License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07471.2
URN: urn:nbn:de:0030-drops-15265
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1526/
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Balthasar, Anne

Equilibrium Tracing in Bimatrix Games

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07471.BalthasarAnne.Paper.1526.pdf (0.2 MB)

Abstract

We analyze the relations of the van den Elzen-Talman algorithm, the Lemke-Howson algorithm and the global Newton method introduced by Govindan and Wilson. It is known that the global Newton method encompasses the Lemke-Howson algorithm; we prove that it also comprises the van den Elzen-Talman algorithm, and more generally, the linear tracing procedure, as a special case. This will lead us to a discussion of traceability of equilibria of index +1. We answer negatively the open question of whether, generically, the van den Elzen-Talman algorithm is flexible enough to trace all equilibria of index +1.

BibTeX - Entry

@InProceedings{balthasar:DagSemProc.07471.2,
  author =	{Balthasar, Anne},
  title =	{{Equilibrium Tracing in Bimatrix Games}},
  booktitle =	{Equilibrium Computation},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7471},
  editor =	{P. Jean-Jacques Herings and Marcin Jurdzinski and Peter Bro Miltersen and Eva Tardos and Bernhard von Stengel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2008/1526},
  URN =		{urn:nbn:de:0030-drops-15265},
  doi =		{10.4230/DagSemProc.07471.2},
  annote =	{Keywords: Bimatrix games, Equilibrium computation, Homotopy methods, Index}
}

Keywords: Bimatrix games, Equilibrium computation, Homotopy methods, Index
Collection: 07471 - Equilibrium Computation
Issue Date: 2008
Date of publication: 04.06.2008

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