Learning Equilibria in Asymmetric Auction Games

Published Online:https://doi.org/10.1287/ijoc.2023.1281

References

  • Andrade GP, Frongillo R, Piliouras G (2021) Learning in matrix games can be arbitrarily complex. Preprint, submitted March 5, https://arxiv.org/abs/2103.03405.Google Scholar
  • Anton JJ, Yao DA (1992) Coordination in split award auctions. Quart. J. Econom. 107(2):681–707.CrossrefGoogle Scholar
  • Armantier O, Florens JP, Richard JF (2008) Approximation of Nash equilibria in Bayesian games. J. Appl. Econometrics 23(7):965–981.CrossrefGoogle Scholar
  • Athey S (2001) Single crossing properties and the existence of pure strategy equilibria in games of incomplete information. Econometrica 69(4):861–889.CrossrefGoogle Scholar
  • Ausubel LM, Baranov O (2019) Core-selecting auctions with incomplete information. Internat. J. Game Theory 49:251–273.CrossrefGoogle Scholar
  • Ausubel LM, Milgrom P (2006) The lovely but lonely Vickrey auction. Combin. Auctions 17:22–26.Google Scholar
  • Bajari P (2001) Comparing competition and collusion: A numerical approach. Econom. Theory 18(1):187–205.CrossrefGoogle Scholar
  • Balduzzi D, Racaniere S, Martens J, Foerster J, Tuyls K, Graepel T (2018) The mechanics of n-player differentiable games. Internat. Conf. Machine Learn. (PMLR), 354–363.Google Scholar
  • Benaim M, Hirsch MW (1999) Mixed equilibria and dynamical systems arising from fictitious play in perturbed games. Games Econom. Behav. 29(1–2):36–72.CrossrefGoogle Scholar
  • Bichler M, Goeree JK (2017) Handbook of Spectrum Auction Design (Cambridge University Press, Cambridge, MA).CrossrefGoogle Scholar
  • Bichler M, Heidekrüger S, Kohring N (2023) bnelearn-asymmetric Version v2021.0151. Accessed January 8, 2023, https://github.com/INFORMSJoC/2021.0151.Google Scholar
  • Bichler M, Fichtl M, Heidekrüger S, Kohring N, Sutterer P (2021) Learning equilibria in symmetric auction games using artificial neural networks. Nature Machine Intelligence 3:687–695.CrossrefGoogle Scholar
  • Bosshard V, Seuken S (2021) The cost of simple bidding in combinatorial auctions. 2021 Conf. Econom. Comput..Google Scholar
  • Bosshard V, Bünz B, Lubin B, Seuken S (2017) Computing Bayes-Nash equilibria in combinatorial auctions with continuous value and action spaces. IJCAI, 119–127.Google Scholar
  • Bosshard V, Bünz B, Lubin B, Seuken S (2020) Computing Bayes-Nash equilibria in combinatorial auctions with verification. J. Artificial Intelligence Res. 69:531–570.CrossrefGoogle Scholar
  • Bowling M (2005) Convergence and no-regret in multiagent learning. Adv. Neural Inform. Processing Systems 17:209–216.Google Scholar
  • Brown GW (1951) Iterative solution of games by fictitious play. Koopmans TC, ed. Activity Analysis of Production and Allocation (Wiley, New York), 374–376.Google Scholar
  • Cai Y, Papadimitriou C (2014) Simultaneous Bayesian auctions and computational complexity. Proc. 15th ACM Conf. Econom. Comput (ACM Press, Palo Alto, CA), 895–910.Google Scholar
  • Carbonell-Nicolau O, McLean RP (2018) On the existence of Nash equilibrium in Bayesian games. Math. Oper. Res. 43(1):100–129.LinkGoogle Scholar
  • Conitzer V, Sandholm T (2008) New complexity results about Nash equilibria. Games Econom. Behav. 63(2):621–641.CrossrefGoogle Scholar
  • Cournot AA (1838) Recherches sur les principes mathématiques de la théorie des richesses. https://gallica.bnf.fr/ark:/12148/bpt6k6117257c.Google Scholar
  • Daskalakis C, Goldberg P, Papadimitriou C (2009) The complexity of computing a Nash equilibrium. SIAM J. Comput. 39(1):195–259.CrossrefGoogle Scholar
  • Etessami K, Yannakakis M (2007) On the complexity of Nash equilibria and other fixed points (extended abstract). Proc. 48th Annual IEEE Sympos. Foundations Comput. Sci. (IEEE Computer Society), 113–123.Google Scholar
  • Ewert M, Heidekrüger S, Bichler M (2022) Approaching the overbidding puzzle in all-pay auctions: Explaining human behavior through Bayesian optimization and equilibrium learning. Proc. 21st Internat. Conf. Autonomous Agents Multiagent Systems (International Foundation for Autonomous Agents and Multiagent Systems), 1586–1588.Google Scholar
  • Fudenberg D, Levine DK (2009) Learning and equilibrium. Annual Rev. Econom. 1(1):385–420.CrossrefGoogle Scholar
  • Goeree JK, Lien Y (2016) On the impossibility of core-selecting auctions. Theoretical Econom. 11(1):41–52.CrossrefGoogle Scholar
