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

<div> 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. </div>