IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v54y2014icp48-58.html
   My bibliography  Save this article

Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification

Author

Listed:
  • Li, Xiaoliang
  • Wang, Dongming

Abstract

In this paper, we are concerned with the problem of determining the existence of multiple equilibria in economic models. We propose a general and complete approach for identifying multiplicities of equilibria in semi-algebraic economies, which may be expressed as semi-algebraic systems. The approach is based on triangular decomposition and real solution classification, two powerful tools of algebraic computation. Its effectiveness is illustrated by three examples of application.

Suggested Citation

  • Li, Xiaoliang & Wang, Dongming, 2014. "Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 48-58.
    • Handle: RePEc:eee:mateco:v:54:y:2014:i:c:p:48-58
    DOI: 10.1016/j.jmateco.2014.08.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406814001098
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2014.08.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
    2. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, September.
    3. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 55-96, January.
    4. Jaskold Gabszewicz, J. & Thisse, J. -F., 1979. "Price competition, quality and income disparities," Journal of Economic Theory, Elsevier, vol. 20(3), pages 340-359, June.
    5. Gjerstad, S., 1996. "Multiple Equilibria in Exchange Economies with Homothetic, Nearly Identical Preferences," Papers 288, Minnesota - Center for Economic Research.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiaoliang Li, 2022. "Cournot duopoly games with isoelastic demands and diseconomies of scale," Papers 2203.09972, arXiv.org.
    2. Casey B. Mulligan, 2018. "Quantifier Elimination for Deduction in Econometrics," NBER Working Papers 24601, National Bureau of Economic Research, Inc.
    3. Casey B. Mulligan & Russell Bradford & James H. Davenport & Matthew England & Zak Tonks, 2018. "Non-linear Real Arithmetic Benchmarks derived from Automated Reasoning in Economics," NBER Working Papers 24602, National Bureau of Economic Research, Inc.
    4. Xiaoliang Li & Li Su, 2021. "Stability of Cournot duopoly games with isoelastic demands and quadratic costs," Papers 2112.05948, arXiv.org, revised Mar 2022.
    5. Xiaoliang Li & Kongyan Chen, 2023. "Equilibria and their stability in an asymmetric duopoly model of Kopel," Papers 2301.12628, arXiv.org.
    6. Xiaoliang Li, 2021. "Analysis of stability and bifurcation for two heterogeneous triopoly games with the isoelastic demand," Papers 2112.05950, arXiv.org.
    7. Xiaoliang Li & Jiacheng Fu & Wei Niu, 2023. "Complex dynamics of knowledgeable monopoly models with gradient mechanisms," Papers 2301.01497, arXiv.org.
    8. Xiaoliang Li & Bo Li, 2023. "A Bertrand duopoly game with differentiated products reconsidered," Papers 2301.01007, arXiv.org.
    9. Li, Xiaoliang & Li, Bo & Liu, Li, 2023. "Stability and dynamic behaviors of a limited monopoly with a gradient adjustment mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    2. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
    3. Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, July.
    4. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    5. Felix Kubler & Karl Schmedders, 2010. "Tackling Multiplicity of Equilibria with Gröbner Bases," Operations Research, INFORMS, vol. 58(4-part-2), pages 1037-1050, August.
    6. Fluet, Claude & Garella, Paolo G., 2002. "Advertising and prices as signals of quality in a regime of price rivalry," International Journal of Industrial Organization, Elsevier, vol. 20(7), pages 907-930, September.
    7. Ashantha Ranasinghe & Xuejuan Su, 2023. "When social assistance meets market power: A mixed duopoly view of health insurance in the United States," Economic Inquiry, Western Economic Association International, vol. 61(4), pages 851-869, October.
    8. Bryan McCannon, 2004. "The impact of a trade embargo on quality," Economics Bulletin, AccessEcon, vol. 6(14), pages 1-7.
    9. Pierre M. Picard & Alessandro Tampieri, 2016. "Income Effects and Vertical Differentiation in International Trade," DEM Discussion Paper Series 16-05, Department of Economics at the University of Luxembourg.
    10. Andr, Francisco J. & Gonzlez, Paula & Porteiro, Nicols, 2009. "Strategic quality competition and the Porter Hypothesis," Journal of Environmental Economics and Management, Elsevier, vol. 57(2), pages 182-194, March.
    11. repec:ebl:ecbull:v:4:y:2005:i:7:p:1-7 is not listed on IDEAS
    12. J. M. Bonnisseau & M. Florig & A. Jofré, 2001. "Continuity and Uniqueness of Equilibria for Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 237-263, May.
    13. George Deltas & Thanasis Stengos & Eleftherios Zacharias, 2011. "Product line pricing in a vertically differentiated oligopoly," Canadian Journal of Economics, Canadian Economics Association, vol. 44(3), pages 907-929, August.
    14. Lambertini, Luca, 1999. "Endogenous timing and the choice of quality in a vertically differentiated duopoly," Research in Economics, Elsevier, vol. 53(1), pages 101-109, March.
    15. John W. Patty, 2005. "Generic Difference of Expected Vote Share and Probability of Victory Maximization in Simple Plurality Elections with Probabilistic Voters," Public Economics 0502006, University Library of Munich, Germany.
    16. Lutz, Stefan, 1998. "Can taxing foreign competition harm the domestic industry?," ZEI Working Papers B 15-1998, University of Bonn, ZEI - Center for European Integration Studies.
    17. Stefan Buehler & Daniel Halbheer, 2011. "Selling when Brand Image Matters," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 167(1), pages 102-118, March.
    18. Eduardo Correia de Souza & Jorge Chami Batista, 2015. "Replacement cycles, income distribution and dynamic price discrimination," Applied Economics, Taylor & Francis Journals, vol. 47(31), pages 3292-3310, July.
    19. Jun Li & Serguei Netessine & Sergei Koulayev, 2018. "Price to Compete … with Many: How to Identify Price Competition in High-Dimensional Space," Management Science, INFORMS, vol. 64(9), pages 4118-4136, September.
    20. Jean-Marc Bonnisseau & Elena Mercato, 2010. "Externalities, consumption constraints and regular economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 123-147, July.
    21. Bonnisseau, Jean-Marc & Nguenamadji, Orntangar, 2010. "On the uniqueness of local equilibria," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 623-632, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:54:y:2014:i:c:p:48-58. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.