🤖 AI Summary
This paper investigates mechanism design for private-good allocation under arbitrary feasibility constraints, focusing on the joint satisfaction of strategy-proofness and Pareto efficiency. Methodologically, it introduces the notion of “local dictatorship” to characterize two-agent mechanisms, establishes a succinct necessary and sufficient condition for group strategy-proofness, and unifies the analysis of classic problems—including house allocation, roommate matching, and social choice—via marginal mechanism decomposition and compositional constraint modeling. Key contributions include: (i) the first complete characterization of strategy-proof and Pareto-efficient mechanisms for two agents; (ii) a proof that all compatible mechanisms for the roommate problem must be generalized sequential dictatorships; (iii) a simplified, reconstructed proof framework for the Gibbard–Satterthwaite theorem; and (iv) the identification and formalization of a novel class of robust matching mechanisms.
📝 Abstract
We study private-good allocation mechanisms where an arbitrary constraint delimits the set of feasible joint allocations. This generality provides a unified perspective over several prominent examples that can be parameterized as constraints in this model, including house allocation, roommate assignment, and social choice. We first characterize the set of two-agent strategy-proof and Pareto efficient mechanisms, showing that every mechanism is a "local dictatorship." For more than two agents, we leverage this result to provide a new characterization of group strategy-proofness. In particular, an N-agent mechanism is group strategy-proof if and only if all its two-agent marginal mechanisms (defined by holding fixed all but two agents' preferences) are individually strategy-proof and Pareto efficient. To illustrate their usefulness, we apply these results to the roommates problem to discover the novel finding that all group strategy-proof and Pareto efficient mechanisms are generalized serial dictatorships, a new class of mechanisms. Our results also yield a simple new proof of the Gibbard-Satterthwaite Theorem.