Abstract
A central issue in price competition with positive network effects is the potential for small price changes to trigger abrupt chain reactions, leading to market tipping, winner-take-all scenarios, and zero-profit equilibria. We show that in a duopoly where consumers are not anonymous but partitioned into at least two groups, a simple group-based network structure can, by itself, generate downward-sloping demand and support profitable shared-market equilibria. These are subgame-perfect pure price equilibria in which both firms earn strictly positive profit. Triggering a bandwagon effect and tipping the market remains possible, but requires aggressive price deviations, or price shocks, that produce demand jumps. However, this is not always profitable, and the fear of bankruptcy can be sufficient to stabilize firms in equilibrium. The result relies on having one group with centripetal influence (stronger impact on peers) and another with centrifugal influence (stronger impact on outsiders). It requires no additional sources of heterogeneity or product differentiation. This mechanism shows that positive network effects - when group structured - can endogenously generate stability in price competition. The analysis reconciles the coexistence of local stability and the potential for tipping, offering a unified explanation of how markets with strong network effects can sustain both competition and profitability. We draw a parallel to Turing's reaction-diffusion patterns and reinterpret Becker's intuition that social influence can produce stable outcomes, even when demand may exhibit upward-sloping segments.

Abstract
This study aims to understand the EU countries progress towards the Europe 2030 sustainable development goals (SDGs) in the areas of good health and well-being, gender equality and reduction of inequalities. Data for some indicators related to these areas were collected from the Eurostat database for the period 2010-2023. In order to analyze this three-way data, we first carried out a preliminary analysis through some graphical representations of the data, and then, we used a method of multivariate data analysis, Double Principal Component Analysis, which allows to identify which countries and/or indicators are close to or quite far from the targets. © 2026 Author(s).

Abstract

Abstract
Humour poses a unique challenge for artificial intelligence, as it often relies on non-literal language, cultural references, and linguistic creativity. The JOKER Lab, now in its fourth year, aims to advance computational humour research through shared tasks on curated, multilingual datasets, with applications in education, computer-mediated communication and translation, and conversational AI. This paper provides an overview of the JOKER Lab held at CLEF 2025, detailing the setup and results of its three main tasks: (1) humour-aware information retrieval, which involves searching a document collection for humorous texts relevant to user queries in either English or Portuguese; (2) pun translation, focussed on humour-preserving translation of paronomastic jokes from English into French; and (3) onomastic wordplay translation, a task addressing the translation of name-based wordplay from English into French. The 2025 edition builds upon previous iterations by expanding datasets and emphasising nuanced, manual evaluation methods. The Task 1 results show a marked improvement this year, apparently due to participants' judicious combination of retrieval and filtering techniques. Tasks 2 and 3 remain challenging, not only in terms of system performance but also in terms of defining meaningful and reliable evaluation metrics.

Abstract
City councils play a crucial role in local governance, directly influencing citizens’ daily lives through decisions made during municipal meetings. These deliberations are formally documented in meeting minutes, which serve as official records of discussions, decisions, and voting outcomes. Despite their importance, municipal meeting records have received little attention in Information Retrieval (IR) and Natural Language Processing (NLP), largely due to the lack of annotated datasets, which ultimately limit the development of computational models. To address this gap, we introduce CitiLink-Minutes, a multilayer dataset of 120 European Portuguese municipal meeting minutes from six municipalities. Unlike prior annotated datasets of parliamentary or video records, CitiLink-Minutes provides multilayer annotations and structured linkage of official written minutes. The dataset contains over one million tokens, with all personal identifiers de-identified. Each minute was manually annotated by two trained annotators and curated by an experienced linguist across four complementary dimensions: (1) personal information, (2) metadata, (3) subjects of discussion, and (4) voting outcomes, totaling over 38,000 individual annotations. Released under FAIR principles and accompanied by baseline results on metadata extraction, topic classification, and vote labeling, CitiLink-Minutes demonstrates its potential for downstream NLP and IR tasks, while promoting transparent access to municipal decisions.

Abstract
With the surge of multimodal models and the demand for effective image Information Retrieval (IR) systems, high-quality text-to-image datasets have become paramount. However, most existing datasets are primarily in English, limiting their applicability to multilingual settings. To address this, we introduce the pt-image-ir-dataset, a manually annotated resource for text-based Image IR in European Portuguese. The dataset comprises 80 diverse queries and a curated pool of 5,201 images, each annotated for relevance by multiple human judges. The proposed dataset is a step forward in supporting the development and evaluation of image IR systems for European Portuguese, addressing a clear gap in multilingual multimodal research. To this end, we have made our dataset publicly available, alongside baseline experimental results, demonstrating its suitability on the Image IR task across different retrieval paradigms, including traditional text-based lexical IR methods, semantic dense retrieval models based on language embeddings, cutting-edge vision-language models and proprietary black-box image retrieval systems. Results demonstrate that vision-language models, particularly OpenCLIP/xlm-roberta-base-ViT-B-32, significantly outperform other approaches (MRR = 0.610).