Polyhedral complementarity problem with quasimonotone decreasing mappings

The fixed point problem of piecewise constant mappings in Rn is investigated. This a polyhedral complementarity problem, which generalization the linear problem. Such arose author?s research on economic equilibrium exchange models, where were considered price simplex. author proposed an original approach complementarity, made it possible to obtain simple algorithms for solving present study methods related problems more general nature and reveals close relationship between complementarity. investigated method analogue well-known Lemke problems. A class described process monotone, as with positive principal minors constraint matrix (class P). It shown that such mapping has always unique point.