Double Implementation under Partially Honest and Fully Strategic Agents in Minority Coalitions

Badr Bahloul, Ahmed Doghmi () and Abderrahmane Ziad ()
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Badr Bahloul: National Institute of Statistics and Applied Economics,Madinat Al Irfane, Rabat Institutes, 10100 Rabat, Morocco
Ahmed Doghmi: National Institute of Statistics and Applied Economics,Madinat Al Irfane, Rabat Institutes, 10100 Rabat, Morocco
Abderrahmane Ziad: CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, UNICAEN UFR SEGGAT - Université de Caen Normandie - UFR de Sciences Économiques, Gestion, Géographie et Aménagement des Territoires - UNICAEN - Université de Caen Normandie - NU - Normandie Université, Université de Setif-1

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Abstract: We study the double implementation of social choice correspondences (SCCs) under both Nash and M -Nash equilibria, where the latter accounts for deviations by minority coalitions of agents. We consider two behavioral assumptions: (i) a strict majority of agents exhibit partial honesty, or (ii) all agents behave fully strategically. Within this enriched framework, we characterize sufficient conditions for double implementation. Introducing the notion of partial honesty-a minimal ethical constraint on agent behavior-we show that weak Pareto dominance together with unanimity ensures double implementation. In the fully strategic setting, we establish that Y -monotonicity and unanimity are jointly sufficient, provided the number of agents is at least three. We illustrate the scope of our results through applications to coalitional games (strong core vs. weak core), matching markets (proper vs. improper sub-solutions of group stable matchings), and allotment economies under restricted preference domains-namely, single-peaked, single-plateaued, and single-dipped preferences.Our findings contribute to implementation theory by incorporating ethical refinement into strategic analysis, thereby enlarging the set of SCCs that are amenable to robust and behaviorally-informed mechanism design.

Keywords: allotment economies; D71; single-peaked preferences. JEL classification: C72; matching problems; coalitional games; partial honesty; Double Implementation; Double Implementation partial honesty coalitional games matching problems allotment economies single-peaked preferences. JEL classification: C72 D71 (search for similar items in EconPapers)
Date: 2025-09-05
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