Game theory در مخابرات
فهرست مطالب فصل یک کتاب:
1 Game Theory for Spectrum Sharing 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Spectrum Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Current Spectrum Control Policy . . . . . . . . . . . . . . . . . . . . 2
1.2.2 New Spectrum Sharing Approaches . . . . . . . . . . . . . . . . . . . 3
1.3 Game Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 Basic De nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Bounded Rationality and Myopic Best Response Updates . . . . . . . 6
1.4 Game Theoretical Models for Dynamic Spectrum Sharing . . . . . . . . . . . 8
1.4.1 Iterative Water-Filling . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.2 Potential Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.3 Supermodular Game . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.4 Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.5 Auction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4.6 Correlated Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5 Conclusions and Open Problems . . . . . . . . . . . . . . . . . . . . . . . . . 26
مولف ها و چکیده مقاله:
Gesualdo Scutari, Member, IEEE, and Daniel P. Palomar, Senior Member, IEEE
Abstract—
The concept of cognitive radio (CR) has recently received
great attention from the research community as a promising
paradigm to achieve efficient use of the frequency resource by allowing
the coexistence of licensed (primary) and unlicensed (secondary)
users in the same bandwidth. In this paper we propose and
analyze a totally decentralized approach, based on game theory,
to design cognitive MIMO transceivers, who compete with each
other to maximize their information rate. The formulation incorporates
constraints on the transmit power as well as null and/or
soft shaping constraints on the transmit covariance matrix, so that
the interference generated by secondary users be confined within
the temperature-interference limit required by the primary users.
We provide a unified set of conditions that guarantee the uniqueness
and global asymptotic stability of the Nash equilibrium of all
the proposed games through totally distributed and asynchronous
algorithms. Interestingly, the proposed algorithms overcome the
main drawback of classical waterfilling based algorithms—the violation
of the temperature-interference limit—and they have the
desired features required for CR applications, such as low-complexity,
distributed implementation, robustness against missing or
outdated updates of the users, and fast convergence behavior.
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1. Introduction to Game Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 What is Game Theory? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Where Did Game Theory Come From? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Why is Game Theory Relevant toWireless
Communications and Networking?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
1.4 How Can I Use Game Theory Properly? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Introduction to Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5.1 Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
1.5.2 Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
1.5.3 Trust Management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
1.6 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.7 Outline of Remaining Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2. Decision Making and Utility Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
2.1 Preference Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Existence of Ordinal Utility Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Finite X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Countable X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 Uncountable X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.4 Uniqueness of Utility Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Preferences Over Lotteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 The von Neumann–Morgenstern Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.2 Von Neumann–Morgenstern and the
Existence of Cardinal Utility Representations
2.4 Other Visions of Expected Utility Representations
2.5 Conclusion
3. Strategic Form Games
3.1 Definition of a Strategic Form Game
3.2 Dominated Strategies and Iterative Deletion of Dominated Strategies
3.3 Mixed Strategies
CONTENTS vii
3.4 Nash Equilibrium
3.4.1 Dealing with Mixed Strategies
3.4.2 Discussion of Nash Equilibrium
3.5 Existence of Nash Equilibria
3.6 Applications
3.6.1 Pricing of Network Resources
3.6.2 Flow Control
4. Repeated and Markov Games
4.1 Repeated Games
4.1.1 Extensive Form Representation
4.1.2 Equilibria in Repeated Games
4.1.3 Repeated Games in Strategic Form .
4.1.4 Node Cooperation: A Repeated Game Example
4.1.5 The “Folk Theorems”
4.2 Markov Games: Generalizing the Repeated Game Idea
4.3 Applications
4.3.1 Power Control in Cellular Networks
4.3.2 Medium Access Control
5. Convergence to Equilibrium: Potential Games
5.1 The “Best Reply” and “Better Reply” Dynamics
5.2 Potential Games
5.2.1 Definition and Basic Properties
5.2.2 Convergence
5.2.3 Identification
5.2.4 Interpretation
5.3 Application: Interference Avoidance
6. Future Directions
6.1 Related Research onWireless Communications and Networking
6.1.1 The Role of Information on Distributed Decisions
6.1.2 Cognitive Radios and Learning .
6.1.3 Emergent Behavior
6.1.4 Mechanism Design
6.1.5 Modeling of Mobility
6.1.6 Cooperation inWireless Systems and Networks
6.2 Conclusions
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