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Extending fixed-point methods for equilibrium computation in markets with differentiated products

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  • Duarte, Marco

Abstract

This paper extends fixed-point approaches for computing equilibrium prices under mixed-logit demand across various conduct models. Building on Morrow and Skerlos (2011), we reformulate iteration functions to improve convergence beyond Bertrand–Nash models of competition, including Cournot and Linear Pricing-Double Marginalization. Monte Carlo simulations and an application to the U.S. automobile industry show our method’s superior reliability in counterfactual price computations.

Suggested Citation

  • Duarte, Marco, 2025. "Extending fixed-point methods for equilibrium computation in markets with differentiated products," Economics Letters, Elsevier, vol. 250(C).
    • Handle: RePEc:eee:ecolet:v:250:y:2025:i:c:s0165176525001120
    DOI: 10.1016/j.econlet.2025.112275
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    References listed on IDEAS

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    1. Robert C. Feenstra & James A. Levinsohn, 1995. "Estimating Markups and Market Conduct with Multidimensional Product Attributes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 19-52.
    2. Timothy B. Armstrong, 2016. "Large Market Asymptotics for Differentiated Product Demand Estimators With Economic Models of Supply," Econometrica, Econometric Society, vol. 84, pages 1961-1980, September.
    3. James Levinsohn & Steven Berry & Ariel Pakes, 1999. "Voluntary Export Restraints on Automobiles: Evaluating a Trade Policy," American Economic Review, American Economic Association, vol. 89(3), pages 400-430, June.
    4. Nathan H. Miller & Matthew C. Weinberg, 2017. "Understanding the Price Effects of the MillerCoors Joint Venture," Econometrica, Econometric Society, vol. 85(6), pages 1763-1791, November.
    5. Marco Duarte & Lorenzo Magnolfi & Mikkel Sølvsten & Christopher Sullivan, 2024. "Testing firm conduct," Quantitative Economics, Econometric Society, vol. 15(3), pages 571-606, July.
      • Marco Duarte & Lorenzo Magnolfi & Mikkel S{o}lvsten & Christopher Sullivan, 2023. "Testing Firm Conduct," Papers 2301.06720, arXiv.org, revised Jan 2024.
    6. Céline Bonnet & Pierre Dubois, 2010. "Inference on vertical contracts between manufacturers and retailers allowing for nonlinear pricing and resale price maintenance," RAND Journal of Economics, RAND Corporation, vol. 41(1), pages 139-164, March.
    7. W. Ross Morrow & Steven J. Skerlos, 2011. "Fixed-Point Approaches to Computing Bertrand-Nash Equilibrium Prices Under Mixed-Logit Demand," Operations Research, INFORMS, vol. 59(2), pages 328-345, April.
    8. repec:cdl:agrebk:qt0z26d2v9 is not listed on IDEAS
    9. repec:cdl:agrebk:qt6gz1t778 is not listed on IDEAS
    10. Matthew Backus & Christopher Conlon & Michael Sinkinson, 2021. "Common Ownership and Competition in the Ready-to-Eat Cereal Industry," NBER Working Papers 28350, National Bureau of Economic Research, Inc.
    11. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    12. Sofia Berto Villas-Boas, 2007. "Vertical Relationships between Manufacturers and Retailers: Inference with Limited Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 625-652.
    13. Alexander Konovalov & Zsolt Sándor, 2010. "On price equilibrium with multi-product firms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 271-292, August.
    14. Christopher Conlon & Jeff Gortmaker, 2020. "Best practices for differentiated products demand estimation with PyBLP," RAND Journal of Economics, RAND Corporation, vol. 51(4), pages 1108-1161, December.
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