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TRANSFORMING GAMES FROM CHARACTERISTIC INTO NORMAL FORM

GIANFRANCO GAMBARELLI

Department of Mathematics, Statistics, Computer Science and Applications, University of Bergamo via dei Caniana 2, 24127 Bergamo, Italy

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https://doi.org/10.1142/S0219198907001291Cited by:3 (Source: Crossref)

Abstract

A technique is proposed to represent games in characteristic function form as games in normal form, enabling the former to exploit the concepts of solution of the latter. A new solution for games in characteristic function form is then introduced and some properties are found. A generalization of a result of von Neumann and Morgenstern is thus obtained.

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References

R. J. Aumann, Essays in Mathematical Economics, ed. M. Shubik (Princeton University Press, Princeton, NJ, 1967) pp. 3–27. Google Scholar
E. Bennett, Games and Economic Behavior 19, 151 (1997), DOI: 10.1006/game.1997.0547. Web of Science, Google Scholar
P. E. M. Borm and S. H. Tijs, Games and Economic Behavior 4(1), 58 (1992), DOI: 10.1016/0899-8256(92)90005-D. Web of Science, Google Scholar
G. Gambarelli, International Journal of Game Theory 12(4), 237 (1983), DOI: 10.1007/BF01769093. Google Scholar
G. Gambarelli, Control and Cybernetics 24(3), 243 (1995). Web of Science, Google Scholar
G. Gambarelli and G. Owen, Essays on Cooperative Games — in honor of Guillermo Owen, Special Issue Theory and Decision 36, ed. G. Gambarelli (Kluwer Academic Publishers, Dordrecht, 2004) pp. 1–18. Google Scholar
Gillies, D. [1953] Some theorems on n-person games, Ph.D. Thesis, Dept. of Math., Princeton University Press, Princeton, NJ . Google Scholar
A. J. Goldman, American Mathematical Monthly 64, 729 (1957), DOI: 10.2307/2309755. Google Scholar
M. Maschler, Essays on Cooperative Games — in honor of Guillermo Owen, Special Issue of Theory and Decision 36, ed. G. Gambarelli (Kluwer Academic Publishers, Dordrecht, 2004) pp. 25–34. Google Scholar
S. Mishra and T. K. Kumar, Game Theoretical Applications to Economics and Operations Research, eds. T. Parthasarathyet al. (Kluwer Academic Publishers, Amsterdam, 1997) pp. 25–31. Google Scholar
J. F. Nash, Econometrica 18, 155 (1950), DOI: 10.2307/1907266. Web of Science, Google Scholar
V. P. Papavassilopulos, Journal of Optimization Theory 19, 419 (1995). Web of Science, Google Scholar
M. Shubik , Game Theory in the Social Sciences ( MIT Press , Cambridge , 1982 ) . Google Scholar
J. von Neumann and O. Morgenstern , Theory of Games and Economic Behavior , 3rd edn. ( Princeton University Press , Princeton, NJ , 1944 ) . Google Scholar