بازی‌های شبکه: بازی‌های تشکیل شبکه و بازی‌ها بر روی شبکه‌ها

__Networking Games: Network Forming Games and Games on Networks__ applies game theory methods to network analyses. Its concentration on rigorous mathematical techniques distinguishes it from other books on game theory. Developed by a mathematician and game theorist with extensive contributions to applied mathematics, game and probability theory, and written for graduate students and professionals, the book's illuminations on network games can be applied to problems in economics (in industrial organization, regulation and competition policy, for instance) and operations research. Cover NETWORKING GAMES Network Forming Games and Games on Networks Copyright Preface Introduction 1 Nash Equilibrium 1.1 Nash equilibrium 1.2 Cooperation and competition 1.3 Examples of load balancing games 1.4 Convex games 2 Congestion Games 2.1 Potential games 2.2 Congestion games 2.3 Player-specific congestion games 2.4 Congestion games with strategy set constraint 3 Routing Games 3.1 The KP-model of optimal routing with unsplittable traffic. The price of anarchy 3.2 Pure strategy equilibrium. Braess's paradox 3.3 Completely mixed equilibrium in the problem with inhomogeneous users and homogeneous channels 3.4 The price of anarchy in the model with parallel channels and unsplittable traffic 3.5 The price of anarchy in the model with linear social cost and unsplittable traffic for an arbitrary network 3.6 The mixed price of anarchy in the model with linear social cost and unsplittable traffic for an arbitrary network 3.7 The price of anarchy in the model with maximal social cost and unsplittable traffic for an arbitrary network 3.8 The Wardrop optimal routing model with splittable traffic 3.9 The optimal routing model with parallel channels. The Pigou model. Braess's paradox 3.10 Potential in the model with splittable traffic for an arbitrary network 3.11 Social cost in the model with splittable traffic for convex latency functions 3.12 The price of anarchy in the model with splittable traffic for linear latency functions 3.13 Potential in the Wardrop model with parallel channels for player-specific linear latency functions 3.14 The price of anarchy in an arbitrary network for player-specific linear latency functions 3.15 The Wardrop model with parallel channels and incomplete information 3.16 Equilibria in the model with incomplete information 3.17 Potential and existence of Wardrop equilibrium in the model with incomplete information 4 Load Balancing Game 4.1 A model of the load balancing game 4.2 The price of anarchy in the general case of N processors 4.3 The price of anarchy in the case of three processors 4.4 A numerical method to calculate the price of anarchy 4.5 Computing experiments 5 Cover Game 5.1 A model of the cover game 5.2 The price of anarchy in the general case of N processors 5.3 The price of anarchy in the case of three processors 5.4 A numerical method to calculate the price of anarchy 5.5 Computing experiments 6 Networks and Graphs 6.1 Classical betweenness centrality for the nodes and edges of a graph 6.2 The PageRank method 6.3 Centrality measure for weighted graphs based on Kirchhoff's law 6.4 Centrality measure for weighted graphs as a solution of cooperative game 6.4.1 The Myerson value 6.4.2 Characteristic function 6.4.3 Allocation principle 6.4.4 Generating function for the number of paths 6.4.5 General case 6.4.6 The Myerson value for a linear graph and star 6.4.7 Transportation networks 6.4.8 The Myerson value as centrality measure for weighted networks 7 Social Networks 7.1 Graph construction for social network 7.2 Centrality measures for social networks 7.3 Modeling professional links by coauthored publications 7.4 Community detection in networks 7.5 Hedonic games 7.6 A search algorithm for Nash stable partition 8 Games on Transportation Networks 8.1 Transportation network and correspondence matrix 8.2 Traffic intensity calculation: an example 8.3 A model of public transport system 8.3.1 The system with two carriers 8.3.2 The system with K carriers 8.4 Optimal distribution and the Wardrop equilibrium principle 8.4.1 Cooperative solution 8.4.2 Wardrop equilibrium 8.4.3 The price of anarchy 9 Models of Transportation Market 9.1 Allocation model over a graph 9.2 Pricing game over a graph 9.3 Allocation game over a graph 9.4 Modeling of air transportation market 9.4.1 Modeling of passenger demand 9.4.2 Logit model of passenger traffic distribution 10 Games With Request Flows in Service Systems 10.1 Arrival time choice in a one-server system with sequential requests 10.1.1 Model of the system with two players 10.1.2 Nash equilibrium in the problem with two players 10.1.3 Model of the system with three and more players 10.2 Arrival time choice in a random-access two-server system with arbitrary requests 10.2.1 Two-server system. Noncooperative game 10.2.2 Game with rational random-access scheme 10.2.3 Deterministic number of players in the rational random-access scheme game 10.2.4 Poisson number of players in the rational random-access scheme game 10.2.5 Game with pure random-access scheme 10.2.6 Deterministic number of players in the pure random-access scheme game 10.2.7 Poisson number of players in the pure random-access scheme game 10.2.8 Comparison of random-access schemes in terms of efficiency 11 Cloud Operator Games 11.1 Cloud computing market 11.2 Game-theoretical model 11.3 Two-player game 11.4 Symmetric case for n-player game 11.5 Numerical simulations 11.6 Two-sided telecommunication market 11.7 Generalized Hotelling specification for two operators 11.8 Two operators and company-dependent client preferences 11.9 Two operators and operator-dependent client preferences 11.10 M operators and company-dependent client preferences References Index Back Cover Networking Games: Network Forming Games and Games on Networks applies game theory methods to network analyses. Its concentration on rigorous mathematical techniques distinguishes it from other books on game theory. Developed by a mathematician and game theorist with extensive contributions to applied mathematics, game and probability theory, and written for graduate students and professionals, the book's illuminations on network games can be applied to problems in economics (in industrial organization, regulation and competition policy, for instance) and operations research. Reviews new directions in networking games, including paradoxes and puzzles designed to inspire competing answers and further investigation Addresses the need of theorists and those applying advanced game theory to problems in various disciplines Evaluates a wide spectrum of game-theoretical models, including routing, distribution of information resources, task management in the organization of computing, social networks, competition and cooperation in transport networks, tasks of pricing, and allocation of resources in the transport services market