Equilibrium Transport with Time-Inconsistent Costs

Published Online:https://doi.org/10.1287/moor.2023.0323

References

  • [1] Abowd JM, Kramarz F, Margolis DN (1999) High wage workers and high wage firms. Econometrica 67(2):251–333.CrossrefGoogle Scholar
  • [2] Acciaio B, Backhoff-Veraguas J, Jia J (2021) Cournot–Nash equilibrium and optimal transport in a dynamic setting. SIAM J. Control Optim. 59(3):2273–2300.CrossrefGoogle Scholar
  • [3] Acciaio B, Backhoff-Veraguas J, Zalashko A (2020) Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization. Stochastic Processes Appl. 130(5):2918–2953.CrossrefGoogle Scholar
  • [4] Arjovsky M, Chintala S, Bottou L (2017) Wasserstein generative adversarial networks. Precup D, The YW, eds. Proc. Internat. Conf. Machine Learn. ICML 2017, Proceedings of Machine Learning Research, vol. 70 (PMLR, New York), 214–223.Google Scholar
  • [5] Backhoff-Veraguas J, Zhang X (2023) Dynamic Cournot-Nash equilibrium: The non-potential case. Math. Financial Econom. 17(2):153–174.CrossrefGoogle Scholar
  • [6] Backhoff-Veraguas J, Bartl D, Beiglböck M, Eder M (2020) Adapted Wasserstein distances and stability in mathematical finance. Finance Stochastics 24(3):601–632.CrossrefGoogle Scholar
  • [7] Backhoff-Veraguas J, Bartl D, Beiglböck M, Wiesel J (2022) Estimating processes in adapted Wasserstein distance. Ann. Appl. Probab. 32(1):529–550.Google Scholar
  • [8] Backhoff-Veraguas J, Beiglbock M, Lin Y, Zalashko A (2017) Causal transport in discrete time and applications. SIAM J. Optim. 27(4):2528–2562.CrossrefGoogle Scholar
  • [9] Barberis N (2012) A model of casino gambling. Management Sci. 58(1):35–51.LinkGoogle Scholar
  • [10] Basak S, Chabakauri G (2010) Dynamic mean-variance asset allocation. Rev. Financial Stud. 23(8):2970–3016.CrossrefGoogle Scholar
  • [11] Bayraktar E, Han B (2023) Existence of Markov equilibrium control in discrete time. SIAM J. Financial Math. 14(4):SC60–SC71.CrossrefGoogle Scholar
  • [12] Bayraktar E, Eckstein S, Zhang X (2025) Stability and sample complexity of divergence regularized optimal transport. Bernoulli 31(1):213–239.CrossrefGoogle Scholar
  • [13] Bayraktar E, Zhang J, Zhou Z (2021) Equilibrium concepts for time-inconsistent stopping problems in continuous time. Math. Finance 31(1):508–530.CrossrefGoogle Scholar
  • [14] Becker GS (1973) A theory of marriage: Part I. J. Political Econom. 81(4):813–846.CrossrefGoogle Scholar
  • [15] Beiglböck M, Pratelli A (2012) Duality for rectified cost functions. Calculus Variations Partial Differential Equations 45:27–41.CrossrefGoogle Scholar
  • [16] Bertsekas D, Shreve SE (1978) Stochastic Optimal Control: The Discrete-Time Case (Academic Press, New York).Google Scholar
  • [17] Björk T, Murgoci A (2014) A theory of Markovian time-inconsistent stochastic control in discrete time. Finance Stochastics 18(3):545–592.CrossrefGoogle Scholar
  • [18] Björk T, Khapko M, Murgoci A (2017) On time-inconsistent stochastic control in continuous time. Finance Stochastics 21(2):331–360.CrossrefGoogle Scholar
  • [19] Björk T, Murgoci A, Zhou XY (2014) Mean–variance portfolio optimization with state-dependent risk aversion. Math. Finance 24(1):1–24.CrossrefGoogle Scholar
  • [20] Blanchet J, Murthy K (2019) Quantifying distributional model risk via optimal transport. Math. Oper. Res. 44(2):565–600.LinkGoogle Scholar
  • [21] Blanchet J, Murthy K, Nguyen VA (2021) Statistical analysis of Wasserstein distributionally robust estimators. Tutorials in Operations Research: Emerging Optimization Methods and Modeling Techniques with Applications (INFORMS, Catonsville, MD), 227–254.LinkGoogle Scholar
  • [22] Boerma J, Tsyvinski A, Wang R, Zhang Z (2023) Composite sorting. Preprint, submitted March 12, https://arxiv.org/abs/2303.06701.Google Scholar
  • [23] Bogachev VI (2007) Measure Theory, vol. II (Springer, Berlin, Heidelberg).CrossrefGoogle Scholar
