Infinite -games with imperfect information
D. Blackwell (1969)
Applicationes Mathematicae
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D. Blackwell (1969)
Applicationes Mathematicae
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C. A. Pensavalle, G. Pieri (2010)
Bollettino dell'Unione Matematica Italiana
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Consider a M-player game in strategic form where the set is a closed interval of real numbers and the payoff function is concave and differentiable with respect to the variable , for any . The aim of this paper is to find appropriate conditions on the payoff functions under the well-posedness with respect to the related variational inequality is equivalent to the formulation of the Tykhonov well-posedness in a game context. The idea of the proof is to appeal to a third equivalence,...
D. Guerrero Sánchez, Vladimir Vladimirovich Tkachuk (2017)
Commentationes Mathematicae Universitatis Carolinae
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Given a subbase of a space , the game is defined for two players and who respectively pick, at the -th move, a point and a set such that . The game stops after the moves have been made and the player wins if ; otherwise is the winner. Since is an evident modification of the well-known point-open game , the primary line of research is to describe the relationship between and for a given subbase . It turns out that, for any subbase , the player has a winning...
Tapani Hyttinen, Saharon Shelah, Jouko Vaananen (2002)
Fundamenta Mathematicae
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By results of [9] there are models and for which the Ehrenfeucht-Fraïssé game of length ω₁, , is non-determined, but it is consistent relative to the consistency of a measurable cardinal that no such models have cardinality ≤ ℵ₂. We now improve the work of [9] in two ways. Firstly, we prove that the consistency strength of the statement “CH and is determined for all models and of cardinality ℵ₂” is that of a weakly compact cardinal. On the other hand, we show that if , T is a countable...
Shunsuke Nakamura, Ryo Hanafusa, Wataru Ogasa, Takeru Kitagawa, Ryohei Miyadera (2013)
Visual Mathematics
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Salvador García-Ferreira, R. A. González-Silva, Artur Hideyuki Tomita (2002)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, we deal with the product of spaces which are either -spaces or -spaces, for some . These spaces are defined in terms of a two-person infinite game over a topological space. All countably compact spaces are -spaces, and every -space is a -space, for every . We prove that if is a set of spaces whose product is a -space, then there is such that is countably compact for every . As a consequence, is a -space iff is countably compact, and if is a -space,...
Frank J. Hall, Miroslav Rozložník (2016)
Czechoslovak Mathematical Journal
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A real matrix is a G-matrix if is nonsingular and there exist nonsingular diagonal matrices and such that , where denotes the transpose of the inverse of . Denote by a diagonal (signature) matrix, each of whose diagonal entries is or . A nonsingular real matrix is called -orthogonal if . Many connections are established between these matrices. In particular, a matrix is a G-matrix if and only if is diagonally (with positive diagonals) equivalent to a column permutation...
Mohammad Soleymani (2024)
Czechoslovak Mathematical Journal
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Let , be matrices. The concept of matrix majorization means the th column of is majorized by the th column of and this is done for all by a doubly stochastic matrix . We define rc-majorization that extended matrix majorization to columns and rows of matrices. Also, the linear preservers of rc-majorization will be characterized.
Daniel Uzcátegui Contreras, Dardo Goyeneche, Ondřej Turek, Zuzana Václavíková (2021)
Communications in Mathematics
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It is known that a real symmetric circulant matrix with diagonal entries , off-diagonal entries and orthogonal rows exists only of order (and trivially of order ) [Turek and Goyeneche 2019]. In this paper we consider a complex Hermitian analogy of those matrices. That is, we study the existence and construction of Hermitian circulant matrices having orthogonal rows, diagonal entries and any complex entries of absolute value off the diagonal. As a particular case, we consider...
Teodor Banica, Ion Nechita, Jean-Marc Schlenker (2014)
Annales mathématiques Blaise Pascal
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We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for the quantity satisfies , with equality if and only if is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of , (2) the study of the critical points of , and (3) the computation of the moments of . We explore here...
Fernando Luque-Vásquez, J. Adolfo Minjárez-Sosa (2017)
Kybernetika
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This work deals with a class of discrete-time zero-sum Markov games whose state process evolves according to the equation where and represent the actions of player 1 and 2, respectively, and is a sequence of independent and identically distributed random variables with unknown distribution . Assuming possibly unbounded payoff, and using the empirical distribution to estimate , we introduce approximation schemes for the value of the game as well as for optimal strategies considering...
Alireza Kamel Mirmostafaee (2018)
Mathematica Bohemica
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Let be a Baire space, be a compact Hausdorff space and be a quasi-continuous mapping. For a proximal subset of we will use topological games and on between two players to prove that if the first player has a winning strategy in these games, then is norm continuous on a dense subset of . It follows that if is Valdivia compact, each quasi-continuous mapping from a Baire space to is norm continuous on a dense subset of .
Sara M. Motlaghian, Ali Armandnejad, Frank J. Hall (2016)
Czechoslovak Mathematical Journal
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Let be the set of all real matrices. A matrix is said to be row-dense if there are no zeros between two nonzero entries for every row of this matrix. We find the structure of linear functions that preserve or strongly preserve row-dense matrices, i.e., is row-dense whenever is row-dense or is row-dense if and only if is row-dense, respectively. Similarly, a matrix is called a column-dense matrix if every column of is a column-dense vector. At the end, the structure...