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Structural Complexities of Matching Mechanisms (2212.08709v3)

Published 16 Dec 2022 in cs.GT, cs.CC, and econ.TH

Abstract: We study various novel complexity measures for two-sided matching mechanisms, applied to the two canonical strategyproof matching mechanisms, Deferred Acceptance (DA) and Top Trading Cycles (TTC). Our metrics are designed to capture the complexity of various structural (rather than computational) concerns, in particular ones of recent interest within economics. We consider a unified, flexible approach to formalizing our questions: Define a protocol or data structure performing some task, and bound the number of bits that it requires. Our main results apply this approach to four questions of general interest; for mechanisms matching applicants to institutions, our questions are: (1) How can one applicant affect the outcome matching? (2) How can one applicant affect another applicant's set of options? (3) How can the outcome matching be represented / communicated? (4) How can the outcome matching be verified? Holistically, our results show that TTC is more complex than DA, formalizing previous intuitions that DA has a simpler structure than TTC. For question (2), our result gives a new combinatorial characterization of which institutions are removed from each applicant's set of options when a new applicant is added in DA; this characterization may be of independent interest. For question (3), our result gives new tight lower bounds proving that the relationship between the matching and the priorities is more complex in TTC than in DA. We nonetheless showcase that this higher complexity of TTC is nuanced: By constructing new tight lower-bound instances and new verification protocols, we prove that DA and TTC are comparable in complexity under questions (1) and (4). This more precisely delineates the ways in which TTC is more complex than DA, and emphasizes that diverse considerations must factor into gauging the complexity of matching mechanisms.

