Index and Stability in Bimatrix Games: A Geometric-Combinatorial Approach / Edition 1

Index and Stability in Bimatrix Games: A Geometric-Combinatorial Approach / Edition 1

by H. Arndt von Schemde
     
 

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

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Overview

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.

Product Details

ISBN-13:
9783540263661
Publisher:
Springer Berlin Heidelberg
Publication date:
09/21/2005
Series:
Lecture Notes in Economics and Mathematical Systems Series, #560
Edition description:
2005
Pages:
158
Product dimensions:
9.21(w) x 6.14(h) x 0.35(d)

Table of Contents

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.

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