Maintaining Perfect Matchings at Low Cost

The min-cost matching problem suffers from being very sensitive to small changes of the input. Even in a simple setting, e.g., when the costs come from the metric on the line, adding two nodes to the input might change the optimal solution completely. On the other hand, one expects that small changes in the input should incur only small changes on the constructed solutions, measured as the number of modified edges. We introduce a two-stage model where we study the trade-off between quality and robustness of solutions. In the first stage we are given a set of nodes in a metric space and we must compute a perfect matching. In the second stage 2k new nodes appear and we must adapt the solution to a perfect matching for the new instance. We say that an algorithm is (alpha,beta)-robust if the solutions constructed in both stages are alpha-approximate with respect to min-cost perfect matchings, and if the number of edges deleted from the first stage matching is at most beta k. Hence, alpha measures the quality of the algorithm and beta its robustness. In this setting we aim to balance both measures by deriving algorithms for constant alpha and beta. We show that there exists an algorithm that is (3,1)-robust for any metric if one knows the number 2k of arriving nodes in advance. For the case that k is unknown the situation is significantly more involved. We study this setting under the metric on the line and devise a (10,2)-robust algorithm that constructs a solution with a recursive structure that carefully balances cost and redundancy

Project-Fair and Truthful Mechanisms for Budget Aggregation

We study the budget aggregation problem in which a set of strategic voters must split a finite divisible resource (such as money or time) among a set of competing projects. Our goal is twofold: We seek truthful mechanisms that provide fairness guarantees to the projects. For the first objective, we focus on the class of moving phantom mechanisms [Freeman et al., 2021], which are -- to this day -- essentially the only known truthful mechanisms in this setting. For project fairness, we consider the mean division as a fair baseline, and bound the maximum difference between the funding received by any project and this baseline. We propose a novel and simple moving phantom mechanism that provides optimal project fairness guarantees. As a corollary of our results, we show that our new mechanism minimizes the $\ell_1$ distance to the mean (a measure suggested by Caragiannis et al. [2022]) for three projects and gives the first non-trivial bounds on this quantity for more than three projects

Investigating the Relationship Between User Ratings and Gamification – A Review of mHealth Apps in the Apple App Store and Google Play Store

Gamification of mHealth apps is regarded as a promising approach to counteract decreasing long-term motivation of mHealth app users. Although gamification has received tremendous attention from researchers interested in mHealth apps, little is known about the extent to which gamification is used in real world mHealth apps today and whether the implementation of gamification actually pays off for app developers by, for example, positively influencing user ratings. Within this research, we investigate the implementation of game mechanics for 1,000 apps from the Apple App Store and Google Play Store as well as the potential relationship between the degree of gamification of mHealth apps and their user ratings. While our results highlight a high degree of adoption of gamification for both app stores, they also indicate a positive relationship between the degree of gamification of an mHealth app and user ratings for the Apple App Store only

Conceptualizing Narratives in Gamified Information Systems

Converging hedonic and utilitarian elements under the label of gamification has become an important phenomenon in information systems over the last decade. Yet, academic discourse on narratives in gamified IS remains scarce. To advance scholarly engagement, this study recontextualizes the concept of narratives for gamified IS. Based on the theoretical lens of hedonic and utilitarian consumption, we conducted a hermeneutic literature review in which we engaged with existing conceptualizations of narratives in a total of 84 studies across various disciplines. Results include a basic conceptualization of narratives complemented by six claims that may shape our way of thinking about narratives in gamified IS. Our findings contribute to a more comprehensive understanding of narratives in gamified IS that goes beyond that of traditional game elements. It may serve as a cornerstone for further discourse on narratives and how to meaningfully design them in gamified IS