We examine an equilibrium concept for 2-person non-cooperative games with boundedly rational agents which we call Nash-2 equilibrium. It is weaker than Nash equilibrium and equilibrium in secure strategies: a player takes into account not only current strategies but also all profitable next-stage responses of the partners to her deviation from the current profile that reduces her relevant choice set. We provide a condition for Nash-2 existence in finite games and complete characterization of Nash-2 equilibrium in strictly competitive games. Nash-2 equilibria in Hotelling price-setting game are found and interpreted in terms of tacit collusion.
The natural language texts (NL-texts) from the newspapers, e-mail lists, various blogs, etc. are the important sources of information being able to stimulate the elaboration of a new plan of actions. The paper describes a new formal approach to developing multilingual algorithms of semantic-syntactic analysis of NL-texts. It is a part of the theory of K-representations - a new theory of designing semantic-syntactic analyzers of NL-texts with the broad use of formal means for representing input, intermediary, and output data. The current version of the theory is set forth in a monograph published by Springer in 2010. One of the principal constituents of this theory is a complex, strongly structured algorithm SemSynt1 carrying out semantic-syntactic analysis of texts from some practically interesting sublanguages of the English, German, and Russian languages. An important feature of this algorithm is that it doesn’t construct any syntactic representation of the inputted NL-text but directly finds semantic relations between text units. The other distinguished feature is that the algorithm is completely described with the help of formal means, that is why it is problem independent and doesn’t depend on a programming system. The peculiarities and some central procedures of the algorithm SemSynt1 are analyzed.
We consider the minimizing total weighted completion time in preemptive equal job length scheduling problem on a single machine with release dates. We propose a polynomial time algorithm that solves the problem. Before this paper, the problem is known to be open.
В статье излагается новый подход к рассмотрению импрессионизма в рамках когнитоники. Это новая научная дисциплина, направленная на компенсацию негативных сдвигов в когнитивно-эмоциональном развитии личности и в развитии общества, вызванных стремительным прогрессом информационно-коммуникационных технологий и процессов глобализации. Предложен оригинальный алгоритм преобразования негативных эмоций (вызванных сообщениями, полученными через социальные сети) в позитивные. Этот алгоритм рассматривает возможные реакции человека (в том числе рекомендуемые реакции) на эмоциональные атаки, осуществляемые через социальные сети. В основе этого алгоритма лежит новый взгляд на импрессионизм. Алгоритм является частью оригинального междисциплинарного курса «Основы безопасной жизни в информационном обществе».
—Ramification in complete discrete valuation fields is studied. For the case of a perfect residue field, there is a well-developed theory of ramification groups. Hyodo introduced the concept of ramification depth associated with the different of an extension and obtained an inequality that combines the concept of ramification depth in a degree p2 cyclotomic extension with the concept of ramification depth in a degree p subextension. The paper gives a detailed consideration of the structure of degree p2 extensions that can be obtained by a composite of two degree p extensions. In this case, it is not required that the residue field be perfect. Using the concepts of wild and ferocious extensions and the defect of the main unit, degree p2 extensions are classified and more accurate estimates for the ramification depth are obtained. In a number of cases, exact formulas for ramification depth are presented.
Introduction and definitions. In some of my publications (see e.g., Grinin 2003, 2004a, 2004b, 2007; Grinin and Korotayev 2009) I have tried to demonstrate that politogenesis is much wider than the state formation process (SFP throughout) because the classical evolutionary scheme from pre-state society to primitive (early) state turns out to have been far less frequent than supposed; the early state formation was only one of many versions of development of complex archaic sociopolitical systems.
 For more details regarding this term see Grinin and Korotayev 2009.