Cooperative Games

Description

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.

Content

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