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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 91: Game theory, economics, social and behavioral sciences

Introduction

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.

Applications and related fields

Combinatorial games (that is, real games for fun), possibly a portion of 90D46.

Subfields

• 91A: Game theory
• 91B: Mathematical economics {For econometrics, see 62P20}
• 91C: Social and behavioral sciences: methodology {For statistics, see 62-XX}
• 91D: Mathematical sociology (including anthropology)
• 91E: Mathematical psychology
• 91F: Other social and behavioral sciences (mathematical treatment)

This area was formed in 2000 from what were parts of 90, 92, and other areas.

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

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

Game theory tutorial [Roger A. McCain]

Rapoport, Anatol: "Directions in mathematical psychology", I-II. Amer. Math. Monthly 83 (1976), no. 2, 85--106 (MR52#12859) and no. 3, 153--172 (MR52#16734)

Estes, W. K.: "Some targets for mathematical psychology", J. Mathematical Psychology 12 (1975), no. 3, 263--282. MR52#16733

Contemporary developments in mathematical psychology. Vol. I: Learning, memory, and thinking. Vol. II: Measurement, psychophysics, and neural information processing. Proceedings of a Symposium, University of Michigan, Ann Arbor, Mich., 1972. Edited by David H. Krantz, Richard C. Atkinson, R. Duncan Luce and Patrick Suppes. W. H. Freeman and Co., San Francisco, Calif., 1974. 299+468 pp. 92A25 MR50#6554-5

MATHSOC: Mathematical Sociology Discussion Group (mailing list)

MPSYCH: Society for Mathematical Psychology (mailing list)

There are USENET newsgroups sci.econ, sci.econ.research (moderated).

Software and tables

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

Other web sites with this focus

Some Game theory pages

David Levine's Economic and Game Theory Page

WebEc - Mathematical and Quantitative Methods in Economics

Options pricing using the Black-Scholes equation.

Society for Mathematical Psychology

Game Theory entries at the Stanford Encyclopedia of Philosophy

Selected topics at this site

• Impacts of nonlinear dynamics in the financial markets.
• [Offsite] What might Mathematical Sociology be?
• Mathematical models of pricing and numerical PDEs
• What is Arrow's Impossibility Theorem (there is no fair voting system)
• Voting and Coalitions via Mathematica code
• Pointer to Game Theory Resources page
• The Golay Code and the game of Mogul
• There is not necessarily an optimal strategy in N-player games for N greater than 2
• Optimal strategies in 2-player non-zero-sum games?
• Hales-Jewett theorem on large multiplayer tic-tac-toe games