Sequential implementation without commitment

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Working paper
Takashi Hayashi and Michele Lombardi
Issue number: 
Adam Smith Business School Discussion Papers
Adam Smith Business School - University of Glasgow
In a finite-horizon intertemporal setting, in which society needs to decide and enforce a socially optimal outcome in each period without being able to commit to future ones, the paper examines problems of implementing dynamic social choice processes. A dynamic social choice process is a social choice function (SCF) that maps every admissible state into a socially optimal outcome on the basis of past outcomes. A SCF is sequentially implementable if there exists a sequence of mechanisms (with observed actions and with simultaneous moves) such that for each possible state of the environment, each (pure strategy) subgame perfect (Nash-)equilibrium of games played sequentially by the same individuals in that state generates the outcome prescribed by the SCF for that state, at every history. The paper identiÖes necessary conditions for SCFs to be sequentially implemented, sequential decomposability and sequential Maskin monotonicity, and shows that they are also su¢ cient under auxiliary conditions when there are three or more individuals. It provides an account of welfare implications of the sequential implementability in the contexts of sequential trading and sequential voting.
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