{"type":"ScholarlyArticle","title":"Average-case Analysis of the Assignment Problem with Independent Preferences","authors":[{"name":"Yansong Gao","slug":"yansong-gao","given":"Yansong","family":"Gao","affiliation":"Applied Mathematics and Computational Science , University of Pennsylvania"},{"name":"Jie Zhang","slug":"jie-zhang","given":"Jie","family":"Zhang","affiliation":"Electronics and Computer Science , University of Southampton"}],"abstract":"The fundamental assignment problem is in search of welfare maximization mechanisms to allocate items to agents when the private preferences over indivisible items are provided by self-interested agents. The mainstream mechanism \\textit{Random Priority} is asymptotically the best mechanism for this purpose, when comparing its welfare  to the optimal social welfare using the canonical \\textit{worst-case approximation ratio}. \r\n\r\nSurprisingly, the efficiency loss indicated by the worst-case ratio does not have a constant bound \\cite{FFZ:14}.Recently, \\cite{DBLP:conf/mfcs/DengG017} shows that when the agents' preferences are drawn from a uniform distribution, its \\textit{average-case approximation ratio} is upper bounded by 3.718. They left it as an open question of whether a constant ratio holds for general scenarios. In this paper, we offer an affirmative answer to this question by showing that the ratio is bounded by $1/\\mu$ when the preference values are independent and identically distributed random variables, where $\\mu$ is the expectation of the value distribution. This upper bound improves the results in \\cite{DBLP:conf/mfcs/DengG017} for the Uniform distribution as well. Moreover, under mild conditions, the ratio has a \\textit{constant} bound for any independent  random values.\r\n\r\nEn route to these results, we develop powerful tools to show the insights that for most valuation inputs, the efficiency loss is small.","doi":"10.24963/ijcai.2019/41","url":"https://ijcai.org/proceedings/2019/41","pdf":"https://ijcai.org/proceedings/2019/0041.pdf","markdown":"https://ijcai.org/proceedings/2019/41.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/41","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":41,"pages":{"first":287,"last":293},"keywords":["Agent-based and Multi-agent Systems: Agent Theories and Models","Agent-based and Multi-agent Systems: Resource Allocation","Agent-based and Multi-agent Systems: Algorithmic Game Theory"],"videos":[],"references":[{"position":1,"raw":"[Abdulkadiroglu and Sönmez, 2013] Atila Abdulkadiroglu and Tayfun Sönmez. Matching Markets: Theory and Prac- tice. Advances in Economics and Econometrics (Tenth World Congress), pages 3-47, 2013.","title":"Advances in Economics and Econometrics (Tenth World Congress)","authors":"Sönmez Abdulkadiroglu, Atila Abdulkadiroglu, Tayfun Sönmez","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Abdulkadiroglu and Sönmez, 1998] Atila Abdulkadiroglu and Tayfun Sönmez. Random serial dictatorship and the core from random endowments in house allocation prob- lems. Econometrica, 66(3):689-702, 1998.","title":"Atila Abdulkadiroglu and Tayfun Sönmez. Random serial dictatorship and the core from random endowments in house allocation problems","authors":"Sönmez Abdulkadiroglu","year":"1998","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Abdulkadiroglu and Sönmez, 1999] Atila Abdulkadiroglu and Tayfun Sönmez. House allocation with existing ten- ants. Journal of Economic Theory, 88(2):233-260, 1999.","title":"Atila Abdulkadiroglu and Tayfun Sönmez. House allocation with existing tenants","authors":"Sönmez Abdulkadiroglu","year":"1999","venue":"Journal of Economic Theory","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Anshelevich et al., 2018] Elliot Anshelevich, Onkar Bhard- waj, Edith Elkind, John Postl, and Piotr Skowron. Approx- imating optimal social choice under metric preferences. Artif. Intell., 264:27-51, 2018.","title":"Approximating optimal social choice under metric preferences","authors":"Elliot Anshelevich, Onkar Bhardwaj, Edith Elkind, John Postl, Piotr Skowron","year":"2018","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Anshelevich, 2016] Elliot Anshelevich. Ordinal approxima- tion in matching and social choice. SIGecom Exchanges, 15(1):60-64, 2016.","title":"Elliot