×

Invariant games. (Juegos invariantes.) (Spanish. English summary) Zbl 0661.90103

Summary: Some games which have symmetry properties with respect to groups of transformations are studied. Under general conditions we reduce the study of an invariant game to the study of a restricted game. As an application we show that the game has a value if the group is transitive. Harmonic analysis allows us to characterize every optimal strategy for the convolution game.

MSC:

91A05 2-person games
91A07 Games with infinitely many players
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] DUNFORD, N., y J. T. SCHWARTZ (1958):Linear Operators vol. I, I Interscience.
[2] KARLIN, S. (1953): “The Theory of Infinite Games{”,Ann. Math., 58, 371–401.} · Zbl 0051.10703 · doi:10.2307/1969794
[3] KARLIN, S., (1959):Mathematical Methods and Theory in Games, Programming and Economics, vol. II, Addison-Wesley.
[4] NACHBIN, L. (1976):The Haar Integral, Robert R. Krieger Publishing Co.
[5] PONTRIAGUIN, L. S. (1978):Grupos Continuos, ed. Mir.
[6] RUDIN, W. (1962):Fourier Analysis on Groups, Interscience. · Zbl 0107.09603
[7] SAEZ, J. (1983): “Medidas ø-invariantes sobre un grupo compacto{”,Publicaciones de la Sección de Matemáticas, Universidad de Valladolid, núm. 6, 157–163.}
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.