False-name-proof matching

Matching a set of agents to a set of objects has many real applications. One well-studied framework is that of priority-based matching, in which each object is assumed to have a priority order over the agents. The Deferred Acceptance (DA) and Top-Trading-Cycle (TTC) mechanisms are the best-known strategy-proof mechanisms. However, in highly anonymous environments, the set of agents is not known a priori, and it is more natural for objects to instead have priorities over characteristics (e.g., the student's GPA or home address). In this paper, we extend the model so that each agent reports not only its preferences over objects, but also its characteristic. We derive results for various notions of strategy-proofness and false-name-proofness, corresponding to whether agents can only report weaker characteristics or also incomparable or stronger ones, and whether agents can only claim objects allocated to their true accounts or also those allocated to their fake accounts. Among other results, we show that DA and TTC satisfy a weak version of false-name-proofness. Furthermore, DA also satisfies a strong version of false-name-proofness, while TTC fails to satisfy it without an acyclicity assumption on priorities.

[1]  V. Crawford.  Comparative statics in matching markets , 1991 .

[2]  Vincent Conitzer,et al.  Worst-case efficiency ratio in false-name-proof combinatorial auction mechanisms , 2010, AAMAS.

[3]  T. Morrill.  An alternative characterization of top trading cycles , 2013 .

[4]  Vincent Conitzer,et al.  Anonymity-Proof Voting Rules , 2008, WINE.

[5]  H. Ergin.  Efficient Resource Allocation on the Basis of Priorities , 2002 .

[6]  Makoto Yokoo,et al.  False-name-proof mechanism design without money , 2011, AAMAS.

[7]  Yeon-Koo Che,et al.  The Role of Priorities in Assigning Indivisible Objects : A Characterization of Top Trading Cycles , 2010 .

[8]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[9]  Onur Kesten,et al.  On two competing mechanisms for priority-based allocation problems , 2006, J. Econ. Theory.

[10]  Thomas Quint,et al.  On Houseswapping, the Strict Core, Segmentation, and Linear Programming , 2003, Math. Oper. Res..

[11]  Makoto Yokoo,et al.  The effect of false-name bids in combinatorial auctions: new fraud in internet auctions , 2004, Games Econ. Behav..

[12]  Jerry R. Green,et al.  Partially Verifiable Information and Mechanism Design , 1986 .

[13]  L. Shapley,et al.  On cores and indivisibility , 1974 .

[14]  S. Pápai,et al.  Strategy-proofness and population-monotonicity for house allocation problems , 2002 .

[15]  Haris Aziz,et al.  Housing Markets with Indifferences: A Tale of Two Mechanisms , 2012, AAAI.

[16]  M. Balinski,et al.  A Tale of Two Mechanisms: Student Placement , 1999 .