Repeated matrix games

1979 ◽  
Vol 16 (04) ◽  
pp. 830-842
Author(s):  
Dana B. Kamerud
Keyword(s):  
Optimal Strategies ◽  
Matrix Game ◽  
Matrix Games ◽  
Value Of A Game ◽  
A Value ◽  
History Of ◽  
Definition Of

A matrix game is played repeatedly, with the actions taken at each stage determining both a reward paid to Player I and the probability of continuing to the next stage. An infinite history of play determines a sequence (Rn ) of such rewards, to which we assign the payoff lim supn (R 1 + · ·· + Rn ). Using the concept of playable strategies, we slightly generalize the definition of the value of a game. Then we find sufficient conditions for the existence of a value and for the existence of stationary optimal strategies (Theorems 8 and 9). An example shows that the game need not have a value (Example 4).

Repeated matrix games

1979 ◽  
Vol 16 (4) ◽  
pp. 830-842
Author(s):  
Dana B. Kamerud
Keyword(s):  
Optimal Strategies ◽  
Matrix Game ◽  
Matrix Games ◽  
Value Of A Game ◽  
A Value ◽  
History Of ◽  
Definition Of

A matrix game is played repeatedly, with the actions taken at each stage determining both a reward paid to Player I and the probability of continuing to the next stage. An infinite history of play determines a sequence (Rn) of such rewards, to which we assign the payoff lim supn (R1 + · ·· + Rn). Using the concept of playable strategies, we slightly generalize the definition of the value of a game. Then we find sufficient conditions for the existence of a value and for the existence of stationary optimal strategies (Theorems 8 and 9). An example shows that the game need not have a value (Example 4).

A Combinatorial method for a class of matrix games

1966 ◽  
Vol 3 (2) ◽  
pp. 495-511
Author(s):  
Rodrigo A. Restrepo
Keyword(s):  
Optimal Strategies ◽  
Matrix Game ◽  
Combinatorial Method ◽  
Matrix Games ◽  
Finite Matrix ◽  
Special Relations ◽  
Class Of Matrices

The optimal strategies of any finite matrix game can be characterized by means of the Snow-Shapley Theorem [1]. However, in order to use this theorem to compute the optimal strategies, it may be necessary to invert a large number of matrices, most of which are not related to the solutions of the game. The present paper will show that when the columns of the pay-off matrix satisfy some special relations, it is possible to enumerate a much smaller class of matrices from which the optimal strategies may be obtained. Furthermore, the maximizing strategies that are determined by these matrices can be written down by inspection as soon as the matrices are specified.

Recursive matrix games

1972 ◽  
Vol 9 (4) ◽  
pp. 813-820 ◽  
Author(s):  
Michael Orkin
Keyword(s):  
Matrix Game ◽  
Matrix Games ◽  
Inductive Proof ◽  
Stationary Strategies ◽  
A Value ◽  
Recursive Games ◽  
Recursive Matrix ◽  
Optimal Stationary Strategies

“Recursive” games were first defined and studied by Everett. Related results can be found in Gillette, Milnor and Shapley, and Blackwell and Ferguson. In this paper we introduce the notion of a recursive matrix game, which we believe eliminates the vagueness but none of the useful generality of the earlier definition. We then give an inductive proof (different from the proof in [3]) that these games have a value, with ∊-optimal stationary strategies available to each player. We also apply the result and show how a class of games studied in a different framework are games of this type and thus have a value.

scholarly journals Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 702 ◽  
Author(s):  
Brikaa ◽  
Zheng ◽  
Ammar
Keyword(s):  
Optimal Strategies ◽  
Programming Algorithm ◽  
Programming Approach ◽  
Matrix Game ◽  
Matrix Games ◽  
Constraint Matrix ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Game Value ◽  
Objective Programming

Imprecise constrained matrix games (such as fuzzy constrained matrix games, interval-valued constrained matrix games, and rough constrained matrix games) have attracted considerable research interest. This article is concerned with developing an effective fuzzy multi-objective programming algorithm to solve constraint matrix games with payoffs of fuzzy rough numbers (FRNs). For simplicity, we refer to this problem as fuzzy rough constrained matrix games. To the best of our knowledge, there are no previous studies that solve the fuzzy rough constrained matrix games. In the proposed algorithm, it is proven that a constrained matrix game with fuzzy rough payoffs has a fuzzy rough-type game value. Moreover, this article constructs four multi-objective linear programming problems. These problems are used to obtain the lower and upper bounds of the fuzzy rough game value and the corresponding optimal strategies of each player in any fuzzy rough constrained matrix games. Finally, a real example of the market share game problem demonstrates the effectiveness and reasonableness of the proposed algorithm. Additionally, the results of the numerical example are compared with the GAMS software results. The significant contribution of this article is that it deals with constraint matrix games using two types of uncertainties, and, thus, the process of decision-making is more flexible.

