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A continuous deformation algorithm on the product space of unit simplices

Author

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  • Doup, T.M.
  • Talman, A.J.J.

    (Tilburg University, Faculty of Economics)

Abstract

A continuous deformation algorithm is introduced on S × [1, (infinity)), where S denotes the product space of unit simplices, with arbitrary grid refinement between two subsequent levels. The set S × [1, (infinity)) is triangulated in such a way that for each m , m = 1, 2, ..., S × { m } is triangulated by the so-called V -triangulation. The algorithm starts by applying a variable dimension algorithm on S until an approximating simplex has been found on level 1. Then the algorithm follows a path of approximating simplices in S × [1, (infinity)), starting on level 1, until a certain level or a certain accuracy of a solution of the underlying problem has been reached. If the algorithm returns to level 1, then we again apply the variable dimension algorithm until a new approximating simplex is found on level 1, etc. We allow solutions to lie on the boundary of S × [1, (infinity)) in which case the algorithm, in general, will follow a path on the boundary of S × [1, (infinity)).
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Suggested Citation

  • Doup, T.M. & Talman, A.J.J., 1985. "A continuous deformation algorithm on the product space of unit simplices," Research Memorandum FEW 168, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiurem:fefeca71-7cb2-4bf8-9419-e7c581f309dc
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    References listed on IDEAS

    as
    1. Doup, T.M. & Talman, A.J.J., 1984. "A new variable dimension simplicial algorithm to find equilibria on the product space of unit simplices," Research Memorandum FEW 146, Tilburg University, School of Economics and Management.
    2. Talman, A.J.J. & van der Laan, G., 1980. "A new subdivision for computing fixed points with a homotopy algorithm," Other publications TiSEM d702630e-5e0d-4c31-bd1e-1, Tilburg University, School of Economics and Management.
    3. Doup, T.M. & van der Laan, G. & Talman, A.J.J., 1984. "The (2n+1-2)-ray algorithm : A new simplicial algorithm to compute economic equilibria," Other publications TiSEM 03240a63-123f-484a-9017-4, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Stuart McDonald & Liam Wagner, 2010. "The Computation of Perfect and Proper Equilibrium for Finite Games via Simulated Annealing," Risk & Uncertainty Working Papers WPR10_1, Risk and Sustainable Management Group, University of Queensland, revised Apr 2010.
    2. Herings, P. Jean-Jacques & van den Elzen, Antoon, 2002. "Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games," Games and Economic Behavior, Elsevier, vol. 38(1), pages 89-117, January.
    3. Stuart McDonald & Liam Wagner, 2013. "A Stochastic Search Algorithm for the Computation of Perfect and Proper Equilibria," Discussion Papers Series 480, School of Economics, University of Queensland, Australia.
    4. Yiyin Cao & Chuangyin Dang & Yabin Sun, 2022. "Complementarity Enhanced Nash’s Mappings and Differentiable Homotopy Methods to Select Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 533-563, February.
    5. Hofkes, M.W., 1988. "Parametrization of simplicial algorithms with an application to an empirical general equilibrium model," Serie Research Memoranda 0037, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    6. Cao, Yiyin & Dang, Chuangyin, 2022. "A variant of Harsanyi's tracing procedures to select a perfect equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 134(C), pages 127-150.

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