Anshelevich. Ordinal approximation in matching and social choice","authors":"Anshelevich","year":"2016","venue":"SIGecom Exchanges","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Archer et al., 2003] Aaron Archer, Christos H. Papadim- itriou, Kunal Talwar, and Éva Tardos. An approximate truthful mechanism for combinatorial auctions with single parameter agents. In SODA, pages 205-214, 2003.","title":"An approximate truthful mechanism for combinatorial auctions with single parameter agents","authors":"Aaron Archer, Christos H Papadimitriou, Kunal Talwar, Éva Tardos","year":"2003","venue":"SODA","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Aziz et al., 2013] Haris Aziz, Felix Brandt, and Markus Brill. The computational complexity of random serial dic- tatorship. In WINE, pages 24-25, 2013.","title":"The computational complexity of random serial dictatorship","authors":"Haris Aziz, Felix Brandt, Markus Brill","year":"2013","venue":"WINE","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Barbera, 2010] Salvador Barbera. Strategy-proof Social Choice. In K. J. Arrow, A. K. Sen, and K. Suzumura, ed- itors, Handbook of Social Choice and Welfare, volume 2, chapter 25. North-Holland: Amsterdam, 2010.","title":"Salvador Barbera. Strategy-proof Social Choice","authors":"Barbera","year":"2010","venue":"Handbook of Social Choice and Welfare","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Bhalgat et al., 2011] Anand Bhalgat, Deeparnab Chakrabarty, and Sanjeev Khanna. Social welfare in one-sided matching markets without money. In APPROX-RANDOM, pages 87-98, 2011.","title":"Social welfare in one-sided matching markets without money","authors":"Anand Bhalgat, Deeparnab Chakrabarty, Sanjeev Khanna","year":"2011","venue":"APPROX-RANDOM","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Bogomolnaia and Moulin, 2001] Anna Bogomolnaia and Hervé Moulin. A New Solution to the Random Assign- ment Problem. Journal of Economic Theory, 100:295- 328, 2001.","title":"A New Solution to the Random Assignment Problem","authors":"Anna Bogomolnaia, Hervé Moulin","year":"2001","venue":"Journal of Economic Theory","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Chawla and Sivan, 2014] Shuchi Chawla and Balasubrama- nian Sivan. Bayesian algorithmic mechanism design. SIGecom Exchanges, 13(1):5-49, 2014.","title":"Shuchi Chawla and Balasubramanian Sivan","authors":"Sivan Chawla","year":"2014","venue":"SIGecom Exchanges","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Chen et al., 2013] Yiling Chen, John Lai, David C. Parkes, and Ariel D. Procaccia. Truth, justice, and cake cutting. Games and Economic Behavior, 77(1):284-297, 2013.","title":"Truth, justice, and cake cutting","authors":"Yiling Chen, John Lai, David C Parkes, Ariel D Procaccia","year":"2013","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Christodoulou et al., 2009] G. Christodoulou, E. Koutsou- pias, and A. Vidali. A lower bound for scheduling mecha- nisms. Algorithmica, 55(4):729-740, 2009.","title":"A lower bound for scheduling mechanisms","authors":"G Christodoulou, E Koutsoupias, A Vidali","year":"2009","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Christodoulou et al., 2016] George Christodoulou, Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg, Jie Zhang, and Jinshan Zhang. Social welfare in one-sided matching mechanisms. In Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems, pages 1297-1298, 2016.","title":"Social welfare in one-sided matching mechanisms","authors":"George Christodoulou, Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W Goldberg, Jie Zhang, Jinshan Zhang","year":"2016","venue":"Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Deng et al., 2017] Xiaotie Deng, Yansong Gao, and Jie Zhang. Smoothed and average-case approximation ratios of mechanisms: Beyond the worst-case analysis. In 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS, pages 16:1-16:15, 2017.","title":"Smoothed and average-case approximation ratios of mechanisms: Beyond the worst-case analysis","authors":"Deng","year":"2017","venue":"International Symposium on Mathematical Foundations of Computer Science, MFCS","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Dughmi and Ghosh, 2010] Shaddin Dughmi and Arpita Ghosh. Truthful assignment without money. In