Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

博弈论 : 矛盾冲突分析 = Game theory : analysis of conflict

Consider the MIMO interfering broadcast channel whereby multiple base stations in a cellular network simultaneously transmit signals to a group of users in their own cells while causing interference to the users in other cells. The basic problem is to design linear beamformers that can maximize the system throughput. In this paper we propose a linear transceiver design algorithm for weighted sum-rate maximization that is based on iterative minimization of weighted mean squared error (MSE). The proposed algorithm only needs local channel knowledge and converges to a stationary point of the weighted sum-rate maximization problem. Furthermore, we extend the algorithm to a general class of utility functions and establish its convergence. The resulting algorithm can be implemented in a distributed asynchronous manner. The effectiveness of the proposed algorithm is validated by numerical experiments.

An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel

In a multiple-antenna system with two transmitters and two receivers, a scenario of data communication, known as the X channel, is studied in which each receiver receives data from both transmitters. In this scenario, it is assumed that each transmitter is unaware of the other transmitter's data (noncooperative scenario). This system can be considered as a combination of two broadcast channels (from the transmitters' points of view) and two multiple-access channels (from the receivers' points of view). Taking advantage of both perspectives, two signaling schemes for such a scenario are developed. In these schemes, some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple-antenna broadcast subchannels or two noninterfering multiple-antenna multiple-access subchannels. The main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain (MG). It is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable MG. In particular, it is shown that in some specific cases, the achieved MG is the same as the MG of the system if full cooperation is provided either between the transmitters or between the receivers. In the second part of the paper, it is shown that by using mixed design schemes, rather than decomposition schemes, and taking the statistical properties of the interference terms into account, the power offset of the system can be improved. The power offset represents the horizontal shift in the curve of the sum-rate versus the total power in decibels.

Communication Over MIMO X Channels: Interference Alignment, Decomposition, and Performance Analysis

Consider the multiple-input multiple-output (MIMO) interfering broadcast channel whereby multiple base stations in a cellular network simultaneously transmit signals to a group of users in their own cells while causing interference to each other. The basic problem is to design linear beamformers that can maximize the system throughput. In this paper, we propose a linear transceiver design algorithm for weighted sum-rate maximization that is based on iterative minimization of weighted mean-square error (MSE). The proposed algorithm only needs local channel knowledge and converges to a stationary point of the weighted sum-rate maximization problem. Furthermore, the algorithm and its convergence can be extended to a general class of sum-utility maximization problem. The effectiveness of the proposed algorithm is validated by numerical experiments.

An Iteratively Weighted MMSE Approach to Distributed Sum-Utility Maximization for a MIMO Interfering Broadcast Channel

System capacity is considered for a group of interfering users employing single-user detection and multiple transmit and receive antennas for flat Rayleigh-fading channels with independent fading coefficients for each path. The focus is on the case where there is no channel state information at the transmitter, but channel state information is assumed at the receiver. It is shown that the optimum signaling is sometimes different from cases where the users do not interfere with each other. In particular, the optimum signaling will sometimes put all power into a single transmitting antenna, rather than divide power equally between independent streams from the different antennas. If the interference is either sufficiently weak or sufficiently strong, we show that either the optimum interference-free approach, which puts equal power into each antenna, or the approach that puts all power into a single antenna is optimum and we show how to find the regions where each approach is best.

MIMO capacity with interference

The system mutual information of a multiple-input multiple-output (MIMO) system with multiple users which mutually interfere is considered. Perfect channel state information is assumed to be known to both transmitters and receivers. Asymptotic performance analysis shows that the system mutual information changes behavior as the interference becomes sufficiently strong. In particular, beamforming is the optimum signaling for all users when the interference is large. We propose several numerical approaches to decide the covariance matrices of the transmitted signals and compare their performance in terms of the system mutual information. We model the system as a noncooperative game and perform iterative water-filling to find the Nash equilibrium distributively. A centralized global approach and a distributed iterative approach based on the gradient projection method are also proposed. Numerical results show that all proposed approaches give better performance than the standard signaling, which is optimum for the case without interference. Both the global and the iterative gradient projection methods are shown to outperform the Nash equilibrium significantly.

Optimized signaling for MIMO interference systems with feedback

Adaptive modulation has been shown to have significant benefits for high-speed wireless data transmission when orthogonal frequency division multiplexing (OFDM) is employed. However, accurate channel state information (CSI) is required at the transmitter to achieve the benefits. Imperfect CSI arises from noisy channel estimates, which may also be outdated due to a delay in getting the CSI to the transmitter. In this paper, we study adaptive OFDM with imperfect CSI for the uncoded variable bit rate case, where a target bit error rate is set. A loading algorithm based on the statistics of the real channel is proposed. Performance results in terms of the average spectral efficiency are provided for adaptive OFDM systems when there is noisy channel estimation or CSI delay. The use of multiple estimates is then proposed to improve the performance. It is shown that multiple estimates from different frequencies or times can enhance the performance significantly, which enables the system to tolerate larger errors in channel estimation or longer delay in CSI

/pdf/adaptive-ofdm-systems-with-imperfect-channel-state-5gfz249tgl.pdf

Adaptive OFDM Systems With Imperfect Channel State Information

Adaptive modulation has been shown to have significant benefits for high-speed wireless data transmission when orthogonal frequency division multiplexing (OFDM) is employed. However, accurate channel state information (CSI) is required at the transmitter to achieve the benefits. Imperfect CSI arises from noisy channel estimates, which may also be outdated due to a delay in getting the CSI to the transmitter. We study adaptive OFDM with both perfect and imperfect CSI for the variable bit rate case, where a target bit error rate is set. Performance results are provided for adaptive OFDM with imperfect CSI. The use of multiple estimates is shown to mitigate the effect of CSI delay. In addition, the fundamental error mechanisms which result in performance degradation are studied. Robust approaches are then proposed that are less sensitive to CSI errors.

Adaptive modulation for variable-rate OFDM systems with imperfect channel information

Optimum signaling is studied for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with multiple links which mutually interfere. Numerical results show that using the optimum approach for cases without interference does not always achieve system capacity. In some cases, the overall system performance is improved by forcing users to use different subcarriers or to transmit using less antennas or both.

Sigen Ye

Papers

Optimized signaling for MIMO interference systems with feedback

Adaptive OFDM Systems With Imperfect Channel State Information

Adaptive modulation for variable-rate OFDM systems with imperfect channel information

Optimum signaling for MIMO-OFDM systems with interference