搜索结果：Rivals

As generative AI commercializes, competitive advantage is shifting from model training toward inference, distribution, and routing. This paper develops a formal game-theoretic model of vertical foreclosure in inference markets, as the formal-model companion to Besanson and Celani (2026). The model isolates two foreclosure mechanisms operating without predatory pricing: quality-of-service (QoS) discrimination against downstream rivals via latency, throughput, context limits, or feature access; and routing bias in assistant-layer interfaces. An extension motivated by Anthropic's April 2026 release of Claude Opus 4.7 alongside the restricted-access Claude Mythos Preview introduces a third mechanism, tier-based access discrimination, parameterized by a tier gap (tau) and partner-exclusivity (kappa). The main result gives an explicit local equilibrium characterization of the QoS gap. Under logit demand and symmetric rivals, the gap is strictly increasing in inference-quality importance (alpha) and downstream margins, and strictly decreasing in API price and rival entry elasticity. Discrimination vanishes at a joint boundary rather than at a simple threshold in alpha alone. A stylized ca

We study competitive dynamic pricing among multiple sellers, motivated by the rise of large-scale experimentation and algorithmic pricing in retail and online marketplaces. Sellers repeatedly set prices using simple learning rules and observe their own realized demand, while possibly observing only a subset of rivals' prices, even though demand depends on all sellers' prices and is subject to random shocks. Each seller runs local price experiments, such as switchback-style designs, and updates a focal price using a linear demand estimate fitted to its own demand data and the competitor prices it observes. Under certain conditions on demand, the resulting dynamics converge to a Conjectural Variations (CV) equilibrium, a classic static equilibrium notion in which each seller best responds under a conjecture that rivals' prices co-move systematically to changes in its own price. Unlike standard CV models that treat conjectures as behavioral primitives, we show that these conjectures arise endogenously from the interaction between the feedback structure and the correlation structure of experimentation. When a seller does not observe some rivals' prices, correlated experimentation induc

Lepton flavor violation in the $τμ$ sector would be a clear sign of Beyond Standard Model physics. We employ the SMEFT framework to study the process $e^+e^-\toτμ$ at the ILC and CLIC. We find that the $e^+e^-$ beam polarizations achievable at these machines allow us to probe the chirality structure of the SMEFT operators. In addition, the high center of mass energy leads to a substantial increase in sensitivity to the four-fermion operators that rivals, and in some cases, surpasses tau decay projections from Belle-II.

We study a sequential price competition among $N$ sellers, each influenced by the pricing decisions of their rivals. Specifically, the demand function for each seller $i$ follows the single index model $λ_i(\mathbf p) = μ_i(\langle \boldsymbol θ_{i,0}, \mathbf p \rangle)$, with known increasing link $μ_i$ and unknown parameter $\boldsymbol θ_{i,0}$, where the vector $\mathbf{p}$ denotes the vector of prices offered by all the sellers simultaneously at a given instant. Each seller observes only their own realized demand - unobservable to competitors - and the prices set by rivals. We propose a novel decentralized policy, PML-GLUCB, that combines penalized MLE with an upper-confidence pricing rule. Our approach (i) \emph{removes the need for coordinated front-loaded exploration phases across sellers} - which is integral to previous models - making our method aligned with realistic market conditions; (ii) generalizes existing approaches that focus solely on linear demand models; (iii) accommodates both binary and real-valued demand observations. Relative to a dynamic benchmark policy, each seller achieves $\widetilde{O}(\sqrt{T})$ regret, which matches the optimal rate known in the li

RNA design aims to identify RNA sequences that fold into a target secondary structure. This task is challenging in terms of computational efficiency. Most existing methods focus on either minimum free energy (MFE)-based or ensemble-based metrics, leaving a gap for a unified approach that performs well across both. We introduce a fast and versatile RNA design algorithm inspired by our previous work on the undesignability of RNA structures and motifs (i.e., sets of contiguous structural loops). Our approach decomposes a target structure into a tree of sub-targets where each leaf node corresponds to a motif and each internal node corresponds to a substructure. We first design partial sequences for each motif, then these partial sequences are selectively and recursively combined via the cube pruning strategy borrowed from computational linguistics, enabling effective optimization of ensemble-based metrics. Finally, a novel whole-structure rival search further refines sequences to suppress misfolded alternatives and enhance MFE-based performance. Our method is highly efficient and also achieves state-of-the-art results on native RNAsolo structures and the Eterna100 benchmark, excelling

