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Complexity Digest
June 21, 2:33 PM
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By Mikhail Burtsev, Yang-Hui He, Evgeny Sobko, Ananyo Bhattacharya & Thore Graepel Artificial intelligence is not replacing human intuition in these fields, but reimagining how questions are asked, explored and understood. Read the full article at: www.nature.com
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Complexity Digest
June 20, 2:36 PM
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Arthur Montanari, Ana Elisa Barioni, and Adilson Motter In a murmuration of starlings, abrupt evasive maneuvers from a few birds in response to a passing falcon can trigger a collective response across the whole group. Within a fraction of a second, local turns are amplified through thousands of neighboring interactions between birds, and the entire flock twists and folds as if it were a single organism. During the annual northbound migration of sardines along the coast of South Africa, dense schools rapidly reorganize into spinning bait balls when dolphins approach, using collective geometry to confuse predators and dilute individual risk. On land, herds of millions of wildebeest coordinate traveling direction and timing across open plains and narrow passages during their yearly migration throughout the Serengeti. Desert locusts also march across long distances in the Sahel and Arabian Peninsula, producing vast swarms that move as a unit when tactile stimulation and high population density trigger a phase transition from individualistic to coordinated behavior in the form of rolling waves. Read the full article at: www.siam.org
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Complexity Digest
June 17, 2:34 PM
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Melanie Mitchell A new term has been coined to describe AI in its current form: “jagged intelligence.” The term captures the fact that the landscape of AI capabilities is profoundly uneven: the tools demonstrate excellent abilities on certain problems but surprising failures on other similar problems. For humans, one kind of skill can often predict abilities at similar skills; this is not the case in the jagged landscape of AI. Last fall, Ilya Sutskever, a cofounder of OpenAI, argued that there are no easy fixes to this problem: “These models somehow just generalize dramatically worse than people. It’s a very fundamental thing.” Read the full article at: yalereview.org
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Complexity Digest
June 16, 2:40 PM
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Mikhail Prokopenko, Nihat Ay, Angelica Breviario, Roland M. Crocker, Paul C. W. Davies, Pauline Davies, Darren Dougan, Roland Fletcher, Michael Harré, Marcus G. Heisler, Zdenka Kuncic, Geraint F. Lewis, Ori Livson, Vivienne Reiner, Jaime Ruiz Serra The Great Filter hypothesis proposes that the emergence of technological societies capable of interstellar travel depends on a small number of exceptionally hard and highly improbable steps. Traditional versions of this hypothesis enumerate such "hard steps" along the trajectory from inanimate matter to complex technological societies, but diverge in their explanations for why these particular steps should be so improbable. The theory of Major Evolutionary Transitions also faces challenges in identifying which steps should be considered universally "hard" across different evolutionary pathways. In contrast, we argue that two deeply structural obstacles dominate the evolutionary landscape: the coding threshold associated with the origin of the genetic code, and the language threshold associated with the emergence of symbolic communication. We examine the developmental precursors of both transitions and analyze the underlying algorithmic bottlenecks: points at which evolving systems separate code from function, while entangling them within information hierarchies. Using a game-theoretic analysis of coupled signaling and coordination dynamics, we then argue that the corresponding multichannel games exhibit unstable equilibria that render the transitions intrinsically difficult. We conjecture that the so-called Great Filter is best understood not as a sequence of isolated improbable events, but as a nested structure of tangled information hierarchies. Under this interpretation, the rarity of advanced societies follows from the difficulty of crossing these coding thresholds in a competitive noisy environment. This perspective reframes the Great Filter as an algorithmic property of evolving systems, highlighting why only a vanishingly small fraction of life may ever traverse the path toward technological societies capable of interstellar travel. Read the full article at: arxiv.org
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Complexity Digest
May 29, 8:43 PM
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Mateo Bouchet, Alejandro Tejedor, Xiangrong Wang, and Yamir Moreno Phys. Rev. Lett. 136, 207401 We study diffusion on multiplex networks with directed interlayer couplings. We demonstrate both numerically and analytically that even with undirected layers, interlayer directionality alone reproduces superdiffusion and the prime regime. We further reveal a new phenomenon, the directionality-induced jamming, whereby directed interlayer links hinder diffusion, fragmenting the system into dynamically disconnected components and preventing convergence to the steady state of the diffusion process. Via an optimization process, we show that this new regime is attainable in both toy models and real-world topologies. These findings underscore the crucial role of interlayer link directionality in shaping the emergent behavior of multiplex systems, with potential implications for the design and control of such systems. Read the full article at: journals.aps.org