Recursive matrix games

1972 ◽  
Vol 9 (04) ◽  
pp. 813-820 ◽  
Author(s):  
Michael Orkin
Keyword(s):  
Matrix Game ◽  
Matrix Games ◽  
Inductive Proof ◽  
Stationary Strategies ◽  
A Value ◽  
Recursive Games ◽  
Recursive Matrix ◽  
Optimal Stationary Strategies

“Recursive” games were first defined and studied by Everett. Related results can be found in Gillette, Milnor and Shapley, and Blackwell and Ferguson. In this paper we introduce the notion of a recursive matrix game, which we believe eliminates the vagueness but none of the useful generality of the earlier definition. We then give an inductive proof (different from the proof in [3]) that these games have a value, with ∊-optimal stationary strategies available to each player. We also apply the result and show how a class of games studied in a different framework are games of this type and thus have a value.

scholarly journals Religious and heuristic meaning of sacred places of memory: «Arasan-Korasan»

2021 ◽  
Vol 70 (3) ◽  
Author(s):  
T.T. Dalayeva ◽  
◽  
А.К. Nurgaliyev ◽  
Keyword(s):  
Sacred Places ◽  
Sacred Place ◽  
Religious Rituals ◽  
A Value ◽  
Sacred Objects ◽  
Phenomenology Of Religion ◽  
Places Of Memory ◽  
History Of ◽  
Definition Of ◽  
Broad Meaning

In general science, the concepts of "sacred" and "sacred" are comprehensively considered by the phenomenology of religion. The phenomenology of religion, analyzing these concepts, gives the following definitions. A saint is a value, or an action, given or created by the creator. In other words, it means sanctity, sanctity. And the concept of holiness is used in the implementation of these divine values, or actions. This concept is usually used in religious rituals and Customs. Sanctification is often characterized by the process of purification, removal, for example, exhalation, removal with a healing plant with adraspan, etc. The article provides a definition of the broad meaning of the concepts of" sacred "and" sacred " for the Kazakh people. Based on this, the research paper presents the results of the study of the history of the sacred place "sacred Arasan – Korasan" in Besmoynak village of Zhambyl District of Almaty region, the ways of religious and ritual pilgrimage of pilgrims, the sacral nature of springs, their importance in healing and healing, their place in the development of tourism, the name of the sacred place in general. The publication in the scientific literature of information about the sacred place of Arasan, about the properties of underground springs in it, contributed to the fact that this place was included in the list of sacred objects of interregional Kazakhstan, including Semirechye, and was protected by the state.

A Combinatorial method for a class of matrix games

1966 ◽  
Vol 3 (02) ◽  
pp. 495-511
Author(s):  
Rodrigo A. Restrepo
Keyword(s):  
Optimal Strategies ◽  
Matrix Game ◽  
Combinatorial Method ◽  
Matrix Games ◽  
Finite Matrix ◽  
Special Relations ◽  
Class Of Matrices

The optimal strategies of any finite matrix game can be characterized by means of the Snow-Shapley Theorem [1]. However, in order to use this theorem to compute the optimal strategies, it may be necessary to invert a large number of matrices, most of which are not related to the solutions of the game. The present paper will show that when the columns of the pay-off matrix satisfy some special relations, it is possible to enumerate a much smaller class of matrices from which the optimal strategies may be obtained. Furthermore, the maximizing strategies that are determined by these matrices can be written down by inspection as soon as the matrices are specified.

Towards the digital land reclamation

2020 ◽  
pp. 5-9
Author(s):  
Sergey Vasil'ev ◽  
Vyacheslav Schedrin ◽  
Aleksandra Slabunova ◽  
Vladimir Slabunov
Keyword(s):  
Retrospective Analysis ◽  
Land Reclamation ◽  
Practical Experience ◽  
Maximum Effect ◽  
Optimal Management ◽  
Scientific Potential ◽  
History Of ◽  
Definition Of ◽  
Further Development ◽  
Full Cooperation

The aim of the research is a retrospective analysis of the history and stages of development of digital land reclamation in Russia, the definition of «Digital land reclamation» and trends in its further development. In the framework of the retrospective analysis the main stages of melioration formation are determined. To achieve the maximum effect of the «digital reclamation» requires full cooperation of practical experience and scientific potential accumulated throughout the history of the reclamation complex, and the latest achievements of science and technology, which is currently possible only through the full digitalization of reclamation activities. The introduction of «digital reclamation» will achieve greater potential and effect in the modernization of the reclamation industry in the «hightech industry», through the use of innovative developments and optimal management decisions.

