Approximate Efficiency in Matching Markets

We propose a measure of approximate ex-ante Pareto efficiency in matching markets. According to this measure, a lottery over matchings is \(\gamma \)-approximately efficient if there is no alternate lottery in which each agent’s ex-ante expected utility increases by an \(\gamma \) factor. A mechanism is \(\gamma \)-approximately efficient if every lottery produced in equilibrium is \(\gamma \)-approximately efficient. We argue this is the natural extension of approximate efficiency in transferable-utility settings to our nontransferable-utility setting. Using this notion, we are able to quantify the intuited efficiency improvement of the so-called Boston mechanism and the recently-proposed choice-augmented deferred acceptance mechanism over the random serial dictatorship mechanism. Furthermore, we provide the first formal statement and analysis of the Raffle mechanism, which is conceptually simpler than the Boston mechanism and has a comparable efficiency guarantee.

[1]  Yeon-Koo Che,et al.  Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms , 2008 .

[2]  D. J. Roberts,et al.  THE INCENTIVES FOR PRICE-TAKING BEHAVIOR IN LARGE EXCHANGE ECONOMIES , 1976 .

[3]  S. Matthew Weinberg,et al.  A Simple and Approximately Optimal Mechanism for an Additive Buyer , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[4]  R. Zeckhauser,et al.  The Efficient Allocation of Individuals to Positions , 1979, Journal of Political Economy.

[5]  Ariel D. Procaccia,et al.  The Unreasonable Fairness of Maximum Nash Welfare , 2019, ACM Trans. Economics and Comput..

[6]  Eric Budish,et al.  The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes , 2010, Journal of Political Economy.

[7]  Nikhil Bansal,et al.  The Santa Claus problem , 2006, STOC '06.

[8]  Hector Chade,et al.  Simultaneous Search , 2006 .

[9]  Judd B. Kessler,et al.  Bringing Real Market Participants' Real Preferences into the Lab: An Experiment that Changed the Course Allocation Mechanism at Wharton , 2016 .

[10]  Muriel Niederle,et al.  Boston versus deferred acceptance in an interim setting: An experimental investigation , 2016, Games Econ. Behav..

[11]  Marek Pycia.  The Cost of Ordinality , 2014 .

[12]  Kurt Mehlhorn,et al.  Popular matchings , 2005, SODA '05.

[13]  Nir Shabbat.  Approximate Revenue Maximization with Multiple Items , 2012 .

[14]  Tim Roughgarden,et al.  Simple versus optimal mechanisms , 2009, EC '09.

[15]  Dan W. Brockt,et al.  The Theory of Justice , 2017 .

[16]  L. Shapley,et al.  Trade Using One Commodity as a Means of Payment , 1977, Journal of Political Economy.

[17]  Chaitanya Swamy,et al.  Welfare maximization and truthfulness in mechanism design with ordinal preferences , 2013, ITCS.

[18]  Nicole Immorlica,et al.  A Unifying Hierarchy of Valuations with Complements and Substitutes , 2014, AAAI.

[19]  Haim Kaplan,et al.  Non-price equilibria in markets of discrete goods , 2011, EC '11.

[20]  Paul R. Milgrom,et al.  Designing Random Allocation Mechanisms: Theory and Applications , 2013 .

[21]  Eric Budish,et al.  Strategy-Proofness in the Large , 2017, The Review of Economic Studies.

[22]  Hervé Moulin,et al.  A New Solution to the Random Assignment Problem , 2001, J. Econ. Theory.

[23]  Avinatan Hassidim,et al.  "Strategic" Behavior in a Strategy-proof Environment , 2016, EC.

[24]  Éva Tardos,et al.  Composable and efficient mechanisms , 2012, STOC '13.

[25]  Yeon-Koo Che,et al.  Expanding 'Choice' in School Choice , 2008 .

[26]  Annamária Kovács,et al.  Bayesian Combinatorial Auctions , 2008, ICALP.

[27]  Simina Brânzei,et al.  Nash Social Welfare Approximation for Strategic Agents , 2016, EC.

[28]  Yeon-Koo Che,et al.  Resolving Conflicting Preferences in School Choice: The 'Boston' Mechanism Reconsidered , 2009 .

[29]  Michal Feldman,et al.  Simultaneous auctions are (almost) efficient , 2012, STOC '13.

[30]  Tim Roughgarden,et al.  The price of anarchy in large games , 2015, STOC.

[31]  Craig Boutilier,et al.  Optimal social choice functions: A utilitarian view , 2015, Artif. Intell..

[32]  Elliot Anshelevich,et al.  Randomized Social Choice Functions under Metric Preferences , 2015, IJCAI.

[33]  Mihalis Yannakakis,et al.  On the approximability of trade-offs and optimal access of Web sources , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.