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Complexity Digest
May 29, 2:47 PM
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Klaus Jaffe Money serves several roles: a medium of exchange to buy and sell without bartering; a unit of account to price goods consistently; a store of value to save purchasing power over time; a means to defer payment of future obligations like credit or loans. An agent based computer simulation program determine quantitatively the relative importance of these services. The main results showed that money for credit was by far the feature that achieved the largest overall production of wealth in the simulated societies. A conclusion from this study suggests that fomenting the use of internationally tradable currencies such as Bitcoin seems to be most promising pathway for international economic growth in the near future. Read the full article at: papers.ssrn.com
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Complexity Digest
May 13, 10:42 AM
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C. Marchuk, L. Ríos, A. González, S. González, G. Pereira and C. von Lücken, "A Computational Economic Complexity Model for Regional Economic Integration: Analysis of the EU, MERCOSUR, URUPABOL, and the AndeanCommunity," 2025 IEEE CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (CHILECON), Valparaíso, Chile, 2025, pp. 1-8, doi: 10.1109/CHILECON66915.2025.11476476. Regional Economic Integration is a process by which countries seek mutual benefits through the reduction of trade, social, and political barriers. This paper introduces a computational mathematical model grounded in Economic Complexity Theory to analyze economic blocs as unified entities. Four case studies are examined: the European Union, MERCOSUR, URUPABOL, and the Andean Community. Using real export data and complexity metrics, we identify the combined productive capacities of member countries. Results reveal that integration enhances product diversity and increases the ubiquity of exports within the bloc. The study demonstrates that regional integration boosts development and strengthens competitiveness in the global economy. The proposed methodological approach provides a novel tool for regional analysis and serves as a foundation for future strategies in economic cooperation and productive planning. This research contributes to understanding how collective capabilities can generate synergies that exceed individual national potentials, particularly in the context of Latin American regional development. Read the full article at: ieeexplore.ieee.org
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Complexity Digest
May 3, 10:26 AM
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The universe creatively sets the rules for its own becoming. Stuart Kauffman is a theoretical biologist and leading complexity scientist who has argued that the self-organization of organisms is as influential in evolution as natural selection. His seminal book on the subject is “The Origins of Order: Self-Organization and Natural Selection in Evolution” (1993). He spoke recently with Noema Editor-in-Chief Nathan Gardels. Read the full article at: www.noemamag.com
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Complexity Digest
May 1, 3:34 PM
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Reda Benkirane Complex Systems, 34(4), 2026 pp. 387–400. Complexity, a term that is both ambiguous and multifaceted, is used widely today. Various legitimate definitions can be proposed for it, as is the case with “ample” notions such as intelligence, consciousness or culture. The recurrent mention of this term can be attributed to the transformation of our societies and their artifacts, as well as the acceleration of time brought by the digital revolution—a technological upheaval comparable to the invention of writing and the printing press. Read the full article at: www.complex-systems.com
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Complexity Digest
April 30, 1:46 PM
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Lluís Danús, William Dinneen, Carolina Torreblanca, Guy Grossman, and Sandra González-Bailón PNAS 123 (18) e2511050123 The term “invisible college” refers to communication networks that help scientists exchange information and advance knowledge. These networks create social capital, granting access to resources like new ideas and support. Measuring those intangible exchanges is an empirical challenge. Here we approximate these ties through the analysis of the “thank you” notes appended to journal articles. Our findings show that scholars disconnected from this layer of academic social capital have lower publication impact. We also show that informal ties provide support not captured by coauthorship ties, which reflect a more rigid form of collaboration. Documenting how informal structures of support operate can help leverage collective resources in the pursuit of shared intellectual goals. Read the full article at: www.pnas.org
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Complexity Digest
April 29, 1:42 PM
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Luis A. Nunes Amaral; Arthur Capozzi; Dirk Helbing
