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

The appendix to the chapter on dynamics supplements the chapter with an overview of dynamic epistemic logic: a branch of logic mainly developed in the decade after the first edition of this handbook was published. Dynamic epistemic logic is an extension of epistemic logic (the logic of knowledge), which focusses on information change, such as communication, usually involving more than one agent. The information of the agents includes information about each other's information, socalled higher-order information. The appendix consists of three parts. In the first part an example scenario is presented which can be captured by dynamic epistemic logic. The second part is a historical overview of the main approaches in dynamic epistemic logic is presented. The last part is a look towards the future which attempts to connect ideas from dynamic approaches to language with dynamic epistemic logic.

Dynamic Epistemic Logic (Update of Chapter 12)

This dissertation presents a logical investigation of epistemic protocols, focussing on protocol-dynamics, epistemic modelling, and epistemic model checking. In Part I, we introduce logics for specifying epistemic protocols including their goals and their dynamics. Chapter 3 departures from the existing discussions about protocols in the field of Dynamic Epistemic Logic by introducing a logic which can specify both the epistemic protocols and their goals within the language. We formalize the verification problem of epistemic protocols under the assumption of meta knowl- edge about the intended goal. The subtlety of this verification problem is discussed in theory and examples. In Chapter 4, we address the question: “How can people get to know a protocol?” For this, we develop logics which are convenient for reasoning about knowledge change and protocol change. With various protocol-changing op- erators we can handle the dynamics of protocols and formalize how actions acquire new meanings as a result of protocol change. We show that all the three logics we introduced can be translated back to Propositional Dynamic Logic (PDL) on standard Kripke models, thus the techniques of modelling and model checking we develop in the other parts of the dissertation can be applied to these logics. In Part II we address the issue of epistemic modelling, in order to study model checking for the logics introduced in Part I. In Chapter 5 we propose new compo- sition operations on static and event models with arbitrary vocabularies, aiming at a compositional method for generating initial epistemic models. We prove decom- position theorems w.r.t. our new operator and demonstrate the use of our methods by various examples. Chapter 6 reports results on counting the number of different models given a finite set of initial assumptions. Restricted to image-finite models, we show that if a modal μ-calculus formula has an infinite model modulo bisimulation thenithas2א0 (cardinalityofthecontinuum)differentmodelsmodulobisimulation. On the other hand, if it does not have any infinite models modulo bisimulation then all its models can be represented in a normal form. Part III introduces abstraction techniques that are particularly useful on making the model checking more efficient. A 3-valued semantics for Public Announcement Logic is defined and studied in Chapter 7 to facilitate abstractions of models. We define a relation with vocabulary and agent mappings between concrete models and their abstractions, thus making it possible to also abstract the signatures of models. We then give a logical characterization of this abstraction relation thus showing it is safe to check properties on the abstract model instead of the original concrete model. Chapter 8 studies the PDL on so-called accelerated Kripke models where the transitions in the models are labelled by regular expressions in order to obtain informative ab- stractions. By making use of a technique of regular expression rewriting, we analyse the complexity of the model checking and satisfiability problems of this logic and give a complete axiomatization. In Part IV (Chapter 9) we survey the epistemic approaches to security protocol verification. We summarize the most important techniques in the Epistemic Tempo- ral Logic and Dynamic Epistemic Logic approaches to security protocol verification, and compare these two approaches in term of convenience. We argue that some se- curity properties can only be faithfully formalized by temporal logic with knowledge operators, but are not expressible by standard temporal logic. However, we need to pay some cost in model checking complexity, in exchange to the expressiveness we gain.

/pdf/epistemic-modelling-and-protocol-dynamics-3eb1r76ajg.pdf

Epistemic modelling and protocol dynamics

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

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

Insertion and deletion are considered to be the basic operations in Biology, more specifically in DNA processing and RNA editing. Based on these evolutionary transformations, a computing model has been formulated in formal language theory known as insertion-deletion systems. Since the biological macromolecules can be viewed as symbols, the gene sequences can be represented as strings. This suggests that the molecular representations can be theoretically analyzed if a biologically inspired computing model recognizes various bio-molecular structures like pseudoknot, hairpin, stem and loop, cloverleaf and dumbbell. In this paper, we introduce a simple grammar system that encompasses many bio-molecular structures including the above mentioned structures. This new grammar system is based on insertion-deletion and matrix grammar systems and is called Matrix insertion-deletion grammars. Finally, we discuss how the ambiguity levels defined for insertion-deletion grammar systems can be realized in bio-molecular structures, thus the ambiguity issues in gene sequences can be studied in terms of grammar systems.

Matrix insertion-deletion systems for bio-molecular structures

Abstract Insertion and deletion are operations that occur commonly in DNA processing and RNA editing. Since biological macromolecules can be viewed as symbols, gene sequences can be represented as strings and structures can be interpreted as languages. This suggests that the bio-molecular structures that occur at different levels can be theoretically studied by formal languages. In the literature, there is no unique grammar formalism that captures various bio-molecular structures. To overcome this deficiency, in this paper, we introduce a simple grammar model called the matrix insertion–deletion system, and using it we model several bio-molecular structures that occur at the intramolecular, intermolecular and RNA secondary levels.

/pdf/modelling-dna-and-rna-secondary-structures-using-matrix-1ytb99hlz7.pdf

Modelling DNA and RNA secondary structures using matrix insertion–deletion systems

Matrix insertion-deletion systems combine the idea of matrix control (a control mechanism well established in regulated rewriting) with that of insertion and deletion (as opposed to replacements). Given a matrix insertion-deletion system, the size of such a system is given by a septuple of integers $$(k;n,i',i'';m,j',j'')$$
 . The first integer k denotes the maximum number of rules in (length of) any matrix. The next three parameters $$n,i',i''$$
 denote the maximal length of the insertion string, the maximal length of the left context, and the maximal length of the right context of insertion rules, respectively. The last three parameters $$m,j',j''$$
 are similarly understood for deletion rules. In this paper, we improve on and complement previous computational completeness results for such systems, showing that matrix insertion-deletion systems of size (1) (3; 1, 0, 1; 1, 0, 1), (3; 1, 0, 1; 1, 1, 0), (3; 1, 1, 1; 1, 0, 0) and (3; 1, 0, 0; 1, 1, 1) (2) (2; 1, 0, 1; 2, 0, 0), (2; 2, 0, 0; 1, 0, 1), (2; 1, 1, 1; 1, 1, 0) and (2; 1, 1, 0; 1, 1, 1), are computationally complete. Further, we also discuss linear and metalinear languages and we show how to simulate grammars characterizing them by matrix insertion-deletion systems of size (3; 1, 1, 0; 1, 0, 0), (3; 1, 0, 1; 1, 0, 0), (2; 2, 1, 0; 1, 0, 0) and (2; 2, 0, 1; 1, 0, 0). We also generate non-semilinear languages using matrices of length three with context-free insertion and deletion rules.

Investigations on the power of matrix insertion-deletion systems with small sizes

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.

Lakshmanan Kuppusamy

Papers

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

Matrix insertion-deletion systems for bio-molecular structures

Modelling DNA and RNA secondary structures using matrix insertion–deletion systems

Investigations on the power of matrix insertion-deletion systems with small sizes

A cooperative game framework for detecting overlapping communities in social networks