ENGLISH

Index and stability in bimatrix games

By H. Arndt von Schemde

Book information

Publisher
Springer
Year
2005
ISBN
3540263667, 9783540263661, 9783540291022
Open Library ID
OL9055682M
Language
english
Format
DJVU
Filesize
1 MB (1085714 bytes)
Series
Lecture Notes in Economics and Mathematical Systems
Edition
1
Pages
157\157
Library
Kolxo3
DPI
300
Orientation
yes
Scanned
yes
Time added
2010-07-29 05:14:56

Description

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.

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