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Cooperative Games

An Introduction to Game Theory – Part II

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Language:  English
Part II of An Introduction to Game Theory gives a thorough presentation of the cooperative theory and can be read before Part I. Knowledge of mathematics corresponding to one semester of university.
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Part II of An Introduction to Game Theory gives a thorough presentation of cooperative game theory at a level suitable for undergraduate students. The focus is on coalitional games with transferable utility with the core, the nucleolus and the Shapley value as the most important concepts studied. A brief chapter on games without transferable utility exemplified with exchange economies is also included. Precise definitions and full proofs of all results are given. The book contains plenty of exercises. Knowledge of Mathematics corresponding to one semester of university studies is required.

About the author

Lars-Åke Lindahl obtained his mathematical education at Uppsala University and Institut Mittag-Leffler and got a Ph.D. in Mathematics in 1971 with a thesis on Harmonic Analysis. Shortly thereafter he was employed as senior lecturer in Mathematics at Uppsala University, where he remained until his retirement in 2010 and for more than 20 years served as chairman of the Math. Department.

He has given lectures in a variety of mathematical subjects such as Calculus, Linear Algebra, Fourier Analysis, Complex Analysis, Convex Optimization, Game Theory and Probability Theory, and he has also written several textbooks and compendia. After his retirement, he has been a consultant to Al Baha University, Saudi Arabia, with a mission to assist in the development of their master's program in Mathematics.

  1. Preface 
  2. Coalitional Games 
    1. Definition
    2. Imputations 
    3. Examples 
    4. The core 
    5. Games with nonempty core 
    6. The nucleolus 
  3. The Shapley Value 
    1. The Shapley solution 
    2. Alternative characterization of the Shapley value 
    3. The Shapley-Shubik power index 
  4. Coalitional Games without Transferable Utility 
    1. Coalitional games without transferable utility 
    2. Exchange economies 
    3. The Nash bargaining solution 
  5. Appendix 1: Convexity 
  6. Appendix 2: Kakutani’s fixed point theorem 
  7. Brief historical notes 
  8. Answers and hints for the exercises
  9. Index

Lars-Åke Lindahl