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Experimenting in Equilibrium

Author

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  • Stefan Wager

    (Graduate School of Business, Stanford University, Stanford, California 94305)

  • Kuang Xu

    (Graduate School of Business, Stanford University, Stanford, California 94305)

Abstract

Classical approaches to experimental design assume that intervening on one unit does not affect other units. There are many important settings, however, where this noninterference assumption does not hold, as when running experiments on supply-side incentives on a ride-sharing platform or subsidies in an energy marketplace. In this paper, we introduce a new approach to experimental design in large-scale stochastic systems with considerable cross-unit interference, under an assumption that the interference is structured enough that it can be captured via mean-field modeling. Our approach enables us to accurately estimate the effect of small changes to system parameters by combining unobtrusive randomization with lightweight modeling, all while remaining in equilibrium. We can then use these estimates to optimize the system by gradient descent. Concretely, we focus on the problem of a platform that seeks to optimize supply-side payments p in a centralized marketplace where different suppliers interact via their effects on the overall supply-demand equilibrium, and we show that our approach enables the platform to optimize p in large systems using vanishingly small perturbations.

Suggested Citation

  • Stefan Wager & Kuang Xu, 2021. "Experimenting in Equilibrium," Management Science, INFORMS, vol. 67(11), pages 6694-6715, November.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:11:p:6694-6715
    DOI: 10.1287/mnsc.2020.3844
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    References listed on IDEAS

    as
    1. Eckles Dean & Karrer Brian & Ugander Johan, 2017. "Design and Analysis of Experiments in Networks: Reducing Bias from Interference," Journal of Causal Inference, De Gruyter, vol. 5(1), pages 1-23, March.
    2. Gérard P. Cachon & Kaitlin M. Daniels & Ruben Lobel, 2017. "The Role of Surge Pricing on a Service Platform with Self-Scheduling Capacity," Manufacturing & Service Operations Management, INFORMS, vol. 19(3), pages 368-384, July.
    3. Susan Athey & Michael Luca, 2019. "Economists (and Economics) in Tech Companies," Journal of Economic Perspectives, American Economic Association, vol. 33(1), pages 209-230, Winter.
    4. Heckman, James J & Lochner, Lance & Taber, Christopher, 1998. "General-Equilibrium Treatment Effects: A Study of Tuition Policy," American Economic Review, American Economic Association, vol. 88(2), pages 381-386, May.
    5. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    6. Raj Chetty, 2009. "Sufficient Statistics for Welfare Analysis: A Bridge Between Structural and Reduced-Form Methods," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 451-488, May.
    7. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    8. Charles F. Manski, 2013. "Identification of treatment response with social interactions," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-23, February.
    9. G W Basse & A Feller & P Toulis, 2019. "Randomization tests of causal effects under interference," Biometrika, Biometrika Trust, vol. 106(2), pages 487-494.
    10. Susan Athey & Dean Eckles & Guido W. Imbens, 2018. "Exact p-Values for Network Interference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 230-240, January.
    11. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    12. Hudgens, Michael G. & Halloran, M. Elizabeth, 2008. "Toward Causal Inference With Interference," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 832-842, June.
    13. James J. Heckman, 2001. "Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture," Journal of Political Economy, University of Chicago Press, vol. 109(4), pages 673-748, August.
    14. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
    15. Krishnamurthy Iyer & Ramesh Johari & Mukund Sundararajan, 2014. "Mean Field Equilibria of Dynamic Auctions with Learning," Management Science, INFORMS, vol. 60(12), pages 2949-2970, December.
    16. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    17. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
    18. Adlakha, Sachin & Johari, Ramesh & Weintraub, Gabriel Y., 2015. "Equilibria of dynamic games with many players: Existence, approximation, and market structure," Journal of Economic Theory, Elsevier, vol. 156(C), pages 269-316.
    19. Sobel, Michael E., 2006. "What Do Randomized Studies of Housing Mobility Demonstrate?: Causal Inference in the Face of Interference," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1398-1407, December.
    20. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2008. "Markov Perfect Industry Dynamics With Many Firms," Econometrica, Econometric Society, vol. 76(6), pages 1375-1411, November.
    21. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute of Labor Economics (IZA).
    22. Michael P. Leung, 2020. "Treatment and Spillover Effects Under Network Interference," The Review of Economics and Statistics, MIT Press, vol. 102(2), pages 368-380, May.
    23. Richard Blundell & Monica Costa Dias & Costas Meghir & John Van Reenen, 2004. "Evaluating the Employment Impact of a Mandatory Job Search Program," Journal of the European Economic Association, MIT Press, vol. 2(4), pages 569-606, June.
    24. Mila Nambiar & David Simchi-Levi & He Wang, 2019. "Dynamic Learning and Pricing with Model Misspecification," Management Science, INFORMS, vol. 65(11), pages 4980-5000, November.
    25. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    26. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
    27. Yurii NESTEROV & Vladimir SPOKOINY, 2017. "Random gradient-free minimization of convex functions," LIDAM Reprints CORE 2851, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Luofeng Liao & Christian Kroer, 2024. "Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium," Papers 2402.02303, arXiv.org, revised Feb 2024.
    2. Jinglong Zhao, 2024. "Experimental Design For Causal Inference Through An Optimization Lens," Papers 2408.09607, arXiv.org, revised Aug 2024.
    3. Ruoxuan Xiong & Alex Chin & Sean J. Taylor, 2024. "Data-Driven Switchback Experiments: Theoretical Tradeoffs and Empirical Bayes Designs," Papers 2406.06768, arXiv.org.
    4. Yuehao Bai & Azeem M. Shaikh & Max Tabord-Meehan, 2024. "A Primer on the Analysis of Randomized Experiments and a Survey of some Recent Advances," Papers 2405.03910, arXiv.org.
    5. Shuze Chen & David Simchi-Levi & Chonghuan Wang, 2024. "Experimenting on Markov Decision Processes with Local Treatments," Papers 2407.19618, arXiv.org, revised Oct 2024.
    6. Nian Si, 2023. "Tackling Interference Induced by Data Training Loops in A/B Tests: A Weighted Training Approach," Papers 2310.17496, arXiv.org, revised Apr 2024.
    7. Ozan Candogan & Chen Chen & Rad Niazadeh, 2024. "Correlated Cluster-Based Randomized Experiments: Robust Variance Minimization," Management Science, INFORMS, vol. 70(6), pages 4069-4086, June.

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