R Soc Open Sci. (2026) 13 (4): 251727 . Organizations learn from market, political and societal responses to their actions. While in some cases both the actions and responses take place in an open manner, in many others, some aspects may be hidden from external observers. The Eurovision Song Contest offers a mostly open-data case in which to study organizational level learning at the levels of organizers and participants. We present here evidence for changes in the rules of the Contest in response to undesired outcomes such as runaway winners. We also find strong evidence of participant learning in the characteristics of competing songs over the 70 years of the Contest. English has been adopted as the lingua franca of the competing songs and pop has become the standard genre. The number of words of lyrics has also grown in response to this collective learning. Remarkably, we find evidence that France, Italy, Portugal and Spain have chosen to ignore the ‘lesson’ that English lyrics increase winning probability, consistent with utility functions that award greater value to featuring national culture than to winning the Contest. These countries—but not Germany—appear to be less susceptible to Anglo-Saxon cultural influence than their peers, a resistance that may extend beyond cultural matters. Read the full article at: royalsocietypublishing.org
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Complexity Digest
April 11, 11:12 AM
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JÉRÔME M. W. GIPPET, COLIN J. CARLSON, TRISTAN KLAFTENBERGER, MATTÉO SCHWEIZER, EVAN A. ESKEW, MEREDITH L. GORE, AND CLEO BERTELSMEIER SCIENCE 9 Apr 2026 Vol 392, Issue 6794 pp. 178-182 The wildlife trade affects a quarter of terrestrial vertebrates and creates opportunities for cross-species pathogen transmission, but its precise role in shaping animal-human pathogen exchange remains unclear. In our analysis of 40 years of global wildlife trade data, we show that traded mammals are 1.5-fold as likely to share pathogens with humans as nontraded mammals, and that illegal and live-animal trade further exacerbate pathogen sharing. Time spent in trade predicts the number of zoonotic pathogens that a wildlife species hosts. On average, a species shares an additional pathogen with humans for every 10 years it is traded. Read the full article at: www.science.org
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Complexity Digest
April 7, 12:11 PM
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Kishore Vasan, Márton Karsai & Albert-László Barabási
Scientific Reports The metaverse is a virtual space enabling interactions beyond geographical boundaries, promising to transform how people engage with each other both in the digital and the physical worlds. The lack of geographical boundaries and travel costs in the metaverse prompts us to ask if the fundamental laws that govern human mobility in the physical world apply. We collected data on avatar movements from Decentraland, along with their network mobility extracted from NFT purchases on Ethereum and Polygon. We find that despite the absence of mobility costs, an individual’s inclination to visit new locations diminishes over time, limiting movement to a small fraction of the metaverse. We also find a lack of correlation between land prices and visitation, a deviation from the patterns characterizing the physical world. Finally, we identify the scaling laws that characterize meta mobility and show that we need to add preferential selection to the existing models to explain quantitative patterns of metaverse mobility. Our ability to predict the characteristics of the emerging meta mobility network implies that the laws governing human mobility are rooted in fundamental patterns of human dynamics, rather than the nature of space and cost of movement. Read the full article at: www.nature.com
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Complexity Digest
June 21, 10:38 AM
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Guido Caldarelli, Oriol Artime, Giulia Fischetti, Stefano Guarino, Andrzej Nowak, Fabio Saracco, Petter Holme, Manlio De Domenico Physics Reports Volume 1186, 5 August 2026, Pages 1-75 The boundaries between physical and social networks have narrowed with the advent of the Internet and its pervasive platforms. This has given rise to a complex adaptive information ecosystem where individuals and machines compete for attention, leading to emergent collective phenomena. The flow of information in this ecosystem is often non-trivial and involves complex user strategies—from the forging or strategic amplification of manipulative content to large-scale coordinated behavior—that trigger misinformation cascades, echo-chamber reinforcement, and opinion polarization. We argue that statistical physics provides a suitable and necessary framework for analyzing the unfolding of these complex dynamics on socio-technological systems. This review systematically covers the foundational and applied aspects of this framework. The review is structured to first establish the theoretical foundation for analyzing these complex systems, examining both structural models of complex networks and physical models of social dynamics (e.g., epidemic and spin models). We then ground these concepts by describing the modern media ecosystem where these dynamics currently unfold, including a comparative analysis of platforms and the challenge of information disorders. The central sections proceed to apply this framework to two central phenomena: first, by analyzing the collective dynamics of information spreading, with a dedicated focus on the models, the main empirical insights, and the unique traits characterizing misinformation; and second, by reviewing current models of opinion dynamics, spanning discrete, continuous, and coevolutionary approaches. In summary, we review both empirical findings based on massive data analytics and theoretical advances, highlighting the valuable insights obtained from physics-based efforts to investigate these phenomena of high societal impact. Read the full article at: www.sciencedirect.com
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Complexity Digest
June 19, 2:33 PM
