Rationalizable Implementation of Social Choice Correspondences

Abstract

A social choice correspondence (SCC) F is a mapping which associates with every state θ ∈ Θ a non empty subset of a set of outcomes. F is implementable in rationalizable strategies provided that there exists a mechanism such that for each state θ, the support of its set of rationalizable outcomes is equal to the socially desirable set F (θ). We find that r-monotonicity is a necessary condition for the rationalizable implementation of F . When there are at least three agents and F satisfies certain auxiliary conditions, r-monotonicity is also sufficient for rationalizable implementation. Finally, we show that a SCC which is never single valued is rationalizably implementable if and only if it satisfies r-monotonicity.

Rationalizable implementation of social choice functions: Complete characterization

“…Focusing on social choice functions, BMT show that strict Maskin monotonicity is necessary for rationalizable implementation, and, furthermore, given two additional technical conditions, strict Maskin monotonicity is also sufficient. In two subsequent papers, Kunimoto and Serrano (2019) and Jain (2021) study rationalizable implementation of social choice correspondences 2 . In this paper, we focus on social choice functions, and our goal is to fully characterize rationalizable implementation when no technical condition is imposed.…”

“…Previous characterization of rationalizable implementation (BMT, Jain (2021), Kunimoto and Serrano (2019)) hinges critically on the following two assumptions.…”

Rationalizable Implementation of Social Choice Functions: Complete Characterization

“…Focusing on social choice functions, BMT show that strict Maskin monotonicity is necessary for rationalizable implementation, and furthermore, given two additional technical additional conditions, strict Maskin monotonicity is also sufficient. In three subsequent papers, Kunimoto and Serrano (2019), Jain (2021) and Xiong (2018) study rationalizable implementation of social choice correspondences. 3 In this paper, we focus on social choice functions, and our goal is to fully characterize rationalizable implementation when no technical condition is imposed.…”

“…Previous characterization of rationalizable implementation (BMT, Jain (2021), Kunimoto and Serran (2019)) hinges critically on the following two assumptions.…”

Virtual Implementation by Bounded Mechanisms: Complete Information

“…In the literature on exact implementation robustness to strategic uncertainty has recently been studied inBergemann et al (2011) ,Kunimoto and Serrano (2016) andJain (2019). The constructive proofs used in this literature rely on the integer game construction.…”