  • [24] Bonhomme S, Lamadon T, Manresa E (2019) A distributional framework for matched employer employee data. Econometrica 87(3):699–739.CrossrefGoogle Scholar
  • [25] Borovicková K, Shimer R (2020) High wage workers work for high wage firms. Working paper, University of Chicago, Chicago.Google Scholar
  • [26] Brenier Y (1991) Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. 44(4):375–417.CrossrefGoogle Scholar
  • [27] Brown LD, Purves R (1973) Measurable selections of extrema. Ann. Statist.CrossrefGoogle Scholar
  • [28] Card D, Heining J, Kline P (2013) Workplace heterogeneity and the rise of West German wage inequality. Quart. J. Econom. 128(3):967–1015.CrossrefGoogle Scholar
  • [29] Charalambos D, Aliprantis B (2013) Infinite Dimensional Analysis: A Hitchhiker’s Guide (Springer, Berlin, Heidelberg).Google Scholar
  • [30] Cuturi M (2013) Sinkhorn distances: Lightspeed computation of optimal transport. Adv. Neural Inform. Processing Systems 26:2292–2300.Google Scholar
  • [31] Delon J, Desolneux A (2020) A Wasserstein-type distance in the space of Gaussian mixture models. SIAM J. Imaging Sci. 13(2):936–970.CrossrefGoogle Scholar
  • [32] Demerjian P, Lev B, McVay S (2012) Quantifying managerial ability: A new measure and validity tests. Management Sci. 58(7):1229–1248.LinkGoogle Scholar
  • [33] Eckstein S, Pammer G (2024) Computational methods for adapted optimal transport. Ann. Appl. Probab. 34(1A):675–713.CrossrefGoogle Scholar
  • [34] Epstein LG, Ji S (2022) Optimal learning under robustness and time-consistency. Oper. Res. 70(3):1317–1329.LinkGoogle Scholar
  • [35] Föllmer H, Schied A (2011) Stochastic Finance: An Introduction in Discrete Time (Walter de Gruyter, Berlin).CrossrefGoogle Scholar
  • [36] Gabaix X, Landier A (2008) Why has CEO pay increased so much? Quart. J. Econom. 123(1):49–100.CrossrefGoogle Scholar
  • [37] Galichon A (2016) Optimal Transport Methods in Economics (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • [38] Gangbo W, McCann RJ (1996) The geometry of optimal transportation. Acta Math 177(2):113–161.CrossrefGoogle Scholar
  • [39] Gao R, Kleywegt A (2022) Distributionally robust stochastic optimization with Wasserstein distance. Math. Oper. Res.LinkGoogle Scholar
  • [40] Givens CR, Shortt RM (1984) A class of Wasserstein metrics for probability distributions. Michigan Math. J. 31(2):231–240.CrossrefGoogle Scholar
  • [41] González-Sanz A, Nutz M (2024) Quantitative convergence of quadratically regularized linear programs. Preprint, submitted August 7, https://arxiv.org/abs/2408.04088.Google Scholar
  • [42] Gunasingam M, Wong TKL (2024) Adapted optimal transport between Gaussian processes in discrete time. Preprint, submitted April 9, https://arxiv.org/abs/2404.06625.Google Scholar
  • [43] Hagedorn M, Law TH, Manovskii I (2017) Identifying equilibrium models of labor market sorting. Econometrica 85(1):29–65.CrossrefGoogle Scholar
  • [44] Han B (2025) Distributionally robust Kalman filtering with volatility uncertainty. IEEE Trans. Automatic Control 70(6):4000–4007.CrossrefGoogle Scholar
  • [45] Han B, Pun CS, Wong HY (2021) Robust state-dependent mean–variance portfolio selection: A closed-loop approach. Finance Stochastics 25(3):529–561.CrossrefGoogle Scholar
  • [46] Hu M, Zhou Y (2022) Dynamic type matching. Manufacturing Service Oper. Management 24(1):125–142.LinkGoogle Scholar
  • [47] Kahneman D, Tversky A (1979) Prospect theory: An analysis of decision under risk. Econometrica 47(2):263–292.CrossrefGoogle Scholar
  • [48] Kallenberg O (2021) Foundations of Modern Probability, 3rd ed. (Springer, Cham, Switzerland).CrossrefGoogle Scholar
  • [49] Kechris A (2012) Classical Descriptive Set Theory, Graduate Texts in Mathematics, vol. 156 (Springer, New York).Google Scholar
  • [50] Kováčová G, Rudloff B (2021) Time consistency of the mean-risk problem. Oper. Res. 69(4):1100–1117.LinkGoogle Scholar
