Smoothness for Simultaneous Composition of Mechanisms with Admission

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10123)


We study social welfare of learning outcomes in mechanisms with admission. In our repeated game there are n bidders and m mechanisms, and in each round each mechanism is available for each bidder only with a certain probability. Our scenario is an elementary case of simple mechanism design with incomplete information, where availabilities are bidder types. It captures natural applications in online markets with limited supply and can be used to model access of unreliable channels in wireless networks. If mechanisms satisfy a smoothness guarantee, existing results show that learning outcomes recover a significant fraction of the optimal social welfare. These approaches, however, have serious drawbacks in terms of plausibility and computational complexity. Also, the guarantees apply only when availabilities are stochastically independent among bidders. In contrast, we propose an alternative approach where each bidder uses a single no-regret learning algorithm and applies it in all rounds. This results in what we call availability-oblivious coarse correlated equilibria. It exponentially decreases the learning burden, simplifies implementation (e.g., as a method for channel access in wireless devices), and thereby addresses some of the concerns about Bayes-Nash equilibria and learning outcomes in Bayesian settings. Our main results are general composition theorems for smooth mechanisms when valuation functions of bidders are lattice-submodular. They rely on an interesting connection to the notion of correlation gap of submodular functions over product lattices.


Valuation Function Combinatorial Auction Submodular Function Differential Privacy Composition Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Agrawal, S.: Optimization under uncertainty: bounding the correlation gap. Ph.D. thesis, Stanford University (2011)Google Scholar
  2. 2.
    Agrawal, S., Ding, Y., Saberi, A., Ye, Y.: Correlation robust stochastic optimization. In: Proceedings of 21st Symposium on Discrete Algorithms (SODA), pp. 1087–1096 (2010)Google Scholar
  3. 3.
    Bhawalkar, K., Roughgarden, T.: Welfare guarantees for combinatorial auctions with item bidding. In: Proceedings of 22nd Symposium on Discrete Algorithms (SODA), pp. 700–709 (2011)Google Scholar
  4. 4.
    Blum, A., Mansour, Y.: Learning, regret minimization, and equilibria. In: Nisan, N., Tardos, É., Roughgarden, T., Vazirani, V. (eds.), Algorithmic Game Theory, chapter 4. Cambridge University Press (2007)Google Scholar
  5. 5.
    Cai, Y., Papadimitriou, C.: Simultaneous Bayesian auctions and computational complexity. In Proceedings of the 15th ACM Conference on Economics and Computation (EC 2014), pp. 895–910 (2014)Google Scholar
  6. 6.
    Caragiannis, I., Kaklamanis, C., Kanellopoulos, P., Kyropoulou, M., Lucier, B., Leme, R.P., Tardos, É.: On the efficiency of equilibria in generalized second price auctions. J. Econom. Theory 156, 343–388 (2015)CrossRefMATHGoogle Scholar
  7. 7.
    Christodoulou, G., Kovács, A., Schapira, M.: Bayesian combinatorial auctions. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5125, pp. 820–832. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-70575-8_67 CrossRefGoogle Scholar
  8. 8.
    Christodoulou, G., Kovács, A., Sgouritsa, A., Tang, B.: Tight bounds for the price of anarchy of simultaneous first price auctions. ACM Trans. Econom. Comput. 4(2), 9 (2016)MathSciNetGoogle Scholar
  9. 9.
    Daskalakis, C., Syrgkanis, V.: Learning in auctions: regret is hard, envy is easy. In: Proceedings of 57th Symposium on Foundations of Computer Science (FOCS) (2016, to appear)Google Scholar
  10. 10.
    Devanur, N., Morgenstern, J., Syrgkanis, V., Weinberg, M.: Simple auctions with simple strategies. In: Proceedings of the 16th ACM Conference on Economics and Computation (EC 2015), pp. 305–322 (2015)Google Scholar
  11. 11.
    Dobzinski, S., Fu, H., Kleinberg, R.D.: On the complexity of computing an equilibrium in combinatorial auctions. In: Proceedings of 26th Symposium on Discrete Algorithms (SODA), pp. 110–122 (2015)Google Scholar
  12. 12.
    Feldman, M., Fu, H., Gravin, N., Lucier, B.: Simultaneous auctions are (almost) efficient. In: Proceedings of 45th Symposium on Theory of Computing (STOC), pp. 201–210 (2013)Google Scholar
  13. 13.
    Hartline, J.D., Syrgkanis, V., Tardos, É.: No-regret learning in repeated Bayesian games. In: Proceedings of 28th Conference on Advanced Neural Information Processing Systems (NIPS), pp. 3043–3051 (2015)Google Scholar
  14. 14.
    Hassidim, A., Kaplan, H., Mansour, Y., Nisan, N.: Non-price equilibria in markets of discrete goods. In Proceedings of 12th Conference on Electronic Commerce (EC), pp. 295–296 (2011)Google Scholar
  15. 15.
    Hoefer, M., Kesselheim, T., Kodric, B.: Smoothness for simultaneous composition of mechanisms with admission. CoRR, abs/1509.00337 (2015)Google Scholar
  16. 16.
    Lucier, B., Borodin, A.: Price of anarchy for greedy auctions. In: Proceedings of 21st Symposium Discrete Algorithms (SODA), pp. 537–553 (2010)Google Scholar
  17. 17.
    Lykouris, T., Syrgkanis, V., Tardos, É.: Learning and efficiency in games with dynamic population. In Proceedings of 27th Symposium Discrete Algorithms (SODA), pp. 120–129 (2016)Google Scholar
  18. 18.
    Paes Leme, R., Tardos, É.: Pure and Bayes-Nash price of anarchy for generalized second price auction. In: Proceedings of 51st Symposium Foundations of Computer Science (FOCS), pp. 735–744 (2010)Google Scholar
  19. 19.
    Roughgarden, T.: Intrinsic robustness of the price of anarchy. Comm. ACM 55(7), 116–123 (2012)CrossRefGoogle Scholar
  20. 20.
    Roughgarden, T.: The price of anarchy in games of incomplete information. In: Proceedings of 13th Conference on Electronic Commerce (EC), pp. 862–879 (2012)Google Scholar
  21. 21.
    Roughgarden, T.: Barriers to near-optimal equilibria. In: Proceedings of 55th Symposium on Foundations of Computer Science (FOCS), pp. 71–80 (2014)Google Scholar
  22. 22.
    Syrgkanis, V., Tardos, É.: Composable and efficient mechanisms. In: Proceedings of 45th Symposium Theory of Computing (STOC), pp. 211–220 (2013)Google Scholar
  23. 23.
    Yan, Q.: Mechanism design via correlation gap. In: Proceedings of 22nd Symposium Discrete Algorithms (SODA), pp. 710–719 (2011)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2016

Authors and Affiliations

  • Martin Hoefer
    • 1
  • Thomas Kesselheim
    • 1
  • Bojana Kodric
    • 1
  1. 1.MPI Informatik and Saarland UniversitySaarbrückenGermany

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