Mechanism Design without Money via Stable Matching

Mechanism design without money has a rich history in social choice literature. Due to thestrong impossibility theorem by Gibbard and Satterthwaite, exploring domains in which thereexist dominant strategy mechanisms is one of the central questions in the field. We propose ageneral framework, called the generalized packing problem (gpp), to study the mechanism designquestions without payment. The gpp possesses a rich structure and comprises a number of well-studied models as special cases, including, e.g., matroid, matching, knapsack, independent set,and the generalized assignment problem.We adopt the agenda of approximate mechanism design where the objective is to design atruthful (or strategyproof) mechanism without money that can be implemented in polynomialtime and yields a good approximation to the socially optimal solution. We study several specialcases of gpp, and give constant approximation mechanisms for matroid, matching, knapsack,and the generalized assignment problem. Our result for generalized assignment problem solvesan open problem proposed in [15].Our main technical contribution is in exploitation of the approaches from stable matching,which is a fundamental solution concept in the context of matching marketplaces, in applicationto mechanism design. Stable matching, while conceptually simple, provides a set of powerfultools to manage and analyze self-interested behaviors of participating agents. Our mechanismuses a stable matching algorithm as a critical component and adopts other approaches likerandom sampling and online mechanisms. Our work also enriches the stable matching theorywith a new knapsack constrained matching model. ∗Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological Uni-versity, Singapore. Email: [email protected], [email protected].†Microsoft Research Asia. Email: [email protected]:1104.2872v1[cs.GT]14Apr2011