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CONTRIBUTIONS to GAME THEORY and MANAGEMENT Volume III GRADUATE SCHOOL OF MANAGEMENT FACULTY OF APPLIED MATHEMATICS & CONTROL PROCESSES St. Petersburg University THE INTERNATIONAL SOCIETY OF DYNAMIC GAMES (Russian Chapter) CONTRIBUTIONS TO GAME THEORY AND MANAGEMENT Volume III The Third International Conference Game Theory and Management June 24-26, 2009, St. Petersburg, Russia Collected papers Edited by Leon A. Petrosyan and Nikolay A. Zenkevich Graduate School of Management St. Petersburg University St. Petersburg 2010 518.9, 517.9, 681.3.07 Contributions to game theory and management. Vol. III. Collected papers presented on the Third International Conference Game Theory and Management / Editors Leon A. Petrosyan, Nikolay A. Zenkevich. – SPb.: Graduate School of Man- agement SPbU, 2010. – 488 p. The collection contains papers accepted for the Third International Confer- ence Game Theory and Management (June 24–26, 2009, St. Petersburg University, St. Petersburg, Russia). The presented papers belong to the field of game theory and its applications to management. The volume may be recommended for researches and post-graduate students of management, economic and applied mathematics departments. c Copyright of the authors, 2010 c Graduate School of Management, SPbU, 2010 ISBN 978-5-9924-0052-6 º þº ¿º º ¹ » º ºüº ¸ ºüº ! "#º $ º% þ'( () ÿ¸ ¾¼½¼º $ .// º ' #" ¹ ú1 û ´¾.$¾4 5 ¾¼¼6 ¸ þ'( (¹ ) ¸ ¹ " ' " ¸ ¹ ¸7µº ") ' ¹ ) " º 9: ") ) #'; "¸ " ¹ " (; " " "¸ ): 5<; ¸ = ) º > )) " " "¸ ¾¼½¼ > þ'( () ÿ¸¾¼½¼ Contents Preface ............................................................. 6 A New Prospect of Additivity in Bankruptcy Problems............. 8 Jos´e Alcalde, Mar´ıa del Carmen Marco-Gil, Jos´eA.Silva On the Metric Approach in the Theory of Matrix Games ........... 22 Abdulla A. Azamov Marketing Strategies for Periodic Subscriptions .................... 29 Luigi De Cesare, Andrea Di Liddo A Dynamic Algorithm for Computing Multiweighted Shapley Val- ues of Cooperative TU Games ..................................... 40 Irinel Dragan A Game Theoretic Approach to Co-Insurance Situations ........... 49 Theo S.H. Driessen, Vito Fragnelli, Ilya V. Katsev, Anna B. Khmelnitskaya On the Notion of Dimension and Codimension of Simple Games .... 67 Josep Freixas, Dorota Marciniak Detection of Paradoxes of Power Indices for Simple Games ......... 82 Josep Freixas, Xavier Molinero How Hierarchical Structures Impact on Competition and Taxation . 91 Alexsandr Galegov and Andrey Garnaev One-Way Flow Dynamic Network Formation Games with Coalition- Homogeneous Costs ................................................104 Hong-wei GAO, Ye-ming DAI, Wen-wen LI, Lin SONG, Ting-ting LV Quality Choice under Competition: Game-theoretical Approach ....118 Margarita A. Gladkova and Nikolay A. Zenkevich Quantum Nash-Equilibrium and Linear Representations of Ortho- lattices .............................................................132 Andrei A. Grib, Georgy N. Parfionov Solution for a Class of Stochastic Coalitional Games ................144 Xeniya Grigorieva Construction of Different Types of Dynamics in an Evolutionary Model of Trades in the Stock Market ...............................162 Gubar Elena D.W.K. Yeung’s Condition for the Coalitional Solution of the Game of Pollution Cost Reduction ........................................171 Anna V. Iljina, Nadezhda V. Kozlovskaya 4 Applying a Reputation Metric in a Two-Player Resource Sharing Game ...............................................................182 Andrey S. Lukyanenko, Andrei V. Gurtov, Vladimir V. Mazalov Fuzzy Conflict Games in Economics and Management: single objec- tive fuzzy bi-matrix games ..........................................192 Andr´eA.Keller Graph-Restricted Games with Coalition Structures .................220 Anna B. Khmelnitskaya An Analogue of the π-strategy in Pursuit and Evasion Differential Games with many Pursuers on a Surface ...........................247 Atamurat Sh. Kuchkarov and Gafurjan I. Ibragimov A Game Theoretical Model of Interaction Between Taxpayers and the Tax Authority ..................................................257 Suriya Sh. Kumacheva Non-Constant Discounting in Differential Games with Random Du- ration ..............................................................267 Jes´us Mar´ın-Solano, Ekaterina V. Shevkoplyas Approximation of the Information Set in a Differential Search Game with a Team of Evaders .............................................280 Semyon V. Mestnikov Generalized Kernels and Bargainig Sets for Cooperative Games with Limited Communication Structure ............................289 Natalia Naumova, Irina Korman Optimization and Game Theoretic Modeling of the Real Estate De- velopment .........................................................303 Gennady A. Ougolnitsky Proportionality in NTU Games: on a Consistent Proportional So- lution ...............................................................313 Sergei L. Pechersky Necessary and Sufficient Conditions for Pareto Optimality in Infi- nite Horizon Cooperative Differential Games .......................322 Puduru Viswanadha Reddy, Jacob Engwerda Uncertainty Aversion and Equilibrium in Normal Form Games .....342 J¨orn Rothe Equilibrium Points in Games with Ordered Outcomes ..............368 Victor V. Rozen Homomorphisms and Congruence Relations for Games with Pref- erence Relations ....................................................387 Tatiana F. Savina 5 The Method of Characteristics in Macroeconomic Modeling ........399 Nina N. Subbotina, Timofei B. Tokmantsev Comparison among Some Optimal Policies in Rank-Based Selection Problems ...........................................................409 Krzysztof Szajowski The Nucleolus and the τ-value of Interval Games ...................421 Elena B. Yanovskaya The Detalization of the Irrational Behavior Proof Condition .......431 David W.K. Yeung, Leon Petrosyan, Vladimir Zhuk and Anna V. Iljina Formal Epistemology: A Survey ....................................441 Xiaojian Zhao Cooperative Side Payments Games with Restricted Transferability . 458 Alexandra B. Zinchenko, Lev S. Oganyan, Gennady G. Mermelshtejn Strong Equilibrium in Differential Games ...........................468 Andrey V. Zyatchin Preface This edited volume contains a selection of papers that are an outgrowth of the Third International Conference on Game Theory and Management with a few additional contributed papers. These papers present an outlook of the current de- velopment of the theory of games and its applications to management and various domains, in particular, energy, the environment and economics. The International Conference on Game Theory and Management, a three day conference, was held in St. Petersburg, Russia in June 24-26, 2009. The conference was organized by Graduate School of Management St. Petersburg University in col- laboration with The International Society of Dynamic Games (Russian Chapter) and Faculty of Applied Mathematics and Control Processes SPU within the frame- work of a National Priority Project in Education. More than 100 participants from 22 countries had an opportunity to hear state-of-the-art presentations on a wide range of game-theoretic models, both theory and management applications. Plenary lectures covered different areas of games and management applications. They had been delivered by Professor Reinhard Selten, Bonn University (Germany), Nobel Prize Winner in Economics in 1994; Professor Pierre Bernhard, University of Nice-Sofia Antipolis, INRIA (France); Professor Dmitry Novikov, Institute of Control Sciences, RAS (Russia); Professor Myrna Wooders, Vanderbilt University (USA). The importance of strategic behavior in the human and social world is in- creasingly recognized in theory and practice. As a result, game theory has emerged as a fundamental instrument in pure and applied research. The discipline of game theory studies decision making in an interactive environment. It draws on math- ematics, statistics, operations research, engineering, biology, economics, political science and other subjects. In canonical form, a game obtains when an individual pursues an objective(s) in a situation in which other individuals concurrently pursue other (possibly conflicting, possibly overlapping) objectives and in the same time the objectives cannot be reached by individual actions of one decision maker. The problem is then to determine each individual’s optimal decision, how these decisions interact to produce equilibria, and the properties of such outcomes. The foundations of game theory were laid some sixty years ago by von Neumann and Morgenstern (1944). Theoretical research and applications in games are proceeding apace, in ar- eas ranging from aircraft and missile control to inventory management, market development, natural resources extraction, competition policy, negotiation tech- niques, macroeconomic and environmental planning, capital accumulation and in- vestment. In all these areas, game theory is perhaps the most sophisticated and fertile paradigm applied mathematics can offer to study and analyze decision mak- ing under real world conditions. The papers presented at this Third International Conference on Game Theory and Management certainly reflect both the maturity and the vitality of modern day game theory and management science in general, and of dynamic games, in particular. The maturity can be seen from the sophistication of the theorems, proofs, 7 methods and numerical algorithms contained in
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