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# 90: Economics, operations research, programming, games

## Introduction

Operations research may be figuratively described as the study of optimal resource allocation. Depending on the options and constraints in the setting, this may involve linear programming, or quadratic-, convex-, integer-, or boolean-programming. This category also includes game theory, which is actually not about games at all but rather about optimization; which combination of strategies leads to an optimal outcome. This area also includes mathematical economics.

## History

For the history of Game Theory try this web site.

Some links to the history of Operations Research can be found at the Military Operations Research Society and on J. E. Beasley's home page.

## Applications and related fields

For numerical optimization techniques (conjugate gradient, simulated annealing, etc.) see 65, Numerical Analysis.

Discrete optimization problems (traveling salesman, etc.) are principally treated in Combinatorics.

The word "programming" in this context is essentially unrelated to computer programming; for that topic see Computer Science

Finance is more properly treated in Behavioural Sciences perhaps, but we have a few comments here.

## Subfields

• 90A: Mathematical economics, For econometrics, see 62P20
• 90B: Operations research and management science (for discrete assignment problems see also 05-XX.)
• 90D: Game theory

This is among the larger of the areas of the Math Reviews database. 90C (Mathematical programming) is one of the largest 3-digit areas (and 90C30 (nonlinear programming) is one of the largest 5-digit areas!), but the other three subfields are also fairly large.

Starting in the year 2000 sections A and D will be removed from this heading; a new primary classification Game theory, economics, social and behavioral sciences will be added which will include most of what has been in those sections.

Browse all (old) classifications for this area at the AMS.

## Textbooks, reference works, and tutorials

Eichhorn, Wolfgang: "What is an economic index? An attempt of an answer", Theory and applications of economic indices (Proc. Internat. Sympos., Univ. Karlsruhe, Karlsruhe, 1976), pp. 3--42. Physica-Verlag, Würzburg, 1978. MR58#4228

Some references for management and operations research:

• Bodin, Lawrence; Golden, Bruce; Assad, Arjang; Ball, Michael: "Routing and scheduling of vehicles and crews. The state of the art", Comput. Oper. Res. 10 (1983), no. 2, 63--211. MR85g:90062
• Grosh, Doris Lloyd: "A primer of reliability theory", John Wiley & Sons, Inc., New York, 1989. 373 pp. ISBN 0-471-63820-X MR91d:90048
• Alj, A.; Faure, R.: "Guide de la recherche opérationnelle" (French: Guide to operations research) in two volumes. Vol. I.: "Les fondements (Foundations)"; Masson, Paris, 1986. 265 pp. ISBN 2-903607-55-9 MR91g:90060. Vol. 2: "Les applications (Applications)"; Masson, Paris, 1990. 434 pp. ISBN 2-903607-61-3 MR91g:90061.

Some references for mathematical programming and optimization:

• "State of the art in global optimization", Computational methods and applications (Conf. Princeton University, Princeton, New Jersey, April 1995) Edited by C. A. Floudas and P. M. Pardalos. Nonconvex Optimization and its Applications, 7. Kluwer Academic Publishers, Dordrecht, 1996. 651 pp. ISBN 0-7923-3838-3 MR97a:90004 (For previous years' conference see MR96f:90013, MR96f:90005)
• "Mathematical programming: the state of the art", (Proc. 11th Intern. Symp. Mathematical Programming, University of Bonn, Bonn, August, 1982), Edited by Achim Bachem, Martin Grötschel and Bernhard Korte. Springer-Verlag, Berlin-New York, 1983. 655 pp. ISBN 3-540-12082-3 MR84j:90004
• V. Chvátal: "Linear Programming", W.H. Freeman 1983, ISBN 0-7167-1195-8.
• Gomory, R. E.: "Mathematical programming", Amer. Math. Monthly 72 1965 no. 2, part II 99--110. MR30#4595
• Geoffrion, Arthur M.: "A guided tour of recent practical advances in integer linear programming", ACM SIGMAP Newslett. No. 17 (1974), 22--32. MR54#14776
• Paris, Quirino: "A primer on Karmarkar's algorithm for linear programming", Stud. Develop. 12 (1985), no. 1-2, 131--155. MR87i:90148

References to game theory:

• Aumann, Robert J.: "What is game theory trying to accomplish?" Frontiers of economics (Sannäs, 1983), 28--99, Blackwell, Oxford, 1985. CMP906458
• Guy, Richard K.: "What is a game?" Games of no chance (Berkeley, CA, 1994), 43--60, Math. Sci. Res. Inst. Publ., 29; Cambridge Univ. Press, Cambridge, 1996. MR98a:90167. An earlier, similar paper appeared in Combinatorial games (Columbus, OH, 1990), 1--21, Proc. Sympos. Appl. Math., 43, Amer. Math. Soc., Providence, RI, 1991. CMP1095537
• Williams, J. D.: "The compleat strategyst, being a primer on the theory of games of strategy." McGraw-Hill Book Co., Inc., New York-Toronto-London, 1954. 234 pp. MR15,812e

Linear programming FAQ: World Wide Web version or Plain-text version

Nonlinear programming FAQ: World Wide Web version or Plain-text version

Newsgroups sci.op-research, sci.econ, sci.econ.research (moderated).

Game theory tutorial [Roger A. McCain]

Options pricing using the Black-Scholes equation.

## Software and tables

Some Game theory pages

Gambit is a library of programs, written in C++, for performing various operations on n-person games, in either extensive or normal form. These programs can either be used by a C++ programmer as a basis for developing specialized code, or they can be accessed through more user friendly interfaces. There are two main programs for accessing the functionality of the Gambit library, the Graphics User Interface (GUI) and the Gambit Command Language (GCL).

A sample game matrix solver

Numerical optimization software is discussed as part of 65K: Mathematical programming, optimization and variational techniques.