Computation of economic equilibria by a sequence of linear complementarity problems.

*(English)*Zbl 0579.90093Summary: This paper reviews computational experience with a modeling format and solution algorithm for partial and general economic equilibrium problems. This approach handles cases characterized by weak inequalities, complementary slackness, and ’nonintegrability’.

The equilibrium is computed by solving a sequence of linear complementarity problems (LCP). Each LCP is obtained by taking a first order Taylor series expansion of the nonlinear equilibrium model, and the LCP is solved by Lemke’s almost complementary pivoting algorithm.

Theoretical results for the convergence of the iterative algorithm are at present available only for the partial equilibrium models. Income effects in the general equilibrium case seem to inhibit similar conclusions. Computational experience with both types of models, however, indicates that the algorithm is both robust and efficient.

The equilibrium is computed by solving a sequence of linear complementarity problems (LCP). Each LCP is obtained by taking a first order Taylor series expansion of the nonlinear equilibrium model, and the LCP is solved by Lemke’s almost complementary pivoting algorithm.

Theoretical results for the convergence of the iterative algorithm are at present available only for the partial equilibrium models. Income effects in the general equilibrium case seem to inhibit similar conclusions. Computational experience with both types of models, however, indicates that the algorithm is both robust and efficient.

##### MSC:

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

65K05 | Numerical mathematical programming methods |

91B50 | General equilibrium theory |

90C90 | Applications of mathematical programming |