Dynamic Set Values for Nonzero-Sum Games with Multiple Equilibriums

Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero-sum case, they may have different values at different equilibriums. Instead of focusing on the existence of individual equilibriums, we study the set of values over all equilibriums, which we call the set value of the game. The set value is unique by nature and always exists (with possible value [Formula: see text]). Similar to the standard value function in control literature, it enjoys many nice properties, such as regularity, stability, and more importantly, the dynamic programming principle. There are two main features in order to obtain the dynamic programming principle: (i) we must use closed-loop controls (instead of open-loop controls); and (ii) we must allow for path dependent controls, even if the problem is in a state-dependent (Markovian) setting. We shall consider both discrete and continuous time models with finite time horizon. For the latter, we will also provide a duality approach through certain standard PDE (or path-dependent PDE), which is quite efficient for numerically computing the set value of the game.

An Equivalent Linear Programming Form of General Linear Fractional Programming: A Duality Approach

Linear fractional programming has been an important planning tool for the past four decades. The main contribution of this study is to show, under some assumptions, for a linear programming problem, that there are two different dual problems (one linear programming and one linear fractional functional programming) that are equivalent. In other words, we formulate a linear programming problem that is equivalent to the general linear fractional functional programming problem. These equivalent models have some interesting properties which help us to prove the related duality theorems in an easy manner. A traditional data envelopment analysis (DEA) model is taken, as an instance, to illustrate the applicability of the proposed approach.

A dual process on shopping well-being across shopping contexts: the role of shopping values and impulse buying

PurposeAdopting the duality approach, this study aims to examine cognitive and affective associations between shopping values, impulse buying tendencies and consumer shopping well-being. In addition, the study also aims to test the moderating role of self-control and compare the proposed relationships across the offline and online shopping contexts.Design/methodology/approachA survey dataset was collected from a sample of 529 offline and online consumers in Vietnam. Structural equation modelling (SEM) was employed to test the proposed relationships among the studied constructs.FindingsThe consequence of impulse buying is positive and affect-based. In addition, the positive associations between shopping values and impulse buying via dual process are validated and moderated by self-control. In addition, the association between cognitive impulse buying and shopping well-being is stronger in the online shopping context, whereas hedonic value has more influence on affective impulse buying in the offline shopping context. All other relationships are not statistically different across the two shopping contexts.Originality/valueThis study introduces an appropriate theoretical framework for studying impulse buying—the duality approach. Second, the research validates the dual process and positive consequence of impulse buying. Third, self-control's moderating role is validated, whereas the studied associations are initially compared across shopping contexts.

Duality in quantum transport models

We develop the `duality approach', that has been extensively studied for classical models of transport, for quantum systems in contact with a thermal `Lindbladian' bath. The method provides (a) a mapping of the original model to a simpler one, containing only a few particles and (b) shows that any dynamic process of this kind with generic baths may be mapped onto one with equilibrium baths. We exemplify this through the study of a particular model: the quantum symmetric exclusion process introduced in [1]. As in the classical case, the whole construction becomes intelligible by considering the dynamical symmetries of the problem.

T-dualization of Gödel string cosmologies via Poisson–Lie T-duality approach

Using the homogeneous Gödel spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in $$\alpha '$$ α ′ including both dilaton and axion fields. We then discuss in detail the (non-)Abelian T-dualization of Gödel string cosmologies via the Poisson–Lie (PL) T-duality approach. In studying Abelian T-duality of the models we get seven dual models in such a way that they are constructed by one-, two- and three-dimensional Abelian Lie groups acting freely on the target space manifold. The results of our study show that the Abelian T-dual models are, under some of the special conditions, self-dual; moreover, by applying the usual rules of Abelian T-duality without further corrections, we are still able to obtain two-loop solutions. We also study the Abelian T-duality of Gödel string cosmologies up to $$\alpha '$$ α ′ -corrections by using the T-duality rules at two-loop order derived by Kaloper and Meissner. Afterwards, non-Abelian duals of the Gödel spacetimes are constructed by two- and three-dimensional non-Abelian Lie groups such as $$A_2$$ A 2 , $$A_2 \oplus A_1$$ A 2 ⊕ A 1 and $$SL(2, \mathbb {R})$$ S L ( 2 , R ) . In this way, the PL self-duality of $$AdS_3 \times \mathbb {R}$$ A d S 3 × R space is discussed.

Shopping value, trust, and online shopping well-being: a duality approach

PurposeBased on a duality approach, this study examines the path from utilitarian value via cognitive trust versus hedonic value via affective trust in online shopping well-being. This study also explores the moderating role of extraversion in the relationships between shopping value and trust.Design/methodology/approachA data set collected from 648 online consumers in Vietnam was used to validate the measures employing confirmatory factor analysis (CFA) and to test the hypotheses using structural equation modelling (SEM).FindingsThe results show that online shopping well-being is determined hedonically and affectively rather than in an utilitarian manner and cognitively. Affective trust positively contributes to online shopping well-being, but cognitive trust does not. The dual-process associations between utilitarian shopping value and cognitive trust and between hedonic shopping value and cognitive trust were also confirmed. Finally, extraversion moderates the cognitive and affective associations between shopping values and trust.Originality/valueThis study contributes to the literature on online shopping by applying a dual perspective to confirm the role of hedonic shopping value and affective trust in positively determining online shopping well-being. As a result, this study provides a deeper understanding about if and why online shopping well-being is affect-based, instead of cognition-based.