  • Hartline J, Syrgkanis V, Tardos E. (2015) No-regret learning in Bayesian games. Cortes C, Lawrence ND, Lee DD, Sugiyama M, Garnett R, eds. Adv. Neural Inform. Processing Systems, vol. 28 (Curran Associates, Inc.), 3061–3069.Google Scholar
  • Hazan E, Agarwal A, Kale S (2007) Logarithmic regret algorithms for online convex optimization. Machine Learn. 69(2–3):169–192.CrossrefGoogle Scholar
  • Jackson MO, Swinkels JM (2005) Existence of equilibrium in single and double private value auctions 1. Econometrica 73(1):93–139.CrossrefGoogle Scholar
  • Kaplan TR, Zamir S (2015) Multiple equilibria in asymmetric first-price auctions. Econom. Theory Bull. 3(1):65–77.CrossrefGoogle Scholar
  • Klainerman S (2010) PDE as a unified subject. Visions in Mathematics (Springer), 279–315.CrossrefGoogle Scholar
  • Klambauer G, Unterthiner T, Mayr A, Hochreiter S (2017) Self-normalizing neural networks. Proc. 31st Internat. Conf. Neural Inform. Processing Systems, 972–981.Google Scholar
  • Klemperer P (2000) Why every economist should learn some auction theory. Preprint, submitted October 12, https://dx.doi.org/10.2139/ssrn.241350.Google Scholar
  • Kokott GM, Bichler M, Paulsen P (2019) The beauty of Dutch: Ex-post split-award auctions in procurement markets with diseconomies of scale. Eur. J. Oper. Res. 278(1):202–210.CrossrefGoogle Scholar
  • Krishna V (2009) Auction Theory (Academic Press).Google Scholar
  • Lebrun B (2006) Uniqueness of the equilibrium in first-price auctions. Games Econom. Behav. 55(1):131–151.CrossrefGoogle Scholar
  • Letcher A, Balduzzi D, Racanière S, Martens J, Foerster JN, Tuyls K, Graepel T (2019) Differentiable game mechanics. J. Machine Learn. Res. 20(84):1–40.Google Scholar
  • Marshall RC, Meurer MJ, Richard JF, Stromquist W (1994) Numerical analysis of asymmetric first price auctions. Games Econom. Behav. 7(2):193–220.CrossrefGoogle Scholar
  • Maskin E, Riley J (2000) Asymmetric auctions. Rev. Econom. Stud. 67(3):413–438.CrossrefGoogle Scholar
  • Mertikopoulos P, Zhou Z (2019) Learning in games with continuous action sets and unknown payoff functions. Math. Programming 173(1–2):465–507.CrossrefGoogle Scholar
  • Milgrom P (2017) Discovering Prices: Auction Design in Markets with Complex Constraints (Columbia University Press).CrossrefGoogle Scholar
  • Monderer D, Shapley LS (1996) Potential games. Games Econom. Behav. 14(1):124–143.CrossrefGoogle Scholar
  • Nash JF (1950) Equilibrium points in n-person games. Proc. Natl. Acad. Sci. USA 36(1):48–49.CrossrefGoogle Scholar
  • Ott M, Beck M (2013) Incentives for overbidding in minimum-revenue core-selecting auctions. Number F16-V3 in Beiträge zur Jahrestagung des Vereins für Socialpolitik 2013: Wettbewerbspolitik und Regulierung in einer globalen Wirtschaftsordnung - Session: Auctions and Licensing (ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften, Leibniz-Informationszentrum Wirtschaft, Kiel, Hamburg).Google Scholar
  • Paszke A, Gross S, Chintala S, Chanan G, Yang E, DeVito Z, Lin Z, Desmaison A, Antiga L, Lerer A (2017) Automatic differentiation in PyTorch. NIPS 2017 Autodiff Workshop.Google Scholar
  • Plum M (1992) Characterization and computation of Nash-equilibria for auctions with incomplete information. Internat. J. Game Theory 20(4):393–418.CrossrefGoogle Scholar
  • Rubinstein A (2016) Settling the complexity of computing approximate two-player Nash equilibria. Preprint, submitted June 14, https://arxiv.org/abs/1606.04550.Google Scholar
  • Salimans T, Ho J, Chen X, Sidor S, Sutskever I (2017) Evolution strategies as a scalable alternative to reinforcement learning. Preprint, submitted March 10, https://arxiv.org/abs/1703.03864.Google Scholar
  • Sanders JB, Farmer JD, Galla T (2018) The prevalence of chaotic dynamics in games with many players. Sci. Rep. 8(1):1–13.CrossrefGoogle Scholar
  • Schäfer F, Anandkumar A (2019) Competitive gradient descent. Adv. Neural Inform. Processing Systems 33:7623–7633.Google Scholar
  • Singh SP, Kearns MJ, Mansour Y (2000) Nash convergence of gradient dynamics in general-sum games. Proc. 16th Conf. Uncertainty Artificial Intelligence, 541–548.Google Scholar
  • Ui T (2016) Bayesian Nash equilibrium and variational inequalities. J. Math. Econom. 63:139–146.CrossrefGoogle Scholar
  • Vickrey W (1961) Counterspeculation, auctions, and competitive sealed tenders. J. Finance 16(1):8–37.CrossrefGoogle Scholar
  • Zinkevich M (2003) Online convex programming and generalized infinitesimal gradient ascent. Proc. 20th Internat. Conf. Machine Learn., 928–936.Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.