Strong Nash implementation and economic applications

Strong Nash implementation remains a central challenge in mechanism design, with no direct analogue to Maskin (1977) seminal theorem for Nash implementation under simple and widely applicable conditions. We revisit the structure of Maskin (1979) result and show that strong Nash implementability imposes a coalitional compatibility requirement, formalized by the coalitional intersection property. We then identify the Restricted Coalitional Intersection Property (RCIP) as a weaker implication of this requirement, imposing only limited compatibility across coalitions when comparing equilibrium outcomes under different preference profiles. To guarantee RCIP, we introduce a structural condition on the environment-Agents with Separately Exclusive Alternatives (ASEA)-which ensures RCIP for coalitions separating such agents. ASEA captures situations in which a pair of agents each strictly prefers its own designated alternative to that of the other, while all remaining agents weakly prefer any socially chosen alternative to these designated alternatives. We show that, in societies with at least three agents and containing at least one such pair, every social choice correspondence that is weakly Pareto optimal and satisfies a strengthened form of Maskin monotonicity-called Y-monotonicity-is implementable in strong equilibrium. We illustrate the applicability of our results in a variety of economic environments, including several-to-one matching markets, fair allocation, efficient sharing of commonly owned technologies, and coalitional games.