One-step-ahead implementation

Abstract

In many situations, agents are involved in an allocation problem that is followed by another allocation problem whose optimal solution depends on how the former problem has been solved. In this paper, we take this dynamic structure of allocation problems as an institutional constraint. By assuming a …nite number of allocation problems, one for each period/stage, and by assuming that all agents in society are involved in each allocation problem, a dynamic mechanism is a period-by-period process. This process generates at any period-t history a period-t mechanism with observable actions and simultaneous moves. We also assume that the objectives that a planner wants to achieve are summarized in a social choice function (SCF), which maps each state (of the world) into a period-by-period outcome process. In each period t, this process selects for each state a period-t socially optimal outcome conditional on the complete outcome history realized up to period t 1. Heuristically, the SCF is one-step-ahead implementable if there exists a dynamic mechanism such that for each state and each realized periodt history, each of its subgame perfect Nash equilibria generates a period-by-period outcome process that coincides with the period-by-period outcome process that the SCF generates at that state from period t onwards. We identify a necessary condition for SCFs to be one-step-ahead implemented, one-step-ahead Maskin monotonicity, and show that it is also su¢ cient under a variant of the condition of no veto-power when there are three or more agents. Finally, we provide an account of welfare implications of one-step-ahead implementability in the contexts of trading decisions and voting problems.

Partial equilibrium mechanism and inter-sectoral coordination: An experiment

“…Our sequential treatment is motivated by the theoretical work of Hayashi and Lombardi (2019), which studies what can be implemented in the multi-period setting in which allocation in the current period must be chosen and finalized, without any commitment to allocations in future periods. This handles more restricted situations than in the existing research on subgameperfect implementation (Moore and Repullo, 1988), which allows that an entire social outcome, once chosen at some stage, can be overturned at any subsequent stage.…”

“…First, although most studies in the subgame-perfect implementation literature allow canceling at any stage, this is not a realistic assumption in the multi-sector setting. Note that when sequential elicitation is applied for the two-sector allocation problem, a realistic specification is that the allocation for one sector is finalized in the first stage, without any commitment to allocation for the other sector to be made in the second stage, and no cancellation of the first sector allocation is allowed afterwards (Hayashi and Lombardi, 2019). This is typically the case when we must finalize housing allocation before school seats are assigned.…”

Constrained implementation

“…While constrained monotonicity is necessary for constrained implementation, it is not su¢ cient. 5 We need an extra condition for the su¢ ciency result.…”

“…See the Appendix. 5 For example, suppose that A 2 = a 2 . As we noted in Section 3, constrained monotonicity is equivalent to monotonicity when A 2 = a 2 .…”

Repeated implementation with overlapping generations of agents

“…A constant SCF is trivially implementable.3 Hayashi and Lombardi (2019) also study implementation in a dynamic setup, but in any given period, the socially desirable alternative depends not only on the state, but also on the history of alternatives that have been selected in the previous periods.…”