We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

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

Learning graph representations is a fundamental task aimed at capturing various properties of graphs in vector space. The most recent methods learn such representations for static networks. However, real-world networks evolve over time and have varying dynamics. Capturing such evolution is key to predicting the properties of unseen networks. To understand how the network dynamics affect the prediction performance, we propose an embedding approach which learns the structure of evolution in dynamic graphs and can predict unseen links with higher precision. Our model, dyngraph2vec, learns the temporal transitions in the network using a deep architecture composed of dense and recurrent layers. We motivate the need for capturing dynamics for the prediction on a toy dataset created using stochastic block models. We then demonstrate the efficacy of dyngraph2vec over existing state-of-the-art methods on two real-world datasets. We observe that learning dynamics can improve the quality of embedding and yield better performance in link prediction.

dyngraph2vec: Capturing Network Dynamics using Dynamic Graph Representation Learning

Besides the topological structure, there are additional information, i.e., node attributes, on top of the plain graphs. Usually, these systems can be well modeled by attributed graphs, where nodes represent component actors, a set of attributes describe users’ portraits and edges indicate their connections. An elusive question associated with attributed graphs is to study how clusters with common internal properties form and evolve in real-world networked systems with great individual diversity, which leads to the so-called problem of attributed graph clustering (AGC). In this paper, we comprehended AGC naturally as a dynamic cluster formation game (DCFG), where each node’s feasible action set can be constrained by every cluster in a discrete-time dynamical system. Specifically, we carried out a deep research on a special case of finite dynamic games, named dynamic social game (DSG), the convergence of the finite Nash equilibrium sequence in a DSG was also proved strictly. By carefully defining the feasible action set and the utility function associated with each node, the proposed DCFG can be well related to a DSG; and we showed that a balanced solution of AGC could be found by solving a finite set of coupled static Nash equilibrium problems in the related DCFG. We, finally, proposed a self-learning algorithm, which can start from any arbitrary initial cluster configuration, and, finally, find the corresponding balanced solution of AGC, where all nodes and clusters are satisfied with the final cluster configuration. Extensive experiments were applied on real-world social networks to demonstrate both effectiveness and scalability of the proposed approach by comparing with the state-of-the-art graph clustering methods in the literature.

Dynamic Cluster Formation Game for Attributed Graph Clustering

In the online social network, the spreading process of rumor contains complex dynamics. The traditional research of the rumor propagation mainly studies the spreading process of rumor from the perspectives of rumor and participating user. The symbiosis and confrontation of rumor and anti-rumor information and the dynamic changes of the influence of anti-rumor information are not emphasized. At the same time, people’s profitability and herd psychology are also ignored. In view of the above problems, we fully consider the anti-rumor information and user’s psychological factors, construct a rumor propagation dynamics model based on evolutionary game and anti-rumor information, and provide a theoretical basis for studying the inherent laws in the spreading process of rumor. First of all, we analyze the interaction pattern and characteristic of rumor in social network. In allusion to the symbiosis of rumor and anti-rumor information and the dynamic changes of the influence of anti-rumor information, we constructed the SKIR rumor propagation model based on the SIR model. Secondly, due to rivalry between rumor and anti-rumor information, as well as the user’s profitability and herd psychology, we use evolutionary game theory to construct the driving force mechanism of information and explore the causes of user behavior in the spreading process of rumor. At the same time, we combine the behavior factors and external factors of the user to build the influence of information by multivariate linear regression method, which provides the theoretical basis for the driving force of information. Finally, combining the SKIR model proposed in this paper, we get a rumor propagation dynamics model based on evolutionary game and anti-rumor information. We have proved by experiments that the model can effectively describe the propagating situation of rumor and the dynamic change rule of the influence of anti-rumor information. On the other hand, it can also reflect the influence of people’s psychology on rumor propagation.

Rumor propagation dynamic model based on evolutionary game and anti-rumor

Community detection in social networks has received much attention from the researchers of multiple disciplines due to its impactful applications such as recommendation systems, link prediction, and anomaly detection. The focus of community detection is to determine the more dense subgraphs of the network which are called communities. The nodes of the community are expected to have similar features and interests. Assuming the nodes as selfish agents, the evolution of communities can be effectively modelled as a community formation game. Game theory provides a systematic framework to model the competition and coordination among the players. In the past decade, there are several contributions from the domain of game theory to address the problem of community detection in social networks. In this paper, we make a comprehensive survey that studies and provides an insight into available game theory-based community detection algorithms. The current study provides the taxonomy of game models and their characteristics along with their performance. We discuss the interesting applications of game theory for social networks and also provide further research directions as well as some open challenges.

A survey on game theoretic models for community detection in social networks

Recommendation Systems are an important tool for aiding discovery of content such as movies, books, and music. Generating personalised recommendations that deliver serendipitous suggestions to the user is a key factor in determining user satisfaction. In this paper, we propose a recommendation algorithm that uses a community-structure based link prediction approach. The proposed link prediction algorithm predicts the links that are most likely to be formed in the network based on two new proposed metrics. These metrics take into account the effects of both the network structure and the attribute information of the items for predicting probable links. The links predicted can be presented as recommendations to the user. An item network consisting of item associations derived from the attribute information usually displays a community structure with items of similar nature being clustered together. Our approach utilises this community structure to expose implicit links in the item network and provides non-obvious recommendations to the user.

A link prediction based approach for recommendation systems

Community detection in social networks is a challenging and complex task, which received much attention from researchers of multiple domains in recent years. The evolution of communities in social networks happens merely due to the self-interest of the nodes. The interesting feature of community structure in social networks is the multi membership of the nodes resulting in overlapping communities. Assuming the nodes of the social network as self-interested players, the dynamics of community formation can be captured in the form of a game. In this paper, we propose a greedy algorithm, namely, Weighted Graph Community Game (WGCG), in order to model the interactions among the self-interested nodes of the social network. The proposed algorithm employs the Shapley value mechanism to discover the inherent communities of the underlying social network. The experimental evaluation on the real-world and synthetic benchmark networks demonstrates that the performance of the proposed algorithm is superior to the state-of-the-art overlapping community detection algorithms.

A cooperative game framework for detecting overlapping communities in social networks

Community detection is a significant research problem in various fields such as computer science, sociology and biology. The singular characteristic of communities in social networks is the multimembership of a node resulting in overlapping communities. But dealing with the problem of overlapping community detection is computationally expensive. The evolution of communities in social networks happens due to the self-interest of the nodes. The nodes of the social network acts as self-interested players, who wish to maximize their benefit through interactions in due course of community formation. Game theory provides a systematic framework tox capture the interactions between these selfish players in the form of games. In this paper, we propose a Community Detection Game (CDG) that works under the cooperative game framework. We develop a greedy community detection algorithm that employs Shapley value mechanism and majority voting mechanism in order to disclose the underlying community structure of the given network. Extensive experimental evaluation on synthetic and real-world network datasets demonstrates the effectiveness of CDG algorithm over the state-of-the-art algorithms.

Annapurna Jonnalagadda

Papers

A survey on game theoretic models for community detection in social networks

A link prediction based approach for recommendation systems

A cooperative game framework for detecting overlapping communities in social networks

Overlapping community detection in social networks using coalitional games

Toward Sarcasm Detection in Reviews—A Dual Parametric Approach with Emojis and Ratings