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Robust Implementation in Rationalizable Strategies in General Mechanisms

Takashi Kunimoto and Rene Saran ()
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Rene Saran: University of Cincinnati

No 10-2020, Economics and Statistics Working Papers from Singapore Management University, School of Economics

Abstract: A social choice function (SCF) is robustly implementable in rationalizable strate-gies if every rationalizable strategy profile on every type space results in outcomes consistent with it. First, we establish an equivalence between robust implementation in rationalizable strategies and “weak rationalizable implementation”. Second, using the equivalence result, we identify weak robust monotonicity as a necessary and al-most sufficient condition for robust implementation in rationalizable strategies. This exhibits a contrast with robust implementation in interim equilibria, i.e., every equilib-rium on every type space achieves outcomes consistent with the SCF. Bergemann and Morris (2011) show that strict robust monotonicity is a necessary and almost sufficient condition for robust implementation in interim equilibria. We argue that strict robust monotonicity is strictly stronger than weak robust monotonicity, which further implies that, within general mechanisms, robust implementation in rationalizable strategies is more permissive than robust implementation in interim equilibria. The gap between robust implementation in rationalizable strategies and that in interim equilibria stems from the strictly stronger nonemptiness requirement inherent in the latter concept.

Keywords: Ex post incentive compatibility; rationalizability; interim equilibrium; robust implementation; weak rationalizable implementation; weak robust monotonicity (search for similar items in EconPapers)
JEL-codes: C72 D78 D80 (search for similar items in EconPapers)
Pages: 51 pages
Date: 2020-04-14
New Economics Papers: this item is included in nep-des, nep-gen, nep-gth, nep-mic and nep-sea
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