A Note on the Lemke-Howson Algorithm

by Lloyd S. Shapley

Download

Full Document

FormatFile SizeNotes
PDF file 0.7 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.

Purchase

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback33 pages $15.00 $12.00 20% Web Discount

The Lemke-Howson algorithm for bimatrix games provides both an elementary proof of the existence of equilibrium points and an efficient computational method for finding at least one equilibrium point. The first half of this report presents a geometrical view of the algorithm that makes its operation especially easy to visualize. Several illustrations are given, including Wilson's example of "inaccessible" equilibrium points. The second half presents an orientation theory for the equilibrium points of (nondegenerate) bimatrix games and the Lemke-Howson paths that interconnect them; in particular, it is shown that there is always one more "negative" than "positive" equilibrium point.

This report is part of the RAND Corporation Report series. The report was a product of the RAND Corporation from 1948 to 1993 that represented the principal publication documenting and transmitting RAND's major research findings and final research.

Permission is given to duplicate this electronic document for personal use only, as long as it is unaltered and complete. Copies may not be duplicated for commercial purposes. Unauthorized posting of RAND PDFs to a non-RAND Web site is prohibited. RAND PDFs are protected under copyright law. For information on reprint and linking permissions, please visit the RAND Permissions page.

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.