Mathematical Game Theory by Faigle, Ulrich -- Read -- Imperial Library of Trantor

Index

Cover Page Title Page Copyright Page Contents Preface Part 1. Introduction

Chapter 1. Mathematical Models of the Real World

1. Mathematical modelling 2. Mathematical preliminaries 3. Systems 4. Games

Part 2. 2-Person Games

Chapter 2. Combinatorial Games

1. Alternating players 2. Recursiveness 3. Combinatorial games 4. Winning strategies 5. Algebra of games 6. Impartial games

Chapter 3. Zero-Sum Games

1. Matrix games 2. Equilibria 3. Convex zero-sum games 4. Lagrange games

Chapter 4. Investing and Betting

1. Proportional investing 2. Fair odds 3. Betting on alternatives 4. Betting and information 5. Common knowledge

Part 3. n-Person Games

Chapter 5. Potentials, Utilities and Equilibria

1. Potentials and utilities 2. Equilibria

Chapter 6. n-Person Games

1. Dynamics of n-person games 2. Equilibria 3. Randomization of matrix games 4. Traffic flows

Chapter 7. Potentials and Temperature

1. Temperature 2. The Metropolis process 3. Temperature of matrix games

Chapter 8. Cooperative Games

1. Cooperative TU-games 2. Vector spaces of TU-games 3. Examples of TU-games 4. Generalized coalitions and balanced games 5. The core 6. Core relaxations 7. Monge vectors and supermodularity 8. Values 9. Boltzmann values 10. Coalition formation

Chapter 9. Interaction Systems and Quantum Models

1. Algebraic preliminaries 2. Complex matrices 3. Interaction systems 4. Quantum systems 5. Quantum games 6. Final remarks

Appendix

1. Basic facts from real analysis 2. Convexity 3. Polyhedra and linear inequalities 4. Brouwer’s fixed-point theorem 5. The Monge algorithm 6. Entropy and Boltzmann distributions 7. Markov chains

Bibliography Index