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Xavier Venel - One of the best experts on this subject based on the ideXlab platform.
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Attainability in Repeated Games with Vector Payoffs
Mathematics of Operations Research, 2015Co-Authors: Dario Bauso, Ehud Lehrer, Eilon Solan, Xavier VenelAbstract:We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called attainable by a player if there is a positive integer such that the player can guarantee that in all finite game longer than that integer, the distance between the set and the cumulative payoff is arbitrarily small, regardless of the strategy Player 2 is using. We provide a necessary and sufficient condition for the Attainability of a convex set, using the concept of B-sets. We then particularize the condition to the case in which the set is a singleton, and provide some equivalent conditions. We finally characterize when all vectors are attainable.
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Attainability in Repeated Games with Vector Payoffs
Mathematics of Operations Research, 2015Co-Authors: Dario Bauso, Ehud Lehrer, Eilon Solan, Xavier VenelAbstract:We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called attainable by a player if there is a finite horizon T such that the player can guarantee that after time T the distance between the set and the cumulative payoff is arbitrarily small, regardless of the strategy Player 2 is using. We provide a necessary and sufficient condition for the Attainability of a convex set, using the concept of B-sets. We then particularize the condition to the case in which the set is a singleton, and provide some equivalent conditions. We finally characterize when all vectors are attainable.
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Attainability in Repeated Games with Vector Payoffs
arXiv: Optimization and Control, 2012Co-Authors: Dario Bauso, Ehud Lehrer, Eilon Solan, Xavier VenelAbstract:We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called {\em attainable} if player 1 can ensure that there is a finite horizon $T$ such that after time $T$ the distance between the set and the cumulative payoff is arbitrarily small, regardless of what strategy player 2 is using. This paper focuses on the case where the attainable set consists of one payoff vector. In this case the vector is called an attainable vector. We study properties of the set of attainable vectors, and characterize when a specific vector is attainable and when every vector is attainable.
Jose Valero - One of the best experts on this subject based on the ideXlab platform.
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the weak connectedness of the Attainability set of weak solutions of the three dimensional navier stokes equations
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2007Co-Authors: Peter E Kloeden, Jose ValeroAbstract:The Attainability set of the weak solutions of the three-dimensional Navier–Stokes equations which satisfy an energy inequality is shown to be a weakly compact and weakly connected subset of the space H, i.e. the Kneser property holds in the weak topology for such weak solutions. The proof of weak connectedness uses the strong connectedness of the Attainability set of the weak solutions of the globally modified Navier–Stokes equations, which is first proved. The weak connectedness of the weak global attractor of the three-dimensional Navier–Stokes equations is also established.
Joke Fleer - One of the best experts on this subject based on the ideXlab platform.
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impaired mood in headache clinic patients associations with the perceived hindrance and Attainability of personal goals
Headache, 2016Co-Authors: Yvette Ciere, Annemieke Visser, John Lebbink, Robbert Sanderman, Joke FleerAbstract:Background Headache disorders are often accompanied by impaired mood, especially in the headache clinic population. There is a large body of literature demonstrating that an illness or disability may affect the way in which patients perceive their personal goals and that the perception that the Attainability of goals is hindered by the illness is a risk factor for impaired mood. However, empirical evidence regarding the extent to which goals are hindered or less attainable as a result of a headache disorder, and how that is related to mood, is currently lacking. Objective The aim of this cross-sectional study was to examine associations between headache severity, goal hindrance and Attainability, and mood in a headache clinic population. Methods The sample consisted of 65 adult patients seeking treatment at a tertiary headache clinic. Prior to their first appointment in the clinic, patients completed self-report measures of headache severity, goals and mood (PANAS). Results Higher self-reported headache intensity was associated with higher goal hindrance (r = .38, P = .004), whereas greater headache frequency was associated with lower goal Attainability (r = .30, P = .022). Higher perceived goal hindrance was associated with lower positive mood (r = −.27, P = .032) and higher negative mood (r = .28, P = .027). Furthermore, lower perceived goal Attainability was associated with higher negative mood (r = −.34, P = .007). Goal perceptions explained an additional 11.4% of the variance in positive mood (F = 3.250, P = .047 <.05) and 10.5% of the variance in negative mood (F = 3.459, P = .039) beyond the effect of age and headache severity. Conclusion The results of this preliminary study suggest that perceptions of increased goal hindrance and decreased goal Attainability may indeed be a risk factor for impaired mood in the headache clinic population and highlight the need for further, longitudinal research. Obtaining more insight into goal processes (eg, what types of goals are specifically disturbed, which goal adjustment strategies are (mal)adaptive) may help to identify ways to improve outcomes in the headache clinic population.
Joachim C Brunstein - One of the best experts on this subject based on the ideXlab platform.
