Introduction to the Theory of Games

1. Front Matter

   Pages i-xviii

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2. On equilibrium of systems

   • J. Szép, F. Forgó

   Pages 1-17

3. The n-person game

   • J. Szép, F. Forgó

   Pages 18-21

4. Existence theorems of equilibrium points

   • J. Szép, F. Forgó

   Pages 22-40

5. Special n-person games and methods to solve them

   • J. Szép, F. Forgó

   Pages 41-59

6. The Scarf—Hansen algorithm for approximating and equilibrium point of a finite n-person game

   • J. Szép, F. Forgó

   Pages 60-71

7. The oligopoly game

   • J. Szép, F. Forgó

   Pages 72-94

8. Two-person games

   • J. Szép, F. Forgó

   Pages 95-102

9. Bimatrix games

   • J. Szép, F. Forgó

   Pages 103-135

10. Matrix games

    • J. Szép, F. Forgó

    Pages 136-141

11. Symmetric games

    • J. Szép, F. Forgó

    Pages 142-146

12. Connection between matrix games and linear programming

    • J. Szép, F. Forgó

    Pages 147-148

13. Methods for solving general matrix games

    • J. Szép, F. Forgó

    Pages 149-170

14. Some special games and methods

    • J. Szép, F. Forgó

    Pages 171-182

15. Decomposition of matrix games

    • J. Szép, F. Forgó

    Pages 183-188

16. Examples of matrix games

    • J. Szép, F. Forgó

    Pages 189-195

17. Games played over the unit square

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    Pages 196-199

18. Some special classes of games on the unit square

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    Pages 200-209

19. Approximate solution of two-person zero-sum games played over the unit square

    • J. Szép, F. Forgó

    Pages 210-218

20. Two-person zero-sum games over metric spaces

    • J. Szép, F. Forgó

    Pages 219-223

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Min­ kowsky lemma, coding theory and the structure of water meet one another in packing and covering theory: quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

• bargaining
• cooperative games
• decision making
• differential equation
• equilibrium
• linear optimization
• minimum
• optimization
• sets

• Institute of Mathematics and Computer Science, Karl Marx University of Economics, Budapest, Hungary

  J. Szép, F. Forgó

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