Game Theory for Wireless Engineers

by MacKenzie, Allen B.; DaSilva, Luiz A.

• ISBN13: 9781598290165
• ISBN10: 1598290169
• Format: Paperback
• Copyright: 2006-02-28
• Publisher: Morgan & Claypool

Summary

Game theory is a field of applied mathematics that describes and analyzes interactive decision situations. It consists of a set of analytical tools that predict the outcome of complex interactions among rational entities, where rationality demands a strict adherence to a strategy based on perceived or measured results.This lecture introduces wireless engineers to game theory. In recent years there has been a great deal of interest in applying game theory to problems in wireless communications and networking. Authors Allen Mackenzie and Luiz DaSilva provide students, researchers, and practitioners the tools they need to understand and participate in this work, provide guidance on the proper and improper uses of game theory, and examine future directions and applications of game theory. No familiarity with game theory is necessary; the authors introduce major game theoretic models and results and apply them to networking problems including medium access, routing, energy-efficient protocols, and others.Key Features:* A discussion of normal-form, repeated, and Markov games with examples selected from the literature* A description of the ways in which learning can be modeledin game theory, with direct applications to the emerging field of cognitive radio* A summary of the challenges and limitations in the application of game theory to the analysis of wireless systems

Table of Contents

Introduction to Game Theory	1	(12)
What is Game Theory?	1	(2)
Where Did Game Theory Come From?	3	(1)
Why is Game Theory Relevant to Wireless Communications and Networking?	4	(1)
How Can I Use Game Theory Properly?	5	(2)
Introduction to Examples	7	(3)
Power Control	7	(1)
Routing	8	(1)
Trust Management	9	(1)
Notation	10	(1)
Outline of Remaining Chapters	10	(3)
Decision Making and Utility Theory	13	(16)
Preference Relationships	13	(1)
Existence of Ordinal Utility Representations	14	(5)
Finite X	15	(1)
Countable X	16	(1)
Uncountable X	16	(2)
Uniqueness of Utility Functions	18	(1)
Preferences Over Lotteries	19	(6)
The von Neumann--Morgenstern Axioms	20	(2)
Von Neumann-Morgenstern and the Existence of Cardinal Utility Representations	22	(3)
Other Visions of Expected Utility Representations	25	(2)
Conclusions	27	(2)
Strategic Form Games	29	(14)
Definition of a Strategic Form Game	29	(2)
Dominated Strategies and Iterative Deletion of Dominated Strategies	31	(1)
Mixed Strategies	32	(1)
Nash Equilibrium	33	(2)
Dealing with Mixed Strategies	34	(1)
Discussion of Nash Equilibrium	35	(1)
Existence of Nash Equilibria	35	(4)
Applications	39	(4)
Pricing of Network Resources	39	(2)
Flow Control	41	(2)
Repeated and Markov Games	43	(14)
Repeated Games	43	(9)
Extensive Form Representation	44	(1)
Equilibria in Repeated Games	45	(1)
Repeated Games in Strategic Form	46	(1)
Node Cooperation: A Repeated Game Example	47	(3)
The ``Folk Theorems''	50	(2)
Markov Games: Generalizing the Repeated Game Idea	52	(1)
Applications	53	(4)
Power Control in Cellular Networks	53	(1)
Medium Access Control	54	(3)
Convergence to Equilibrium: Potential Games	57	(8)
The ``Best Reply'' and ``Better Reply'' Dynamics	57	(3)
Potential Games	60	(4)
Definition and Basic Properties	60	(1)
Convergence	61	(1)
Identification	62	(1)
Interpretation	63	(1)
Application: Interference Avoidance	64	(1)
Future Directions	65	(4)
Related Research on Wireless Communications and Networking	65	(4)
The Role of Information on Distributed Decisions	65	(2)
Cognitive Radios and Learning	67	(1)
Emergent Behavior	67	(1)
Mechanism Design	68	(1)
Modeling of Mobility	68	(1)
Cooperation in Wireless Systems and Networks	68	(1)
Conclusions	69