Sampling from the Gibbs Distribution in Congestion Games

Published Online:https://doi.org/10.1287/moor.2022.1322

References

  • [1] Ackermann H, Röglin H (2008) On the convergence time of the best response dynamics in player-specific congestion games. Preprint, submitted May 8, https://arxiv.org/abs/0805.1130.Google Scholar
  • [2] Ackermann H, Röglin H, Vöcking B (2008) On the impact of combinatorial structure on congestion games. J. ACM 55(6):1–22.Google Scholar
  • [3] Anari N, Gharan SO, Vinzant C (2018) Log-concave polynomials, entropy, and a deterministic approximation algorithm for counting bases of matroids. Proc. 59th Annual Sympos. Foundations Comput. Sci., 35–46.Google Scholar
  • [4] Anari N, Liu K, Gharan SO, Vinzant C (2018) Log-concave polynomials III: Mason’s ultra-log-concavity conjecture for independent sets of matroids. Preprint, submitted July 2, https://arxiv.org/abs/1807.00929.Google Scholar
  • [5] Anari N, Liu K, Gharan SO, Vinzant C (2019) Log-concave polynomials II: High-dimensional walks and an FPRAS for counting bases of a matroid. Proc. 51st Annual ACM SIGACT Sympos. Theory Comput., 1–12.Google Scholar
  • [6] Anari N, Liu K, Gharan SO, Vinzant C, Vuong TD (2021) Log-concave polynomials IV: Approximate exchange, tight mixing times, and near-optimal sampling of forests. Proc. 53rd Annual ACM SIGACT Sympos. Theory Comput., 408–420.Google Scholar
  • [7] Arman A, Gao P, Wormald N (2019) Fast uniform generation of random graphs with given degree sequences. Proc. 60th Annual Sympos. Foundations Comput. Sci., 1371–1379.Google Scholar
  • [8] Asadpour A, Saberi A (2009) On the inefficiency ratio of stable equilibria in congestion games. Internet and Network Economics, 545–552.CrossrefGoogle Scholar
  • [9] Auletta V, Ferraioli D, Pasquale F, Persiano G (2013) Mixing time and stationary expected social welfare of logit dynamics. Theory Comput. Systems 53(1):3–40.CrossrefGoogle Scholar
  • [10] Auletta V, Ferraioli D, Pasquale F, Persiano G (2018) Metastability of logit dynamics for coordination games. Algorithmica 80(11):3078–3131.CrossrefGoogle Scholar
  • [11] Auletta V, Ferraioli D, Pasquale F, Penna P, Persiano G (2015) Logit dynamics with concurrent updates for local interaction potential games. Algorithmica 73(3):511–546.CrossrefGoogle Scholar
  • [12] Auletta V, Ferraioli D, Pasquale F, Penna P, Persiano G (2016) Convergence to equilibrium of logit dynamics for strategic games. Algorithmica 76(1):110–142.CrossrefGoogle Scholar
  • [13] Bezáková I, Bhatnagar N, Vigoda E (2007) Sampling binary contingency tables with a greedy start. Random Structures Algorithms 30(1–2):168–205.CrossrefGoogle Scholar
  • [14] Blume LE (1993) The statistical mechanics of strategic interaction. Games Econom. Behav. 5(3):387–424.CrossrefGoogle Scholar
  • [15] Bobkov SG, Tetali P (2006) Modified logarithmic Sobolev inequalities in discrete settings. J. Theoretical Probab. 19(2):289–336.CrossrefGoogle Scholar
  • [16] Brändén P, Huh J (2018) Hodge-Riemann relations for Potts model partition functions. Preprint, submitted November 5, https://arxiv.org/abs/1811.01696.Google Scholar
  • [17] Brändén P, Huh J (2020) Lorentzian polynomials. Ann. Math. 192(3):821–891.CrossrefGoogle Scholar
