Schemde Index and Stability in Bimatrix Games

A Geometric-Combinatorial Approach
2005
ISBN: 978-3-540-29102-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 560, 158 Seiten, eBook

Reihe: Lecture Notes in Economics and Mathematical Systems

The index of an equilibrium in a game gives information about the `stability` of the equilibrium, for example with respect to game dynamics. Unfortunately, index theory is often very technical. This book presents a new geometric construction that visualises the index in an intuitive way. For example, a 3×n game, for any n, can be represented by a figure in the plane, from which one can read off any equilibrium, and its index as a geometric orientation. With this insight, the index can be characterised in strategic terms alone. Moreover, certain `hyperstable` equilibrium components are seen to have nonzero index. The construction gives an elementary proof that two-player games have a Nash equilibrium, and, in an unusual direction, the powerful fixed point theorem of Brouwer.

Zielgruppe

Research

Autoren/Hrsg.

Schemde, H. Arndt von

Inhaltsverzeichnis

Eqilibrium Components with Arbitrary Index.- A Reformulation of the Index for Equilibria in Bimatrix Games.- Sperner’s Lemma and Labelling Theorems.- A Strategic Characterisation of the Index.- Outside Option Equilibrium Components.- Index Zero and Hyperstability.