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personal goals and subjective well being a longitudinal study
Journal of Personality and Social Psychology, 1993Co-Authors: Joachim C BrunsteinAbstract:This study examined the extent to which 3 dimensions of personal goals - commitment, Attainability, and progress - were predictive of students' subjective well-being over 1 semester. At the beginning of a new term, 88 Ss provided a list of their personal goals. Goal attributes and subjective well-being were measured at 4 testing periods. Goal commitment was found to moderate the extent to which differences in goal Attainability accounted for changes in subjective well-being. Progress in goal achievement mediated the erect of the Goal Commitment × Goal Attainability on Subjective Well-Being interaction. Results are discussed in terms of a need for addition and refinement of assumptions linking personal goals to subjective well-being
A G Chentsov - One of the best experts on this subject based on the ideXlab platform.
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attraction sets in abstract Attainability problems equivalent representations and basic properties
Russian Mathematics, 2013Co-Authors: A G ChentsovAbstract:In this paper we use the following abbreviations: FB (filter base), MS (measurable space), AS (attraction set), DS (directed set), AD (Attainability domain), GE (generalized element), s/s (subset), ApS (approximate solution), TS (topological space), and u/f (ultrafilter). We consider general questions connected with the asymptotic Attainability; the latter is understood as the Attainability of certain states under asymptotic constraints. One natural concrete variant of the problem which we consider below is related to the construction of the AD of a controlled system at a fixed time moment and the study of its properties. This concrete problem is not stable with respect to disturbances, in particular, for weakened constraints. One can treat weakened constraints (phase constraints, edge and intermediate ones) in this problem as asymptotic restrictions. Respectively, the limit of real AD which correspond to weakened constraints can be considered as an AS; from the practical point of view it plays the same role as a “regular ” AD does. Together with AD, with the strict and approximate fulfillment of constraints one can consider sheaves of trajectories of the controlled system and thus obtain sets in a functional space equipped with the corresponding topology. The latter can be generated by a metric, but this is not necessarily so (for example, in cases typical for control problems with continuous time, the topology of pointwise convergence is not metrizable). Therefore it is natural to consider logically similar problems on the Attainability in TS, though this can require the application of more complex constructions for AS. This approach is used in the present paper. In addition, using such general statements of the problem, it is natural to assume asymptotic analogs of constraints which are not necessary connected with the weakening of some standard conditions. Really, weakening conditions of such a kind, we form a family of sets of feasible elements for each constraint weakened in a concrete way (generated by the set of mentioned conditions). From this moment we “deal” with the obtained family (really, this is a result of the relaxation procedure for the initial problem), using the minimal set of properties of sets that compose it. But this means that from the beginning we can assume that the family of s/s of the space of regular solutions (or controls) is given, not questioning how this family has been obtained (it is advisable to reduce the set of properties “to the minimum”). In particular, we do not tend to connect this family with a successive weakening of some “rigid ” conditions. In this case the question on the Attainability in TS has an asymptotic character. Let us consider a very simple example of a static problem, fixing two finite-dimensional spaces R m and R n (m and n are natural numbers), and a bounded mapping f from R m to R n .F or de finiteness,
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representation of attraction elements in abstract Attainability problems with asymptotic constraints
Russian Mathematics, 2012Co-Authors: A G ChentsovAbstract:We consider an abstract Attainability problem with asymptotic constraints in a topological space. We construct an extension in the class of ultrafilters of widely interpreted measurable spaces. We study an example of a static problem on the asymptotic Attainability in the class of layer functions.
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extensions of abstract problems of Attainability nonsequential version
Proceedings of the Steklov Institute of Mathematics, 2007Co-Authors: A G ChentsovAbstract:Extension constructions of the problem of Attainability in a topological space are studied. The constructions are based on compactification of the whole space of solutions or some of its fragments.
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Finitely Additive Measures and Problems of Asymptotic Analysis
IFAC Proceedings Volumes, 1998Co-Authors: A G ChentsovAbstract:Abstract Questions of asymptotic Attainability under perturbations of integral constraints are considered. The generalized representation in the class of vector finitely additive measures is investigated. Different variants of the weakening of initial conditions are compared. In addition, the unboundedness of the space of controls is assumed . General scheme of analysis of attraction sets is considered.
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Asymptotic Attainability: General Questions
Asymptotic Attainability, 1997Co-Authors: A G ChentsovAbstract:In the previous chapters, we considered numerous examples and whole classes of problems dealing with effects arising under the perturbation of the conditions on the choice of controls. Namely, we formed controls with a premeditated but “small” breakdown of a complex of conditions and investigated the realization “as a limit” of the corresponding desirable states for us. However, this “smallness” is often “seeming”. In reality, the influence of controls may be deep. It is displayed “on the level of asymptotics” under the realization of elements which are very far from those attainable under rigid fulfillment of conditions (see Section 1.2). In essence, we have here effects which are typical for ill-posed problems [27, 38]; the sets of the asymptotical Attainability play the role of a peculiar regularizations of the initial statements. Beginning with this chapter, we are going to systematically investigate the given occurrences for some class of problems with restrictions of an integral character. However, we shall preliminarily discuss (in the next section) the given question on a profound level. Later, we shall introduce general designations and definitions connected with the problem of the asymptotic Attainability.
