Efficient assignment with interdependent values

We study the “house allocation” problem in which n agents are assigned n objects, one for each agent, when the agents have interdependent values. We show that there exists no mechanism that is Pareto efficient and ex post incentive compatible, and the only mechanism that is group ex post incentive compatible is constant across states. By contrast, we demonstrate that a Pareto efficient and Bayesian incentive compatible mechanism exists in the two agent house-allocation problem, given sufficient congruence of preferences and the standard single crossing property. ∗We thank So Yoon Ahn, Yuchen Liu, Kelly Rader, Keeyoung Rhee, and especially Fanqi Shi for excellent research assistance. We also thank Oguz Afacan, Eduardo Azevedo, Dirk Bergemann, Wing-Sum Cheung, Jon Eguia, Daniel Fragiadakis, Tadashi Hashimoto, Navin Kartik, Konrad Mierendorff, Benny Moldovanu, Bruno Strulovici, and seminar participants at Seoul National University, Stanford University, MITRE Auctions and Matching Workshop at University of Michigan, the 2012 NBER Market Design Workshop, and SING8 at Budapest for comments. Yeon-Koo Che and Jinwoo Kim acknowledge the financial support from the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology through its World Class University Grant (R32-2008-000-10056-0). This work was completed while Jinwoo Kim and Fuhito Kojima were visiting Yonsei and Columbia University, whose support and hospitality are gratefully acknowledged. †Che: Department of Economics, Columbia University, and YERI, Yonsei University (email: [email protected]); Kim: Department of Economics, Seoul National University (email: [email protected]); Kojima: Department of Economics, Stanford University ([email protected]).