilibrium.…”

“…We …rst show that the Walrasian correspondence de…ned over this class of exchange economies is not implementable in subgame perfect equilibrium. Indeed, the assumption of di¤erentiability cannot be relaxed unless one imposes parametric restrictions on the environment, like assumption EE.3 in Moore-Repullo (1988).Next, assuming di¤erentiability, we construct a sequential mechanism that fully implements the Walrasian correspondence in subgame perfect and strong subgame perfect equilibrium.. We take care of the boundary problem that was prominent in the Nash implementation literature. Moreover, our mechanism is based on price-allocation announcements and …ts the very description of Walrasian Equilibrium.…”

Bayesian implementation in exchange economies with state dependent preferences and feasible sets

“…For complete information environments, characterization results were given by Maskin [14], Hurwicz, Maskin, Postlewaite [12], Repullo [28], Sajio [29], Moore and Repullo [19], Dutta and Sen [5], Danilov [4], and others for Nash implementation; Moore and Repullo [18], Abreu and Sen [2] and others for implementation using re®ne-ments of Nash equilibrium; Matsushima [15] and Abreu and Sen [3] for virtual Nash implementation. For incomplete information environments, characterization results were given by Postlewaite and Schmeidler [25], Palfrey, and Srivastava [20,21], Mookherjee and Reichelstein [17], Jackson [13], Hong [9] among many others for Bayesian implementation; by Palfrey and Srivastava [23] and Mookherjee and Reichelstein [17] for implementation in using re®nements of Bayesian equilibrium; Abreu and Matsushima [1], Matsushima [16], Duggan [7], and Tian [35] for virtual Bayesian implementation.…”