In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered. George Dantzig is properly acclaimed as the "father of linear programming." Linear programming is a mathematical technique used to optimize a situation. It can be used to minimize traffic congestion or to maximize the scheduling of airline flights. He formulated its basic theoretical model and discovered its underlying computational algorithm, the "simplex method," in a pathbreaking memorandum published by the United States Air Force in early 1948. Linear Programming and Extensions provides an extraordinary account of the subsequent development of his subject, including research in mathematical theory, computation, economic analysis, and applications to industrial problems. Dantzig first achieved success as a statistics graduate student at the University of California, Berkeley. One day he arrived for a class after it had begun, and assumed the two problems on the board were assigned for homework. When he handed in the solutions, he apologized to his professor, Jerzy Neyman, for their being late but explained that he had found the problems harder than usual. About six weeks later, Neyman excitedly told Dantzig, "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." Dantzig had no idea what he was talking about. He later learned that the "homework" problems had in fact been two famous unsolved problems in statistics.

The influential book that established the mathematical discipline of linear programming In the worlds of finance, business, and management, mathematicians and economists frequently encounter problems of optimization. In this classic book, George Dantzig shows how the methods of linear programming can provide solutions. Drawing on a wealth of examples, he introduces the basic theory of linear inequalities and describes the powerful simplex method used to solve them. He discusses the price concept, the transportation problem, and matrix methods, and covers key mathematical concepts such as the properties of convex sets and linear vector spaces. Dantzig demonstrates how linear programming can be applied to a host of optimization problems, from minimizing traffic congestion to maximizing the scheduling of airline flights. An invaluable resource for students and practitioners alike, Linear Programming and Extensions is an extraordinary account of the development and uses of this versatile mathematical technique, blending foundational research in mathematical theory with computation, economic analysis, and applications to industrial problems.

The authors, two of the most prominent game theorists of this generation, havedevoted a number of years to the development of the theory presented here, and to its economicapplications. They propose rational criteria for selecting one particular uniformly perfectequilibrium point as the solution of any noncooperative game. And, because any cooperative game canbe remodelled as a noncooperative bargaining game, their theory defines a one-point solution for anycooperative game as well.By providing solutions - based on the same principles of rational behavior- for all classes of games, both cooperative and noncooperative, both those with complete and withincomplete information, Harsanyi and Selten's approach achieves a remarkable degree of theoreticalunification for game theory as a whole and provides a deeper insight into the nature ofgame-theoretic rationality.The book applies this theory to a number of specific game classes, suchas unanimity games; bargaining with transaction costs; trade involving one seller and severalbuyers; two-person bargaining with incomplete information on one side, and on both sides. The lastchapter discusses the relationship of the authors' theory to other recently proposed solutionconcepts, particularly the Kohberg-Mertens stability theory.John C. Harsanyi is Flood ResearchProfessor in Business Administration and Professor of Economics, University of California, Berkeley.Reinhard Selten is Professor of Economics Institute of Social and Economic Sciences: University ofBonn, Federal Republic of Germany.