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## Аксиоматика некооперативного подхода к коалиционным играм

An axiomatics of power indices in voting with quota was proposed. It relies on the additivity and dictator axioms. Established was an important property that the player’s power index is representable as the sum of contributions of the coalitions in which it is a pivot member. The coalition contributions are independent of the players’ weights or the quota. The general theorem of power index representation and the theorem of representation for a power index of anonymous players were formulated and proved.

This book is devoted to game theory and its applications to environmental problems, economics, and management. It collects contributions originating from the 12th International Conference on “Game Theory and Management” 2018 (GTM2018) held at Saint Petersburg State University, Russia, from 27 to 29 June 2018.

The collecton contains paper accepted for the Seventh International Conference Game theory and Management (June 26-28, 2013, St. Petersburg State University, St. Petersburg, Russia). The presented papers belong to the field of game theory and its application to mamagement.

The volume may be recommended for researchers and post-graduate students of management, economic and applied mathematics departments.

Sited and reviewed in: Math-Net.Ru and RSCI. Abstracted and indexed in: Mathematical Reviews, Zentralblatt MATH and VINITI.

The problem of axiomatic and algorithmic constructions of the threshold decision making is studied in the case when individual opinions are given as m-graded strict preferences (with m ≥ 3). It is shown that the only rule satisfying the introduced axioms is the threshold rule. Two explicit algorithms are presented: the ordering algorithm, under which the vector-grades of alternatives are successively written out, and an enumerating social decision function corresponding to the natural order of the weak order equivalence classes.

This book is devoted to game theory and its applications to environmental problems, economics, and management. It collects contributions originating from the 12th International Conference on “Game Theory and Management” 2018 (GTM2018) held at Saint Petersburg State University, Russia, from 27 to 29 June 2018.

The paper proposes a list of requirements for a game able to describe individually motivated social interactions: be non-cooperative, able to construct multiple coalitions in an equilibrium and incorporate intra and inter coalition externalities. For this purpose the paper presents a family of non-cooperative games for coalition structure construction with an equilibrium existence theorem for a game in the family. Few examples illustrate the approach. One of the results is that efficiency is not equivalent to cooperation as an allocation in one coalition. Further papers will demonstrate other applications of the approach.

Expands axiomatic core of the modern theory of competition. Showing the main problems and inconsistencies of the axiomatic core.

We use so-called “Imputation Distribution Procedure” approach to sustain long-term cooperation in n-person multicriteria game in extensive form.

We offer a general approach to describing power indices that account for preferences as suggested by F. Aleskerov. We construct two axiomatizations of these indices. Our construction generalizes the Laruelle-Valenciano axioms for Banzhaf (Penrose) and Shapley-Shubik indices. We obtain new sets of axioms for these indices, in particular, sets without the anonymity axiom.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.