Grey Game Theory and Its Applications in Economic Decision-Making

ISBN-13: 9781420087390 / Angielski / Twarda / 2009 / 360 str.

Zhigeng Fang;Yi Lin

Opis

To make the best decisions, you need the best information. However, because most issues in game theory are grey, nearly all recent research has been carried out using a simplified method that considers grey systems as white ones. This often results in a forecasting function that is far from satisfactory when applied to many real situations. Grey Game Theory and Its Applications in Economic Decision Making introduces classic game theory into the realm of grey system theory with limited knowledge. The book resolves three theoretical issues:

• A game equilibrium of grey game
• A reasonable explanation for the equilibrium of a grey matrix of static nonmatrix game issues based on incomplete information
• The Centipede Game paradox, which has puzzled theory circles for a long time and greatly enriched and developed the core methods of subgame Nash perfect equilibrium analysis as a result

The book establishes a grey matrix game model based on pure and mixed strategies. The author proposes the concepts of grey saddle points, grey mixed strategy solutions, and their corresponding structures and also puts forward the models and methods of risk measurement and evaluation of optimal grey strategies. He raises and solves the problems of grey matrix games. The book includes definitions of the test rules of information distortion experienced during calculation, the design of tokens based on new interval grey numbers, and new arithmetic laws to manipulate grey numbers. These features combine to provide a practical and efficient tool for forecasting real-life economic problems."

Many challenges, including limited rationales, future uncertainties, and limited knowledge, exist in game theory. This book shows how grey systems theory can solve these types of problems. It presents the theoretical framework of grey matrices, grey bi-matrices, and grey evolutions to provide an effective tool for solving real-world economic problems. The author incorporates highly efficient solutions and the design of the solutions’ structures with related fundamental research.

Spis treści

Study of the Grey Matrix Game Model Based on Pure Strategy. Pure Strategy Solution of a Grey Matrix Game Based on an Interval Grey Number Not to Be Determined Directly. Grey Matrix Game Model Based on Grey Mixed Strategy. Study of Elementary Transformations of the Grey Matrix and the Invertible Grey Matrix. Matrix Solution Method of a Grey Matrix Game. Potential Optimal Strategy Solution’s Venture and Control Problems Based on the Grey Interval Number Matrix Game. Concession and Damping Equilibriums of Duopolistic Strategic Output-Making Based on Limited Rationality and Knowledge. Nash Equilibrium Analysis Model of Static and Dynamic Games of Grey Pair-Wise Matrices. Chain Structure Model of Evolutionary Games Based on Limited Rationality and Knowledge. Bounded Rationality Grey Game Model of First-Price Sealed-Bid Auction.

O autorze

Zhigeng Fang is professor and doctoral tutor at the College of Economics and management, Nanjing University of Aeronautics and Astronautics (NUAA), China. From 1996 to 1999, he studied at Xi’an University of Technology, earning a master’s degree in management science and engineering management. From 2003 to 2007, he attended NUAA, earning a doctoral degree in systems engineering. His academic part-time positions include under-secretary-general of IEEE International Professional Committee of Grey Systems; governor of the Chinese Society for Optimization, Overall Planning and Economic Mathematics; managing director of Complex Systems Research Committee; secretary-general of Grey Systems Society of China; under-secretary-general of the Systems Engineering Society of Jiangsu Province, China; deputy director of the Post-Evaluation Research Center of Jiangsu Province; deputy director of the Grey Systems Research Institute of NUAA. He is a member of Services Science Global and the Services and Logistics Technical Committee of IEEE Intelligent Transportation Systems Society. His main research directions lie in the fields of theory and methods of uncertain prediction and decision, Grey game theory, applied economic, and energy economics.