Index and Stability in Bimatrix Games

A Geometric-Combinatorial Approach
1. Auflage 2005
ISBN: 978-3-540-29102-2
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 158 Seiten

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.

Autoren/Hrsg.

Inhaltsverzeichnis

1;Preface;6
2;Contents;7
3;Introduction;9
4;Equilibrium Components with Arbitrary Index;14
5;A Reformulation of the Index for Equilibria in Bimatrix Games;38
6;Sperner's Lemma and Labelling Theorems;66
7;A Strategic Characterisation of the Index;92
8;Outside Option Equilibrium Components;107
9;Index Zero and Hyperstability;122
10;References;148
11;Symbolindex;151
12;Index;153