Game Theory: Lectures for Economists and Systems ScientistsThe basis for this book is a number of lectures given frequently by the author to third year students of the Department of Economics at Leningrad State University who specialize in economical cybernetics. The main purpose of this book is to provide the student with a relatively simple and easy-to-understand manual containing the basic mathematical machinery utilized in the theory of games. Practical examples (including those from the field of economics) serve mainly as an interpretation of the mathematical foundations of this theory rather than as indications of their actual or potential applicability. The present volume is significantly different from other books on the theory of games. The difference is both in the choice of mathematical problems as well as in the nature of the exposition. The realm of the problems is somewhat limited but the author has tried to achieve the greatest possible systematization in his exposition. Whenever possible the author has attempted to provide a game-theoretical argument with the necessary mathematical rigor and reasonable generality. Formal mathematical prerequisites for this book are quite modest. Only the elementary tools of linear algebra and mathematical analysis are used. |
Other editions - View all
Game Theory: Lectures for Economists and Systems Scientists Nikolai N. Vorob'ev Limited preview - 2012 |
Game Theory: Lectures for Economists and Systems Scientists Nikolai N. Vorob'ev No preview available - 2011 |
Common terms and phrases
0-1 reduced form A₁ admissible situations Analogously arbitrary assume attained bi-matrix game characteristic function choose class of strategic coalition condition conditionally compact Consider constant sum game convex function convex game cooperative games core corresponding defined Definition denoted determined dominated dual linear programming equal equation equilibrium situation EXERCISES FOR SECTION exists Figure finite function H game possesses Hence implies imputations belonging inessential games inf f(x,y k₁ lemma in Section linear programming problems matrix game minimaxes mixed strategies necessary and sufficient noncooperative games nonnegative obtain payoff function payoff matrix player II probability PROOF Prove the second pure optimal strategy pure strategies right-hand side saddle point satisfied set of players Shapley vector situation in mixed situations for player strategic equivalence strategy for player strategy X summands sup ƒ(x,y sup H theorem in Section unit square valid verify vN-M solution