An algorithm based on a sequence of linear complementarity problems applied to a walrasian equilibrium model: An example |
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Authors: | Lars Mathiesen |
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Institution: | (1) Center for Applied Research, Norwegian School of Economics and Business Administration, 5035 Bergen-Sandviken, Norway |
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Abstract: | The Walrasian equilibrium problem is cast as a complementarity problem, and its solution is computed by solving a sequence
of linear complementarity problems (SLCP). Earlier numerical experiments have demonstrated the computational efficiency of
this approach. So far, however, there exist few relevant theoretical results that characterize the performance of this algorithm.
In the context of a simple example of a Walrasian equilibrium model, we study the iterates of the SLCP algorithm. We show
that a particular LCP of this process may have no, one or more complementary solutions. Other LCPs may have both homogeneous
and complementary solutions. These features complicate the proof of convergence for the general case.
For this particular example, however, we are able to show that Lemke's algorithm computes a solution to an LCP if one exists,and that the iterative process converges globally. |
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Keywords: | Walrasian equilibrium sequence of linear complementarity problems numerical example |
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