ACM Con- ference on Electronic Commerce, pages 325-334, 2010.","title":"Shaddin Dughmi and Arpita Ghosh. Truthful assignment without money","authors":"Ghosh Dughmi","year":"2010","venue":"ACM Conference on Electronic Commerce","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Durrett, 2011] Rick Durrett. Probability: Theory and exam- ples. Cambridge University Press, 2011.","title":"Rick Durrett. Probability: Theory and examples","authors":"Durrett","year":"2011","venue":null,"doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Esseen, 1945] Carl-Gustav Esseen. Fourier analysis of dis- tribution functions. a mathematical study of the laplace- gaussian law. Acta Mathematica, 77:1-125, 1945.","title":"Fourier analysis of distribution functions. a mathematical study of the laplacegaussian law","authors":"Carl-Gustav Esseen","year":"1945","venue":"Acta Mathematica","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Filos-Ratsikas et al., 2014] Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, and Jie Zhang. Social welfare in one-sided matchings: Random priority and beyond. In Algorithmic Game Theory, SAGT 2014, pages 1-12, 2014.","title":"Social welfare in one-sided matchings: Random priority and beyond","authors":"Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Jie Zhang","year":"2014","venue":"Algorithmic Game Theory, SAGT 2014","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Filos-Ratsikas et al., 2015] Aris Filos-Ratsikas, Minming Li, Jie Zhang, and Qiang Zhang. Facility location with double-peaked preferences. In Proceedings of the Twenty- Ninth AAAI Conference on Artificial Intelligence, pages 893-899, 2015.","title":"Facility location with double-peaked preferences","authors":"Aris Filos-Ratsikas, Minming Li, Jie Zhang, Qiang Zhang","year":"2015","venue":"Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Hajaj et al., 2015] Chen Hajaj, John P. Dickerson, Avinatan Hassidim, Tuomas Sandholm, and David Sarne. Strategy- proof and efficient kidney exchange using a credit mech- anism. In Proceedings of the Twenty-Ninth AAAI Con- ference on Artificial Intelligence, January 25-30, 2015, Austin, Texas, USA., pages 921-928, 2015.","title":"Strategyproof and efficient kidney exchange using a credit mechanism","authors":"Chen Hajaj, John P Dickerson, Avinatan Hassidim, Tuomas Sandholm, David Sarne","year":"2015","venue":"Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Hartline and Lucier, 2010] Jason D. Hartline and Brendan Lucier. Bayesian algorithmic mechanism design. In Pro- ceedings of the 42nd ACM Symposium on Theory of Com- puting, STOC 2010, pages 301-310, 2010.","title":"Bayesian algorithmic mechanism design","authors":"Jason D Hartline, Brendan Lucier","year":"2010","venue":"Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Hartline and Roughgarden, 2009] Jason D. Hartline and Tim Roughgarden. Simple versus optimal mechanisms. In ACM-EC, pages 225-234, 2009.","title":"Simple versus optimal mechanisms","authors":"Jason D Hartline, Tim Roughgarden","year":"2009","venue":"ACM-EC","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Hylland and Zeckhauser, 1979] Aanund Hylland and Richard Zeckhauser. The Efficient Allocation of Indi- viduals to Positions. The Journal of Political Economy, 87(2):293-314, 1979.","title":"The Efficient Allocation of Individuals to Positions","authors":"Zeckhauser Hylland, Aanund Hylland, Richard Zeckhauser","year":"1979","venue":"The Journal of Political Economy","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Katta and Sethuraman, 2006] Akshay-Kumar Katta and Jay Sethuraman. A solution to the random assignment prob- lem on the full preference domain. Journal of Economic theory, 131(1):231-250, 2006.","title":"A solution to the random assignment problem on the full preference domain","authors":"Akshay-Kumar Katta, Jay Sethuraman","year":"2006","venue":"Journal of Economic theory","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Kesten, 2009] Onur Kesten. Why do popular mechanisms lack efficiency in random environments? Journal of Eco- nomic Theory, 144:2209-2226, 2009.","title":"Why do popular mechanisms lack efficiency in random environments","authors":"Onur Kesten","year":"2009","venue":"Journal of Economic Theory","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Koutsoupias, 