  • [51] Kuhn D, Esfahani PM, Nguyen VA, Shafieezadeh-Abadeh S (2019) Wasserstein distributionally robust optimization: Theory and applications in machine learning. Operations Research & Management Science in the Age of Analytics, INFORMS TutORials in Operations Research (INFORMS, Catonsville, MD), 130–166.LinkGoogle Scholar
  • [52] Laibson D (1997) Golden eggs and hyperbolic discounting. Quart. J. Econom. 112(2):443–478.CrossrefGoogle Scholar
  • [53] Lassalle R (2013) Causal transference plans and their Monge-Kantorovich problems. Preprint, submitted March 27, https://arxiv.org/abs/1303.6925.Google Scholar
  • [54] Ma J, Wong TKL, Zhang J (2021) Time-consistent conditional expectation under probability distortion. Math. Oper. Res. 46(3):1149–1180.LinkGoogle Scholar
  • [55] Mohajerin Esfahani P, Kuhn D (2018) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Programming 171(1):115–166.CrossrefGoogle Scholar
  • [56] Parthasarathy KR (2005) Probability Measures on Metric Spaces, vol. 352 (American Mathematical Society, Providence, RI).Google Scholar
  • [57] Peyré G, Cuturi M (2019) Computational optimal transport: With applications to data science. Foundations Machine Learn. 11(5–6):355–607.CrossrefGoogle Scholar
  • [58] Pflug GC, Pichler A (2012) A distance for multistage stochastic optimization models. SIAM J. Optim. 22(1):1–23.CrossrefGoogle Scholar
  • [59] Pflug GC, Pichler A (2014) Multistage Stochastic Optimization, Springer Series in Operations Research and Financial Engineering, vol. 1104 (Springer, Cham, Switzerland).CrossrefGoogle Scholar
  • [60] Pichler A, Weinhardt M (2022) The nested Sinkhorn divergence to learn the nested distance. Comput. Management Sci. 19(2):269–293.CrossrefGoogle Scholar
  • [61] Pichler A, Liu RP, Shapiro A (2022) Risk-averse stochastic programming: Time consistency and optimal stopping. Oper. Res. 70(4):2439–2455.LinkGoogle Scholar
  • [62] Postel-Vinay F, Robin JM (2002) Equilibrium wage dispersion with worker and employer heterogeneity. Econometrica 70(6):2295–2350.CrossrefGoogle Scholar
  • [63] Schrott S, Beiglböck M, Pammer G (2023) Denseness of biadapted Monge mappings. Ann. de l’Institut Henri Poincaré-Probabilités Statistiques 61(1):329–349.Google Scholar
  • [64] Seguy V, Damodaran BB, Flamary R, Courty N, Rolet A, Blondel M (2018) Large-scale optimal transport and mapping estimation. 6th Internat. Conf. Learn. Representations, ICLR 2018 (OpenReview.net), 1–15.Google Scholar
  • [65] Shimer R, Smith L (2000) Assortative matching and search. Econometrica 68(2):343–369.CrossrefGoogle Scholar
  • [66] Song J, Price DJ, Guvenen F, Bloom N, Von Wachter T (2019) Firming up inequality. Quart. J. Econom. 134(1):1–50.CrossrefGoogle Scholar
  • [67] Steen LA, Seebach JA (1978) Counterexamples in Topology (Springer, New York).CrossrefGoogle Scholar
  • [68] Strotz R (1955) Myopia and inconsistency in dynamic utility maximization. Rev. Econom. Stud. 23(3):165–180.CrossrefGoogle Scholar
  • [69] Stuart AM, Wolfram MT (2020) Inverse optimal transport. SIAM J. Appl. Math. 80(1):599–619.CrossrefGoogle Scholar
  • [70] Sundaram RK (1996) A First Course in Optimization Theory (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [71] Taşkesen B, Shafieezadeh-Abadeh S, Kuhn D (2023) Semi-discrete optimal transport: Hardness, regularization and numerical solution. Math. Programming 199(1–2):1033–1106.CrossrefGoogle Scholar
  • [72] Torous W, Gunsilius F, Rigollet P (2021) An optimal transport approach to causal inference. Preprint, submitted August 12, https://arxiv.org/abs/2108.05858.Google Scholar
  • [73] Villani C (2009) Optimal Transport: Old and New, Grundlehren der mathematischen Wissenschaften, vol. 338 (Springer, Berlin, Heidelberg).CrossrefGoogle Scholar
  • [74] Xu T, Li WK, Munn M, Acciaio B (2020) COT-GAN: Generating sequential data via causal optimal transport. Adv. Neural Inform. Processing Systems 33:8798–8809.Google Scholar
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