  • [18] Camerer CF (2010) Behavioural game theory. Behavioural and Experimental Economics, 42–50.Google Scholar
  • [19] Chien S, Sinclair A (2011) Convergence to approximate Nash equilibria in congestion games. Games Econom. Behav. 71(2):315–327.CrossrefGoogle Scholar
  • [20] Cryan M, Guo H, Mousa G (2019) Modified log-Sobolev inequalities for strongly log-concave distributions. Proc. 60th Annual Sympos. Foundations Comput. Sci., 1358–1370.Google Scholar
  • [21] Del Pia A, Ferris M, Michini C (2017) Totally unimodular congestion games. Proc. 28th Annual ACM-SIAM Sympos. Discrete Algorithms, 577–588.Google Scholar
  • [22] Diaconis P, Saloff-Coste L (1996) Logarithmic Sobolev inequalities for finite Markov chains. Ann. Appl. Probab. 6(3):695–750.CrossrefGoogle Scholar
  • [23] Dyer M, Greenhill C, Kleer P, Ross J, Stougie L (2021) Sampling hypergraphs with given degrees. Discrete Math. 344(11):112566.CrossrefGoogle Scholar
  • [24] Even-Dar E, Kesselman A, Mansour Y (2007) Convergence time to Nash equilibrium in load balancing. ACM Trans. Algorithms 3(3):32.CrossrefGoogle Scholar
  • [25] Fabrikant A, Papadimitriou C, Talwar K (2004) The complexity of pure Nash equilibria. Proc. 36th Annual ACM Sympos. Theory Comput., 604–612.Google Scholar
  • [26] Fanelli A, Moscardelli L (2011) On best response dynamics in weighted congestion games with polynomial delays. Distributed Comput. 24(5):245–254.CrossrefGoogle Scholar
  • [27] Feder T, Mihail M (1992) Balanced matroids. Proc. 24th Annual ACM Sympos. Theory Comput., 26–38.Google Scholar
  • [28] Ferraioli D (2013) Logit dynamics: A model for bounded rationality. ACM SIGecom Exchanges 12(1):34–37.CrossrefGoogle Scholar
  • [29] Fotakis D (2010) Congestion games with linearly independent paths: Convergence time and price of anarchy. Theory Comput. Systems 47(1):113–136.CrossrefGoogle Scholar
  • [30] Fujishige S, Goemans M, Harks T, Peis B, Zenklusen R (2015) Congestion games viewed from m-convexity. Oper. Res. Lett. 43(3):329–333.CrossrefGoogle Scholar
  • [31] Garey MR, Johnson DS (1990) Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman & Co., New York).Google Scholar
  • [32] Goel S (2004) Modified logarithmic Sobolev inequalities for some models of random walk. Stochastic Processes Appl. 114(1):51–79.CrossrefGoogle Scholar
  • [33] Gourvès L, Monnot J (2009) On strong equilibria in the max cut game. Proc. Fifth Internat. Workshop Internet Network Econom., 608–615.Google Scholar
  • [34] Gurvits L (2010) On multivariate Newton-like inequalities. Advances in Combinatorial Mathematics, 61–78.Google Scholar
  • [35] Helgason T (1974) Aspects of the theory of hypermatroids. Hypergraph Seminar (Springer, Berlin/Heidelberg), 191–213.Google Scholar
  • [36] Hermon J, Salez J (2019) Modified log-Sobolev inequalities for strong-Rayleigh measures. Preprint, submitted February 7, https://arxiv.org/abs/1902.02775.Google Scholar
  • [37] Holzman R, Law-Yone N (1997) Strong equilibrium in congestion games. Games Econom. Behav. 21(1–2):85–101.CrossrefGoogle Scholar
  • [38] Ieong S, McGrew R, Nudelman E, Shoham Y, Sun Q (2005) Fast and compact: A simple class of congestion games. Proc. 20th Natl. Conf. Artificial Intelligence, 489–494.Google Scholar