2014] Elias Koutsoupias. Scheduling without payments. Theory Comput. Syst., 54(3):375-387, 2014.","title":"Scheduling without payments","authors":"Elias Koutsoupias","year":"2014","venue":"Theory Comput. Syst","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Mennle and Seuken, 2014] Timo Mennle and Sven Seuken. An axiomatic approach to characterizing and relaxing strategyproofness of one-sided matching mechanisms. In ACM-EC, pages 37-38, 2014.","title":"An axiomatic approach to characterizing and relaxing strategyproofness of one-sided matching mechanisms","authors":"Seuken Mennle, Timo Mennle, Sven Seuken","year":"2014","venue":"ACM-EC","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Mu'alem and Nisan, 2008] Ahuva Mu'alem and Noam Nisan. Truthful approximation mechanisms for restricted combinatorial auctions. Games and Economic Behavior, 64(2):612-631, 2008.","title":"Ahuva Mu'alem and Noam Nisan. Truthful approximation mechanisms for restricted combinatorial auctions","authors":"' Mu, Nisan","year":"2008","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Nisan and Ronen, 1999] Noam Nisan and Amir Ronen. Al- gorithmic mechanism design (extended abstract). In Pro- ceedings of the Thirty-First Annual ACM Symposium on Theory of Computing (STOC), pages 129-140, 1999.","title":"Noam Nisan and Amir Ronen. Algorithmic mechanism design (extended abstract)","authors":"Ronen Nisan","year":"1999","venue":"Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing (STOC)","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Nisan et al., 2007] Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay V. Vazirani, editors. Algorithmic Game Thoery. Cambridge University Press, 2007.","title":"Algorithmic Game Thoery","authors":"Nisan","year":"2007","venue":null,"doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Pathak and Sethuraman, 2011] P. A. Pathak and J. Sethura- man. Lotteries in student assignment: An equivalence re- sult. Theoretical Economics, 6, 2011.","title":"Lotteries in student assignment: An equivalence result","authors":"P A Pathak, J Sethuraman","year":"2011","venue":"Theoretical Economics","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Procaccia and Tennenholtz, 2009] Ariel D Procaccia and Moshe Tennenholtz. Approximate mechanism design without money. In ACM-EC, pages 177-186, 2009.","title":"Approximate mechanism design without money","authors":"D Ariel, Moshe Procaccia, Tennenholtz","year":"2009","venue":"ACM-EC","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Roth and Sotomayor, 1990] A. E. Roth and M. Sotomayor. Two-Sided Matching: A Study in Game-Theoretic Model- ing and Analysis. Cambridge University Press, 1990.","title":"Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis","authors":"A E Roth, M Sotomayor","year":"1990","venue":null,"doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Sönmez and Ünver, 2011] Tayfun Sönmez and Utku Ünver. Matching, allocation and exchange of discrete resources. Handbook of Social Economics, 1A:781-852, 2011.","title":"Tayfun Sönmez and Utku Ünver. Matching, allocation and exchange of discrete resources","authors":"Ünver Sönmez","year":"2011","venue":"Handbook of Social Economics","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Svensson, 1999] Lars-Gunnar Svensson. Strategy-proof al- location of indivisible goods. Social Choice and Welfare, 16(4):557-567, 1999.","title":"Strategy-proof allocation of indivisible goods","authors":"Lars-Gunnar Svensson, Svensson","year":"1999","venue":"Social Choice and Welfare","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Zhang, 2018] Jie Zhang. Average-case approximation ratio of scheduling without payments. In Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, (AAAI-18), pages 1298-1305, 2018.","title":"Average-case approximation ratio of scheduling without payments","authors":"Jie Zhang","year":"2018","venue":"Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Zhou, 1990] Lin Zhou. On a Conjecture by Gale about One- Sided Matching Problems. Journal of Economic Theory, 52:123-135, 1990.","title":"On a Conjecture by Gale about One-Sided Matching Problems","authors":"Lin Zhou","year":"1990","venue":"Journal of Economic Theory","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}