Ebook: Introduction to the Theory of Games

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.

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Content:
Front Matter....Pages i-xviii
On equilibrium of systems....Pages 1-17
The n-person game....Pages 18-21
Existence theorems of equilibrium points....Pages 22-40
Special n-person games and methods to solve them....Pages 41-59
The Scarf—Hansen algorithm for approximating and equilibrium point of a finite n-person game....Pages 60-71
The oligopoly game....Pages 72-94
Two-person games....Pages 95-102
Bimatrix games....Pages 103-135
Matrix games....Pages 136-141
Symmetric games....Pages 142-146
Connection between matrix games and linear programming....Pages 147-148
Methods for solving general matrix games....Pages 149-170
Some special games and methods....Pages 171-182
Decomposition of matrix games....Pages 183-188
Examples of matrix games....Pages 189-195
Games played over the unit square....Pages 196-199
Some special classes of games on the unit square....Pages 200-209
Approximate solution of two-person zero-sum games played over the unit square....Pages 210-218
Two-person zero-sum games over metric spaces....Pages 219-223
Sequential games....Pages 224-229
Games against nature....Pages 230-236
Cooperative games in characteristic function form....Pages 237-248
Solution concepts for n-person cooperative games....Pages 249-276
Stability of pay-off configurations....Pages 277-292
A bargaining model of cooperative games....Pages 293-308
The solution concept of Nash for n-person cooperative games....Pages 309-314
Examples of cooperative games....Pages 315-337
Game theoretical treatment of multicriteria decision making problems....Pages 338-352
Games with incomplete information....Pages 353-369
Games with incomplete information....Pages 370-374
Back Matter....Pages 375-392

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Content:
Front Matter....Pages i-xviii
On equilibrium of systems....Pages 1-17
The n-person game....Pages 18-21
Existence theorems of equilibrium points....Pages 22-40
Special n-person games and methods to solve them....Pages 41-59
The Scarf—Hansen algorithm for approximating and equilibrium point of a finite n-person game....Pages 60-71
The oligopoly game....Pages 72-94
Two-person games....Pages 95-102
Bimatrix games....Pages 103-135
Matrix games....Pages 136-141
Symmetric games....Pages 142-146
Connection between matrix games and linear programming....Pages 147-148
Methods for solving general matrix games....Pages 149-170
Some special games and methods....Pages 171-182
Decomposition of matrix games....Pages 183-188
Examples of matrix games....Pages 189-195
Games played over the unit square....Pages 196-199
Some special classes of games on the unit square....Pages 200-209
Approximate solution of two-person zero-sum games played over the unit square....Pages 210-218
Two-person zero-sum games over metric spaces....Pages 219-223
Sequential games....Pages 224-229
Games against nature....Pages 230-236
Cooperative games in characteristic function form....Pages 237-248
Solution concepts for n-person cooperative games....Pages 249-276
Stability of pay-off configurations....Pages 277-292
A bargaining model of cooperative games....Pages 293-308
The solution concept of Nash for n-person cooperative games....Pages 309-314
Examples of cooperative games....Pages 315-337
Game theoretical treatment of multicriteria decision making problems....Pages 338-352
Games with incomplete information....Pages 353-369
Games with incomplete information....Pages 370-374
Back Matter....Pages 375-392
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