Time consistent cooperative solutions for multistage games with vector payoffs
To ensure sustainable cooperation in multistage games with vector payoffs we use the payment schedule based approach. The main dynamic properties of cooperative solutions used in single-criterion multistage games are extended to multicriteria games.
We design two recurrent payment schedules that satisfy such advantageous properties as the efficiency and the time consistency conditions, non-negativity and irrational behavior proofness.
We use so-called “Imputation Distribution Procedure” approach to sustain long-term cooperation in n-person multicriteria game in extensive form.
Measuring indirect importance of various attributes is a very common task in marketing analysis for which researchers use correlation and regression techniques. We have listed and illustrated some common problems with widely used latent importance measures. A more theoretically sound approach - the Shapley Value decomposition - was applied to a rich data set of US internet stores. The use of store-level data instead of respondent-level data allowed us to reveal the factors, which are powerful in explaining, why some stores have higher rates of willingness to make repeat purchases than the others. By confronting the indirect importance and performance measures for three different internet stores, we have revealed strengths, weaknesses, attributes that the company should bring customers' attention to and attributes that do not require immediate improvement.
Measuring indirect importance of various attributes is a very common task in marketing analysis for which researchers use correlation and regression techniques. We have listed and illustrated some common problems with widely used latent importance measures. A more theoretically sound approach – the Shapley Value decomposition – was applied to a rich data set of US internet stores. The use of store-level data instead of respondent-level data allowed us to reveal the factors, which are powerful in explaining, why some stores have higher rates of willingness to make repeat purchases than the others. By confronting the indirect importance and performance measures for three different internet stores, we have revealed strengths, weaknesses, attributes that the company should bring customers’ attention to and attributes improvement of which is not of a high priority.
This paper is devoted to modern approaches to the estimation of external conflict in the theory of evidence based on axioms. The conflict measure is defined on the set of beliefs obtained from several sources of information. It is shown that the conflict measure should be a monotone set function with respect to sets of beliefs. Some robust procedures for evaluation of conflict measure that are stable to small changes in evidences are introduced and discussed. The analysis of conflict among forecasts about the value of shares of Russian companies of investment banks is presented. In this analysis the conflict measure estimates inconsistency of recommendations of investment banks, while the Shapley values of this measure on the set of evidences characterize the contribution of each investment bank to the overall conflict. The relationship between conflict and precision of forecasts is also investigated.
Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.