الصفحة 1
الصفحة 1
Methods in Nonlinear Analysis
Nonlinear analysis has developed rapidly in the last three decades. Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials scattered throughout the literature from the methodology point of view, and presents them in a systematic way. It contains the basic theories and methods with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications.There are five chapters that cover linearization, fixed-point theorems based on compactness and convexity, topological degree theory, minimization and topological variational methods. Each chapter combines abstract, classical and applied analysis. Particular topics included are bifurcation, perturbation, gluing technique, transversality, Nash–Moser technique, Ky Fan's inequality and Nash equilibrium in game theory, setvalued mappings and differential equations with discontinuous nonlinear terms, multiple solutions in partial differential equations, direct method, quasiconvexity and relaxation, Young measure, compensation compactness method and Hardy space, concentration compactness and best constants, Ekeland variational principle, infinite-dimensional Morse theory, minimax method, index theory with group action, and Conley index theory.
Internet and network economics ; 4th International Workshop, WINE 2008, Shanghai, China, December 17-20, 2008. Proceedings
This book constitutes the refereed proceedings of the 4th International Workshop on Internet and Network Economics, WINE 2008, held in Shanghai, China, in December 2008.The 68 revised full papers presented together with 10 invited talks were carefully reviewed and selected from 126 submissions. The papers are organized in topical sections on market equilibrium, congestion games, information markets, nash equilibrium, network games, solution concepts, algorithms and optimization, mechanism design, equilibrium, online advertisement, sponsored search auctions, and voting problems.
Index and Stability in Bimatrix Games : A Geometric-Combinatorial Approach
The contribution of this thesis can be divided into two parts. The first part concerns methods and techniques. By introducing a new geometriccombinatorial construction for bimatrix games, this thesis gives a new, intuitive re-interpretation of the index. This re-interpretation is to a large extent self-contained and does not require a background in algebraic topology. The second part of this thesis concerns the relationship between the index and strategic properties. In this context, the thesis provides two new results, both of which are obtained by means of the new construction and are explained in further detail below. The first result shows that, in non-degenerate bimatrix games, the index can fully be described by a simple strategic property.
Game Theory and Mutual Misunderstanding : Scientific Dialogues in Five Acts
This book consists of five acts and two interludes, which are all written as dialogues between three main characters and other supporting characters. Each act discusses the epistemological, institutional and methodological foundations of game theory and economics, while using various stories and examples. A featured aspect of those discussions is that many forms of mutual misunderstanding are involved in social situations as well as in those fields themselves. One Japanese traditional comic story called the Konnyaku Mondo is representative and gives hints of how our thought is constrained by incorrect beliefs. Each dialogue critically examines extant theories and common misunderstanding in game theory and economics in order to find possible future developments of those fields.
Game Theory : Decisions, Interaction and Evolution
This introduction to game theory is written from a mathematical perspective. Its primary purpose is to be a first course for undergraduate students of mathematics, but it also contains material which will be of interest to advanced students or researchers in biology and economics.An understanding of basic calculus and probability is assumed but no prior knowledge of game theory is required. Detailed solutions are provided for the numerous exercises.
Game Theory : A Multi-Leveled Approach
This book presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book concludes with a problem section. Hints, answers and solutions are included.
CONCUR 2008 - Concurrency Theory ; 19th International Conference, CONCUR 2008, Toronto, Canada, August 19-22, 2008. Proceedings
This book constitutes the refereed proceedings of the 19th International Conference on Concurrency Theory, CONCUR 2008, held in Toronto, Canada, August 19-22, 2008.
Learning Theory ; Vol. 3559 : 18th Annual Conference on Learning Theory, COLT 2005, Bertinoro, Italy, June 27-30, 2005, Proceedings
The technical program contained 45 papers selected from 120 submissions, 3 open problems selected from among 5 contributed, and 2 invited lectures. The invited lectures were given by Sergiu Hart on “Uncoupled Dynamics and Nash Equilibrium”, and by Satinder Singh on “Rethinking State, Action, and Reward in Reinforcement Learning”. These papers were not included in this volume. The Mark Fulk Award is presented annually for the best paper co-authored by a student. The student selected this year was Hadi Salmasian for the paper titled “The Spectral Method for General Mixture Models” co-authored with Ravindran Kannan and Santosh Vempala. The number of papers submitted to COLT this year was exceptionally high. In addition to the classical COLT topics, we found an increase in the number of submissions related to novel classi?cation scenarios such as ranking. This - crease re?ects a healthy shift towards more structured classi?cation problems, which are becoming increasingly relevant to practitioners.
