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URN: urn:nbn:de:0030-drops-15265
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1526/
Balthasar, Anne

Equilibrium Tracing in Bimatrix Games

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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:DSP:2008:1526,
  author =	{Anne Balthasar},
  title =	{Equilibrium Tracing in Bimatrix Games},
  booktitle =	{Equilibrium Computation},
  year =	{2008},
  editor =	{P. Jean-Jacques Herings and Marcin Jurdzinski and Peter Bro Miltersen and Eva Tardos and Bernhard von Stengel},
  number =	{07471},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1526},
  annote =	{Keywords: Bimatrix games, Equilibrium computation, Homotopy methods, Index}
}

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

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