An algorithm based on a sequence of linear complementarity problems applied to a Walrasian equilibrium model: An example.

*(English)*Zbl 0613.90098The 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.

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.

##### MSC:

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |

90C90 | Applications of mathematical programming |

91B50 | General equilibrium theory |

65K05 | Numerical mathematical programming methods |

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