Abstract
We propose a new method for finding equilibrium in a linear exchange model with fixed budgets. The algorithm rests on consideration of the two dual polyhedral complexes generated by an associated transportation problem of the model. The algorithm uses the thoroughly developed fragments of the method of potentials for a transportation problem, which enables us to considering only systems of linear equations with a triangular matrix at every step. The algorithm admits starting with an arbitrary initial price vector. We prove the finiteness of the algorithm.
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Original Russian Text © V.I. Shmyrev, 2008, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2008, Vol. XI, No. 2, pp. 139–154.
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Shmyrev, V.I. An algorithm for finding equilibrium in the linear exchange model with fixed budgets. J. Appl. Ind. Math. 3, 505–518 (2009). https://doi.org/10.1134/S1990478909040097
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DOI: https://doi.org/10.1134/S1990478909040097