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

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  • 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
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    References listed on IDEAS

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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, January.
    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. 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.
    4. Gjerstad, S., 1996. "Multiple Equilibria in Exchange Economies with Homothetic, Nearly Identical Preferences," Papers 288, Minnesota - Center for Economic Research.
    5. 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.
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    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. Xiaoliang Li & Li Su, 2021. "Stability of Cournot duopoly games with isoelastic demands and quadratic costs," Papers 2112.05948, arXiv.org, revised Mar 2022.
    4. Xiaoliang Li & Kongyan Chen, 2023. "Equilibria and their stability in an asymmetric duopoly model of Kopel," Papers 2301.12628, arXiv.org.
    5. Xiaoliang Li & Bo Li, 2023. "A Bertrand duopoly game with differentiated products reconsidered," Papers 2301.01007, arXiv.org.
    6. 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.
    7. Xiaoliang Li, 2021. "Analysis of stability and bifurcation for two heterogeneous triopoly games with the isoelastic demand," Papers 2112.05950, arXiv.org.
    8. Xiaoliang Li & Jiacheng Fu & Wei Niu, 2023. "Complex dynamics of knowledgeable monopoly models with gradient mechanisms," Papers 2301.01497, 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).

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