Vyshnivetsky Castle Library of Prince Mychailo Servaty Vyshnivetsky – Historical Book Heritage and Object of Bibliological and Historical Reconstruction

2014 ◽  
Vol 3 ◽  
pp. 166-182
Author(s):  
Iryna Tsiborovska-Rymarovych
Keyword(s):  
18Th Century ◽  
Historical Analysis ◽  
Cultural Significance ◽  
Historical Sources ◽  
Cultural Images ◽  
The Enlightenment ◽  
Printed Books ◽  
History Of ◽  
Grand Duchy Of Lithuania ◽  
Definition Of

The article has as its object the elucidation of the history of the Vyshnivetsky Castle Library, definition of the content of its fund, its historical and cultural significance, correlation of the founder of the Library Mychailo Servaty Vyshnivetsky with the Book.The Vyshnivetsky Castle Library was formed in the Ukrainian historical region of Volyn’, in the Vyshnivets town – “family nest” of the old Ukrainian noble family of the Vyshnivetskies under the “Korybut” coat of arm. The founder of the Library was Prince Mychailo Servaty Vyshnivetsky (1680–1744) – Grand Hetman and Grand Chancellor of the Grand Duchy of Lithuania, Vilno Voievoda. He was a politician, an erudite and great bibliophile. In the 30th–40th of the 18th century the main Prince’s residence Vyshnivets became an important centre of magnate’s culture in Rich Pospolyta. M. S. Vyshnivetsky’s contemporaries from the noble class and clergy knew quite well about his library and really appreciated it. According to historical documents 5 periods are defined in the Library’s history. In the historical sources the first place is occupied by old-printed books of Library collection and 7 Library manuscript catalogues dating from 1745 up to the 1835 which give information about quantity and topical structures of Library collection.The Library is a historical and cultural symbol of the Enlightenment epoch. The Enlightenment and those particular concepts and cultural images pertaining to that epoch had their effect on the formation of Library’s fund. Its main features are as follow: comprehensive nature of the stock, predominance of French eighteenth century editions, presence of academic books and editions on orientalistics as well as works of the ideologues of the Enlightenment and new kinds of literature, which generated as a result of this movement – encyclopaedias, encyclopaedian dictionaries, almanacs, etc. Besides the universal nature of its stock books on history, social and political thought, fiction were dominating.The reconstruction of the history of Vyshnivetsky’s Library, the historical analysis of the provenances in its editions give us better understanding of the personality of its owners and in some cases their philanthropic activities, and a better ability to identify the role of this Library in the culture life of society in a certain epoch.

(A review). BRAUN-BLANQUETIA. Recueil de travaux de geobotanique / review of geobotanical monographs. Vol. 46. Centenaire de la phytosociologie. CAMERINO, 2010. 423 p.

2011 ◽  
pp. 143-147
Author(s):  
L. G. Naumova ◽  
V. B. Martynenko ◽  
S. M. Yamalov
Keyword(s):  
Plant Association ◽  
Northern Asia ◽  
The Third ◽  
International Botanical ◽  
International Botanical Congress ◽  
History Of ◽  
Definition Of

Date of «birth» of phytosociology (phytocenology) is considered to be 1910, when at the third International Botanical Congress in Brussels adopted the definition of plant association in the wording Including Flaó and K. Schröter (Flahault, Schröter, 1910; Alexandrov, 1969). The centenary of this momentous event in the history of phytocenology devoted to the 46th edition of the Yearbook «Braun-Blanquetia», which began to emerge in 1984 in Camerino (Italy) and it has a task to publish large geobotanical works. During the years of the publication of the Yearbook on its pages were published twice work of the Russian scientists — «The steppes of Mongolia» (Z. V. Karamysheva, V. N. Khramtsov. Vol. 17. 1995), and «Classification of continental hemiboreal forests of Northern Asia» (N. B. Ermakov in collaboration with English colleagues and J. Dring, J. Rodwell. Vol. 28. 2000).

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