Path-following algorithms have proved practical for the solution of fixed-point problems arising in economics and game theory. But the value of the methodology is diminished by the possibility of multiple solutions, since there is no guarantee of finding more than one solution even if many paths are traced. This Note describes a way of transforming problems so that the paths are modified while the solutions remain unchanged. As a result, previously inaccessible solutions may become accessible. It is shown that for any piecewise-linear problem in general position there is a solution-preserving transformation that makes all solutions simultaneously accessible.
This report is part of the RAND Corporation Note series. The note was a product of the RAND Corporation from 1979 to 1993 that reported other outputs of sponsored research for general distribution.
This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.