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Fabio Oddi, Federico Naldini, Leo D'Amato, Grégory Marlière, Paola Pellegrini, Vito Trianni Recent research is exploring self-organised traffic management as a solution for scaling to complex real-world networks. In such a system, trains predict their neighbourhood, produce traffic plan hypotheses, and agree via consensus with neighbours on a future traffic plan to be implemented. This paper investigates a structural parameter within this pipeline: the predictive neighbourhood horizon. The horizon is used by trains to identify future potential conflicts with neighbours, and to establish the local interaction topology, that is, the subset of trains to negotiate with. As the primary design variable, the horizon directly determines the size and density of the social interaction graph, whereas its impact on the complexity of local sub-problems and the distributed consensus dynamics represents a trade-off to be explored. Through a closed-loop simulation framework the study evaluates how variations of the horizon impact the overall decentralised coordination process, from initial conflict detection to distributed schedule consensus. The analysis focuses on investigating the potential trade-off introduced by the horizon choice: balancing local tractability and computational responsiveness with the need for global schedule coherence and feasibility in safety-critical environments. Contrary to intuition, our empirical results indicate that the short time horizons suffice, while long values compromise local tractability and computational responsiveness with no gain in global schedule optimality. Read the full article at: arxiv.org
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Complexity Digest
June 17, 1:38 PM
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Henrique Ferraz de Arruda, Andreia Sofia Teixeira, Pranay Gundala Reddy, Anindya Mondal, Kleber Andrade Oliveira, Filipi Nascimento Silva Despite raising concerns about the mental health effects associated with the usage of TikTok, little is known about how related content is framed by creators and received by audiences. We collect the content of 28,341 TikTok videos and 80,130 comments from Mental Health Awareness Month (May) in 2023 and 2024 via the TikTok Research API, and study how the tone of awareness varies across topics and years. We characterize "tone" as the emotional and interpersonal framing of mental health discourse, operationalized through sentiment and toxicity measures. We extract topics from video text using BERTopic and log-odds keywords, then quantify topic-conditioned sentiment (XLM-T) and toxicity (Detoxify) separately for video transcriptions and comments. Sentiment captures the affective valence of content, while toxicity reflects the presence of harmful or abusive language. We find a stable set of recurring themes across years, spanning clinical conditions, emotional disclosure, self-care, and campaign-oriented content, with engagement highly skewed toward a small subset of topics. All sentiment and toxicity analyses are computed separately for video content and comments, allowing us to distinguish between content production and audience reception. Sentiment in videos is often negative for emotionally charged topics, while comments tend to shift toward more mixed or positive polarity, especially for suicide prevention. Toxicity is low in median overall, but exhibits longer-tailed outliers in comments than in videos that are more pronounced in comments and concentrated in specific topics (e.g., "Duet", "Suicide Prevention", and "Psychisch"). Overall, our results provide a topic-level decomposition of mental health discourse on TikTok during awareness-month campaigns. Read the full article at: arxiv.org
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Complexity Digest
May 30, 3:40 PM
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Takashi Ikegami, Hiroki Kojima, and Akiko Kashiwagi Entropy 2026, 28(5), 523 Collective systems often exhibit emergent behaviors that cannot be reduced to the properties of individual components. A central question is whether individuality itself is a precondition for collective organization, or whether it arises from it. Here we develop and empirically test Community First Theory, which proposes that collective organization is the generative substrate from which individual dynamical identity emerges. To operationalize this claim, we introduce non-trivial information closure (NTIC), which quantifies whether an individual’s temporal predictability is self-determined or distributed across collective relations. Using high-resolution tracking of complete Tetrahymena populations across four generations, we show that information closure emerges transiently in the middle phase of the cell cycle, flanked by strong collective coupling. Cells in the information-closed regime show significantly greater divergence from parental phenotypes, demonstrating that community organization actively generates behavioral diversity. These results provide initial empirical support for Community First Theory in a single-model system and suggest that NTIC offers a substrate-independent tool for locating agency transitions in collective systems. Read the full article at: www.mdpi.com
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Complexity Digest
May 29, 3:47 PM
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Rebecca Carstens, Raj Deshpande, Pau Esteve, Nicoló Fidelibus, Sara Linde Neven, Ramona Ottow, Lokamruth K.R., Paula Rodríguez-Sánchez, Luca Santagata, Javier M. Buldú, Brennan Klein & Maddalena Torricelli