  • [39] Jerrum M, Sinclair A (1993) Polynomial-time approximation algorithms for the Ising model. SIAM J. Comput. 22(5):1087–1116.CrossrefGoogle Scholar
  • [40] Jerrum M, Sinclair A, Vigoda E (2004) A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries. J. ACM 51(4):671–697.CrossrefGoogle Scholar
  • [41] Jerrum M, Son JB, Tetali P, Vigoda E (2004) Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains. Ann. Appl. Probab. 14(4):1741–1765.CrossrefGoogle Scholar
  • [42] Kleer P (2021) Sampling from the Gibbs distribution in congestion games. Proc. 22nd ACM Conf. Econom. Comput., 679–680.Google Scholar
  • [43] Kleer P, Schäfer G (2017) Potential function minimizers of combinatorial congestion games: Efficiency and computation. Proc. 18th ACM Conf. Econom. Comput., 223–240.Google Scholar
  • [44] Levin DA, Luczak MJ, Peres Y (2010) Glauber dynamics for the mean-field Ising model: Cut-off, critical power law, and metastability. Probab. Theory Related Fields 146(1–2):223–265.CrossrefGoogle Scholar
  • [45] Mamageishvili A, Penna P (2016) Tighter bounds on the inefficiency ratio of stable equilibria in load balancing games. Oper. Res. Lett. 44(5):645–648.CrossrefGoogle Scholar
  • [46] Martin RA, Randall D (2000) Sampling adsorbing staircase walks using a new Markov chain decomposition method. Proc. 41st Annual Sympos. Foundations Comput. Sci., 492–502.Google Scholar
  • [47] Mäs M, Nax HH (2016) A behavioral study of “noise” in coordination games. J. Econom. Theory 162:195–208.CrossrefGoogle Scholar
  • [48] McFadden D (1973) Conditional logit analysis of qualitative choice behavior. Frontiers in Econometrics, 105–142.Google Scholar
  • [49] McKay BD (1984) Asymptotics for 0-1 matrices with prescribed line sums. Enumeration and Design (Academic Press, Cambridge, MA), 225–238.Google Scholar
  • [50] Mihail M, Vazirani U (1989) On the expansion of 0-1 polytopes. J. Combin. Theory Ser. BGoogle Scholar
  • [51] Murota K (1998) Discrete convex analysis. Math. Programming 83(1–3):313–371.CrossrefGoogle Scholar
  • [52] Murota K (2003) Discrete convex analysis. SIAM Monograph on Discrete Mathematics and Applications (Society for Industrial and Applied Mathematics).CrossrefGoogle Scholar
  • [53] Murota K (2009) Recent developments in discrete convex analysis. Research Trends in Combinatorial Optimization, 219–260.Google Scholar
  • [54] Penna P (2018) The price of anarchy and stability in general noisy best-response dynamics. Internat. J. Game Theory 47(3):839–855.CrossrefGoogle Scholar
  • [55] Rosenthal RW (1973) A class of games possessing pure-strategy Nash equilibria. Internat. J. Game Theory 2:65–67.CrossrefGoogle Scholar
  • [56] Sandholm WH (2010) Population Games and Evolutionary Dynamics (MIT Press, Cambridge, MA).Google Scholar
  • [57] Schrijver A (2003) Combinatorial optimization: Polyhedra and efficiency. Matroids, Trees, Stable Sets, vol. B, Algorithms and Combinatorics (Springer-Verlag, Berlin).Google Scholar
  • [58] Sinclair A (1992) Improved bounds for mixing rates of Markov chains and multicommodity flow. Combin. Probab. Comput. 1(4):351–370.CrossrefGoogle Scholar
  • [59] Skopalik A, Vöcking B (2008) Inapproximability of pure Nash equilibria. Proc. 40th Annual ACM Sympos. Theory Comput., 355–364.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.