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References (67)
  1. Stable matching mechanisms are not obviously strategy-proof. Journal of Economic Theory, 177:405–425, 2018.
  2. Unbalanced random matching markets: The stark effect of competition. Journal of Political Economy, 125(1):69 – 98, 2017.
  3. A supply and demand framework for two-sided matching markets. Journal of Political Economy, 124(5):1235–1268, 2016.
  4. Credible auctions: A trilemma. Econometrica, 88(2):425–467, 2020.
  5. Nick Arnosti. Deferred acceptance is unpredictable. Blog Post, 2020. Accessed April 2023.
  6. School choice: A mechanism design approach. American Economic Review, 93(3):729–747, 2003.
  7. Gibbard-Satterthwaite success stories and obvious strategyproofness. In Proceedings of the 18th ACM Conference on Economics and Computation (EC), page 565, 2017.
  8. Bulow-Klemperer-style results for welfare maximization in two-sided markets. In Proceedings of the 31st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2452–2471, 2020.
  9. The menu-size complexity of revenue approximation. Games and Economic Behavior, 134:281–307, 2022. Originally appeared in Proceedings of STOC’17.
  10. A simple and approximately optimal mechanism for an additive buyer. Journal of the ACM, 67(4):24:1–24:40, 2020.
  11. Auctions versus negotiations. The American Economic Review, pages 180–194, 1996.
  12. BPS (Boston Public Schools) Strategic Planning Team. Recommendation to implement a new BPS assignment algorithm, 2005.
  13. The complexity of the comparator circuit value problem. ACM Transactions on Computation Theory (TOCT), 6(4):1–44, 2014.
  14. Representing all stable matchings by walking a maximal chain. Mimeo, 2019.
  15. The short-side advantage in random matching markets. In Proceedings of the 5th Symposium on Simplicity in Algorithms (SOSA), pages 257–267, 2022.
  16. Strong duality for a multiple-good monopolist. Econometrica, 85(3):735–767, 2017.
  17. Machiavelli and the Gale-Shapley algorithm. The American Mathematical Monthly, 88:485–494, 08 1981.
  18. Shahar Dobzinski. Computational efficiency requires simple taxation. In Proceedings of the 57th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 209–218, 2016.
  19. The communication complexity of payment computation. In Proceedings of the 53rd Annual ACM Symposium on Theory of Computing (STOC), pages 933–946, 2021.
  20. On the hardness of dominant strategy mechanism design. In Proceedings of the 54th Annual ACM Symposium on Theory of Computing (STOC), pages 690–703, 2022.
  21. The competition complexity of auctions: A Bulow-Klemperer result for multi-dimensional bidders. In Proceedings of the 18th ACM Conference on Economics and Computation (EC), page 343, 2017.
  22. A simple and approximately optimal mechanism for a buyer with complements. In Proceedings of the 18th ACM Conference on Economics and Computation (EC), page 323, 2017.
  23. Strategyproofness-exposing mechanism descriptions. In Proceedings of the 24th ACM Conference on Economics and Computation (EC), 2023.
  24. The Stable Marriage Problem: Structure and Algorithms. MIT Press, 1989.
  25. On the computational properties of obviously strategy-proof mechanisms. Mimeo, 2021.
  26. A theory of auditability for allocation and social choice mechanisms. Working Paper, 2023.
  27. A structural and algorithmic study of stable matching lattices of “nearby” instances, with applications. Mimeo, 2018.
  28. A stable marriage requires communication. Games and Economic Behavior, 118:626–647, 2019. Originally appeared in Proceedings of SODA’15.
  29. Yannai A. Gonczarowski. Bounding the menu-size of approximately optimal auctions via optimal-transport duality. In Proceedings of the 50th Annual ACM Symposium on Theory of Computing (STOC), pages 123–131, 2018.
  30. College admissions and the stability of marriage. American Mathematical Monthly, 69:9–14, 1962.
  31. Some remarks on the stable matching problem. Discrete Applied Mathematics, 11(3):223–232, 1985.
  32. Peter J. Hammond. Straightforward individual incentive compatibility in large economies. The Review of Economic Studies, 46(2):263–282, 1979.
  33. Approximate revenue maximization with multiple items. Journal of Economic Theory, 172:313–347, 2017. Originally appeared in Proceedings of EC’12.
  34. Selling multiple correlated goods: Revenue maximization and menu-size complexity. Journal of Economic Theory, 183:991–1029, 2019. Originally appeared in Proceedings of EC’13.
  35. Simple versus optimal mechanisms. In Proceedings of the 10th ACM Conference on Electronic Commerce (EC), pages 225–234, 2009.
  36. Improving transparency and verifiability in school admissions: Theory and experiment. Available at SSRN 3572020, 2023.
  37. The complexity of counting stable marriages. SIAM Journal on Computing, 15(3):655–667, 1986.
  38. Marriage, honesty, and stability. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 53–62, 2005.
  39. A simply exponential upper bound on the maximum number of stable matchings. In Proceedings of the 50th Annual ACM Symposium on Theory of Computing (STOC), pages 920–925, 2018.
  40. In which matching markets does the short side enjoy an advantage? In Proceedings of the 32nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1374–1386, 2021.
  41. Ron Kupfer. The influence of one strategic agent on the core of stable matchings. In Proceedings of the 16th International Conference on Web and Internet Economics (WINE), 2020.
  42. The opportunities and risks of k-12 student placement algorithms. The Brookings Institute, 2019. Accessed April 2023.
  43. Shengwu Li. Obviously strategy-proof mechanisms. American Economic Review, 107(11):3257–87, 2017.
  44. The cutoff structure of top trading cycles in school choice. The Review of Economic Studies, 88(4):1582–1623, 2021.
  45. Jinpeng Ma. Strategy-proofness and the strict core in a market with indivisibilities. International Journal of Game Theory, 23(1):75–83, 1994.
  46. Markus Möller. Transparent matching mechanisms. Available at SSRN 4073464, 2022.
  47. Obviously strategy-proof implementation of assignment rules: A new characterization. International Economic Review, 63(1):261–290, 2021.
  48. Finding stable matchings that are robust to errors in the input. In Proceedings of the 26th Annual European Symposium on Algorithms (ESA), volume 112, pages 60:1–60:11, 2018.
  49. The stable marriage problem. Communications of the ACM, 14(7), 1971.
  50. Boris Pittel. The average number of stable matchings. SIAM Journal on Discrete Mathematics, 2(4):530–549, 1989.
  51. At most 3.55nsuperscript3.55𝑛3.55^{n}3.55 start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT stable matchings. In Proceedings of the 62nd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 217–227, 2022.
  52. A theory of simplicity in games and mechanism design. Mimeo (Originally appeared as “Obvious Dominance and Random Priority” in Proceedings of EC’19), 2021.
  53. Modeling assumptions clash with the real world: Transparency, equity, and community challenges for student assignment algorithms. In Proceedings of the ACM Conference on Human Factors in Computing Systems (CHI), 2021.
  54. Alvin E. Roth. The economics of matching: stability and incentives. Mathematics of Operations Research, 7(4):617–628, 1982.
  55. Alvin E. Roth. Incentive compatibility in a market with indivisible goods. Economics Letters, 9(2):127–132, 1982.
  56. Alvin E. Roth. On the allocation of residents to rural hospitals: A general property of two-sided matching markets. Econometrica, 54(2):425–427, 1986.
  57. Weak versus strong domination in a market with indivisible goods. Journal of Mathematical Economics, 4(2):131–137, 1977.
  58. Exponential communication separations between notions of selfishness. In Proceedings of the 53rd Annual ACM Symposium on Theory of Computing (STOC), pages 947–960, 2021.
  59. Ilya Segal. The communication requirements of social choice rules and supporting budget sets. Journal of Economic Theory, 136(1):341–378, 2007.
  60. Jay Sethuraman. An alternative proof of a characterization of the ttc mechanism. Operations Research Letters, 44(1):107–108, 2016.
  61. On cores and indivisibility. Journal of Mathematical Economics, 1(1):23–37, 1974.
  62. The complexity of computing the random priority allocation matrix. Mathematics of Operations Research, 40(4):1005–1014, 2015.
  63. The menu complexity of “one-and-a-half-dimensional” mechanism design. In Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2026–2035, 2018.
  64. Ashok Subramanian. A new approach to stable matching problems. SIAM Journal on Computing, 23(4):671–700, 1994.
  65. Clayton Thomas. Classification of priorities such that deferred acceptance is osp implementable. In Proceedings of the 22nd ACM Conference on Economics and Computation (EC), pages 860–860, 2021.
  66. Peter Troyan. Obviously strategy-proof implementation of top trading cycles. International Economic Review, 60(3):1249–1261, 2019.
  67. Kyle Woodward. Self-auditable auctions. Technical report, Working paper, 2020.
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