Scientific Reports (2026) Elite football is believed to have evolved in recent years, yet systematic evidence for the pace and form of that change remains sparse. Drawing on event-level records for 13,018 matches across ten top-tier men’s and women’s leagues in England, Spain, Germany, Italy, and the United States (2020–2025), we quantify match dynamics through two complementary lenses: conventional performance statistics and pitch-passing networks that track ball movement across spatial regions of the field. Between 2020 and 2025, average passing volume, pass accuracy, and the proportion of passes made under pressure all increased, with the largest year-on-year changes occurring in women’s competitions. Network measures reveal that normalized outreach decreased, indicating teams increasingly concentrate ball circulation into shorter-range passing connections rather than wide spatial distribution. These trends are consistent across countries and tiers, yet persistent national differences indicate that stylistic diversity remains. Notably, women’s competitions exhibit stronger rates of change across most metrics, consistent with an accelerating professionalization, while the systematic decline in network outreach across all competitions is consistent with a sport-wide shift toward shorter, more concentrated passing structures. Read the full article at: www.nature.com
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Complexity Digest
May 16, 10:13 AM
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Qianyang Chen, Mikhail Prokopenko Active matter generates order or patterns through nonequilibrium dynamics. An open research challenge is to determine how efficiently a nonequilibrium self-organising system can convert consumed energy into macroscopic order. We study an information-theoretic quantity that directly addresses this challenge by estimating the entropy reduction induced by a small control-parameter perturbation, relative to the generalised work required for the perturbation. This quantity has previously been considered mainly in an equilibrium or near-equilibrium context, and here we extend this framework and apply it to two nonequilibrium self-organising systems: persistent and active Ising models. We observe that the thermodynamic efficiency of nonequilibrium systems maximises at phase transitions, as in equilibrium systems. Furthermore, we compare thermodynamic efficiency and inferential efficiency across control parameters. While these two quantities are equal in equilibrium as a consequence of the fluctuation-dissipation theorem, we report that they diverge out of equilibrium, and the gap reflects how far the system is from equilibrium. Read the full article at: arxiv.org
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Complexity Digest
May 11, 10:50 AM
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Mario Franco & Carlos Gershenson
Front. Artif. Intell., Volume 9 - 2026 Nowadays, neural networks act as a synonym for artificial intelligence. Present neural network models, although remarkably powerful, are inefficient both in terms of data and energy. Several alternative forms of neural networks have been proposed to address some of these problems. Specifically, spiking neural networks are suitable for efficient hardware implementations. However, effective learning algorithms for spiking networks remain elusive, although it is suspected that effective plasticity mechanisms could alleviate the problem of data efficiency. Here, we present a new framework for spiking neural networks—Spark (https://github.com/Nogarx/Spark)—built upon the idea of modular design, from simple components to entire models. The aim of this framework is to provide an efficient and streamlined pipeline for spiking neural networks. We showcase this framework by solving the sparse-reward cartpole problem with simple plasticity mechanisms. We hope that a framework compatible with traditional ML pipelines may accelerate research in the area, specifically for continuous and unbatched learning, akin to the one animals exhibit Read the full article at: www.frontiersin.org
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Complexity Digest
May 2, 10:32 AM
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Alberto Aleta, Andreia Sofia Teixeira, Guilherme Ferraz de Arruda, Andrea Baronchelli, Alain Barrat, János Kertész, Albert Díaz-Guilera, Oriol Artime, Michele Starnini, Giovanni Petri, Márton Karsai, Siddharth Patwardhan, Kathryn Coronges, Ann McCranie, Alessandro Vespignani, Yamir Moreno, Santo Fortunato Journal of Complex Networks, Volume 14, Issue 2, April 2026, cnag007, Multilayer network science has emerged as a central framework for analysing interconnected and interdependent complex systems. Its relevance has grown substantially with the increasing availability of rich, heterogeneous data, which makes it possible to uncover and exploit the inherently multilayered organisation of many real-world networks. In this review, we summarise recent developments in the field. On the theoretical and methodological front, we outline core concepts and survey advances in community detection, dynamical processes, temporal networks, higher-order interactions, and machine-learning-based approaches. On the application side, we discuss progress across diverse domains, including interdependent infrastructures, spreading dynamics, computational social science, economic and financial systems, ecological and climate networks, science-of-science studies, network medicine, and network neuroscience. We conclude with a forward-looking perspective, emphasizing the need for standardised datasets and software, deeper integration of temporal and higher-order structures, and a transition toward genuinely predictive models of complex systems. Read the full article at: academic.oup.com
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Complexity Digest
May 1, 10:31 AM
