The mixed strategy equilibrium of the three-firm location game with discrete location choices

In the paper, we derive a symmetric MSE for the three-firm location game on the discrete strategy space. Rather than being uniformly distributed, the MSE for the game has a multimodal distribution. Our theory is more convincing to predict equilibria of three-firm location games in the real world or controlled experiments, where players face finitely many choices.mixed strategy equilibrium, multimodal distribution, discrete strategy space

From Common to Special: When Multi-Attribute Learning Meets Personalized Opinions

Visual attributes, which refer to human-labeled semantic annotations, have gained increasing popularity in a wide range of real world applications. Generally, the existing attribute learning methods fall into two categories: one focuses on learning user-specific labels separately for different attributes, while the other one focuses on learning crowd-sourced global labels jointly for multiple attributes. However, both categories ignore the joint effect of the two mentioned factors: the personal diversity with respect to the global consensus; and the intrinsic correlation among multiple attributes. To overcome this challenge, we propose a novel model to learn user-specific predictors across multiple attributes. In our proposed model, the diversity of personalized opinions and the intrinsic relationship among multiple attributes are unified in a common-to-special manner. To this end, we adopt a three-component decomposition. Specifically, our model integrates a common cognition factor, an attribute-specific bias factor and a user-specific bias factor. Meanwhile Lasso and group Lasso penalties are adopted to leverage efficient feature selection. Furthermore, theoretical analysis is conducted to show that our proposed method could reach reasonable performance. Eventually, the empirical study carried out in this paper demonstrates the effectiveness of our proposed method

Assessing (and Addressing) Reporting Heterogeneity in Visual Analogue Scales (VAS) with an Application to Gender Difference in Quality of Life

In this study, we propose several new methods to account for reporting heterogeneity in self-reported data coming from Visual Analogue Scales (VAS) using corresponding VAS-based anchoring vignettes. Compared to usual Likert scale measures, VAS have the advantage that they lead to more nuanced assessments. Yet, like responses to Likert scale, VAS may suffer from individual-specific reporting heterogeneity. To the best of our knowledge, such reporting heterogeneity and potential solutions to solve this problem in the context of VAS measures have not yet been addressed in the literature. Using VAS-based anchoring vignettes and standard vignettes assumptions (vignette equivalence and response consistency), we show how standard fixed-effect approaches and double-index models can be used to address individual-specific reporting heterogeneity in VAS. We also show that several other methods such as Generalized Ordered Response models and Hierarchical Ordered Probit (HOPIT) models can be used to meaningfully adjust for potential reporting heterogeneity under the weaker assumption that VAS responses should be interpreted as ordered rather than cardinal data. We then apply our methods to real data assessing gender differences in Quality of Life (QoL) among students in Switzerland. While female students report higher levels of QoL than male students -as commonly found in the literature- we also show that female students tend to rate the QoL of corresponding comparable anchoring vignettes higher than male students. Accounting for these gender differences in response behaviors, we show that female students actually appear to be worse off in terms of QoL than male students. This finding suggests that reporting heterogeneity may be important in assessing gender differences in QoL and that the commonly found female advantage in QoL assessments may at least be partially due to differences in reporting behavior

Familiarity-dependent computational modelling of indoor landmark selection for route communication: a ranking approach

Landmarks play key roles in human wayfinding and mobile navigation systems. Existing computational landmark selection models mainly focus on outdoor environments, and aim to identify suitable landmarks for guiding users who are unfamiliar with a particular environment, and fail to consider familiar users. This study proposes a familiarity-dependent computational method for selecting suitable landmarks for communicating with familiar and unfamiliar users in indoor environments. A series of salience measures are proposed to quantify the characteristics of each indoor landmark candidate, which are then combined in two LambdaMART-based learning-to-rank models for selecting landmarks for familiar and unfamiliar users, respectively. The evaluation with labelled landmark preference data by human participants shows that people’s familiarity with environments matters in the computational modelling of indoor landmark selection for guiding them. The proposed models outperform state-of-the-art models, and achieve hit rates of 0.737 and 0.786 for familiar and unfamiliar users, respectively. Furthermore, semantic relevance of a landmark candidate is the most important measure for the familiar model, while visual intensity is most informative for the unfamiliar model. This study enables the development of human-centered indoor navigation systems that provide familiarity-adaptive landmark-based navigation guidance