On the Accessibility of Fixed Points

by Lloyd S. Shapley


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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.

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