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Adam B. Barrett, Borjan Milinkovic, Pedro A. M. Mediano, Fernando E. Rosas, Daniel Bor, Lionel Barnett, Anil K. Seth The integrated information theory of consciousness (IIT) is uniquely ambitious in proposing a mathematical formula, derived from apparently fundamental properties of conscious experience, to describe the quantity and quality of consciousness for any physical system that possesses it. IIT has generated considerable debate, which has engendered some misunderstandings and misrepresentations. Here we address and hope to remedy this. We begin by concisely summarising the essentials of IIT. Given IIT is supposed to apply universally, we do this with reference to an arbitrary patch of matter, as opposed to the usual system of discrete computational units. Then, after briefly summarising IIT's theoretical and empirical achievements, we focus on five points which we consider especially important for driving forward new theory and increasing understanding. First, a high value of the measure Φ is not synonymous with `more consciousness'. We describe how Φ might be replaced with a suite of quantities to obtain a multi-dimensional characterisation of states of consciousness. Second, we describe with nuance the distinct flavour of panpsychism implied by IIT -- whereby space (and time) are tiled with substrates of (proto-) consciousness -- and find this is not problematic for the theory. Third, Φ is not well-defined for real physical systems, and has not been computed on any real physical system. Fourth, so far only proxies for IIT measures have been computed, and not approximations. Fifth, for IIT to fit with current successful theories in fundamental physics, a reformulation in terms of continuous fields would be needed. Read the full article at: arxiv.org
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Complexity Digest
April 29, 2:35 PM
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Yasuhiro Hashimoto, Hiroki Sato, and Takashi Ikegami Entropy 2026, 28(4), 398
Social media platforms offer unprecedented opportunities to study cultural evolution by analyzing digital traces. This study presents a methodological framework for analyzing the temporal dynamics of cultural modules in hashtag co-occurrence networks. We address the inherent challenges of analyzing dense, skewed, and highly variable cultural networks by introducing a perturbation ensemble clustering approach that distinguishes stable from unstable structural elements. By applying the Leiden algorithm to a perturbed ensemble of hashtag networks, we identify robust core modules and their stable periphery, and distinguish them from floating elements with unstable associations. Analysis of four years of data from a major photo-sharing platform reveals complex patterns in the evolution of cultural modules, including both stable associations and dynamic reorganizations. Our findings demonstrate how ensemble clustering techniques can effectively capture the interplay between stability and change in evolving cultural systems.
Read the full article at: www.mdpi.com
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Complexity Digest
April 29, 11:04 AM
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Tetsushi Ohdaira Chaos, Solitons & Fractals
Volume 208, Part 4, July 2026, 118382 This study modifies the model in the previous studies and considers three types of inter-individual relationships: regular, random, and scale-free ring lattices. Furthermore, we introduce defectors, who do not contribute to the public goods; cooperators, who contribute to the public goods; and loners, who do not participate in the public goods framework. We assume that each of these three types of individuals punishes other individuals with a probability proportional to the difference between their own payoff and their opponent's average payoff including them. Using this modified pool punishment model, this study shows the following. Firstly, the damage to the average payoff due to excessive punishment is kept significantly low. Secondly, antisocial punishment is not evolutionarily advantageous, and cooperators always become advantageous. Finally, the final average payoff is always higher than that of pool punishment in existing studies and roughly comparable to that of peer punishment in existing studies. The results of this study provide new insights that the claim of the existing study is not always correct; that is, even if antisocial punishment is possible, it does not have an evolutionary advantage, and cooperators always become advantageous, which in turn solves the problem of antisocial punishment. This study is being conducted as part of efforts to improve specialized education at Kanagawa Institute of Technology. Read the full article at: www.sciencedirect.com
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April 7, 4:07 PM
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Tim Pollmann and Jochen Staudacher Complexities 2026, 2(1), 7
Shapley values are the most widely used point-valued solution concept for cooperative games and have recently garnered attention for their applicability in explainable machine learning. Due to the complexity of Shapley value computation, users mostly resort to Monte Carlo approximations for large problems. We take a detailed look at an approximation method grounded in multilinear extensions proposed in 2021 under the name “Owen sampling”. We point out why Owen sampling is biased and propose unbiased alternatives based on combining multilinear extensions with stratified sampling and importance sampling. Finally, we discuss empirical results of the presented algorithms for various cooperative games, including real-world explainability scenarios.
Read the full article at: www.mdpi.com
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