Biological and social scientists have long been interested in understanding how to reconcile individual and collective interests in iterated Prisoner's Dilemma. Many effective strategies have been proposed, and they are often categorized into one of two classes, `partners' and `rivals.' More recently, another class, `friendly rivals,' has been identified in longer-memory strategy spaces. Friendly rivals qualify as both partners and rivals: They fully cooperate with themselves, like partners, but never allow their co-players to earn higher payoffs, like rivals. Although they have appealing theoretical properties, it is unclear whether they would emerge in evolving population because most previous works focus on memory-one strategy space, where no friendly rival strategy exists. To investigate this issue, we have conducted large-scale evolutionary simulations in well-mixed and group-structured populations and compared the evolutionary dynamics between memory-one and memory-three strategy spaces. In a well-mixed population, the memory length does not make a major difference, and the key factors are the population size and the benefit of cooperation. Friendly rivals play a minor role b

Graph neural networks (GNNs) are widely believed to excel at node representation learning through trainable neighborhood aggregations. We challenge this view by introducing Fixed Aggregation Features (FAFs), a training-free approach that transforms graph learning tasks into tabular problems. This simple shift enables the use of well-established tabular methods, offering strong interpretability and the flexibility to deploy diverse classifiers. Across 14 benchmarks, well-tuned multilayer perceptrons trained on FAFs rival or outperform state-of-the-art GNNs and graph transformers on 12 tasks -- often using only mean aggregation. The only exceptions are the Roman Empire and Minesweeper datasets, which typically require unusually deep GNNs. To explain the theoretical possibility of non-trainable aggregations, we connect our findings to Kolmogorov-Arnold representations and discuss when mean aggregation can be sufficient. In conclusion, our results call for (i) richer benchmarks benefiting from learning diverse neighborhood aggregations, (ii) strong tabular baselines as standard, and (iii) employing and advancing tabular models for graph data to gain new insights into related tasks.

The non-rival nature of data creates a dilemma for firms: sharing data unlocks value but risks eroding competitive advantage. Existing data synthesis methods often exacerbate this problem by creating data with symmetric utility, allowing any party to extract its value. This paper introduces the Encapsulation-Forging (EnFo) framework, a novel approach to generate rival synthetic data with asymmetric utility. EnFo operates in two stages: it first encapsulates predictive knowledge from the original data into a designated ``key'' model, and then forges a synthetic dataset by optimizing the data to intentionally overfit this key model. This process transforms non-rival data into a rival product, ensuring its value is accessible only to the intended model, thereby preventing unauthorized use and preserving the data owner's competitive edge. Our framework demonstrates remarkable sample efficiency, matching the original data's performance with a fraction of its size, while providing robust privacy protection and resistance to misuse. EnFo offers a practical solution for firms to collaborate strategically without compromising their core analytical advantage.

Large language models (LLMs) possess strong multilingual capabilities, and combining Reinforcement Learning from Human Feedback (RLHF) with translation tasks has shown great potential. However, we observe that this paradigm performs unexpectedly poorly when applied to colloquial subtitle translation tasks. In this work, we investigate this issue and find that the offline reward model (RM) gradually diverges from the online LLM due to distributional shift, ultimately leading to undesirable training outcomes. To address this, we propose RIVAL, an adversarial training framework that formulates the process as a min-max game between the RM and the LLM. RIVAL iteratively updates the both models, with the RM trained to distinguish strong from weak translations (qualitative preference reward), and the LLM trained to enhance its translation for closing this gap. To stabilize training and improve generalizability, we also incorporate quantitative preference reward (e.g., BLEU) into the RM, enabling reference-free quality modeling aligned with human evaluation. Through extensive experiments, we demonstrate that the proposed adversarial training framework significantly improves upon translatio

This paper explores vision-based localization through a biologically-inspired approach that mirrors how humans and animals link views or perspectives when navigating their world. We introduce two sequential generative models, VAE-RNN and VAE-Transformer, which transform first-person perspective (FPP) observations into global map perspective (GMP) representations and precise geographical coordinates. Unlike retrieval-based methods, our approach frames localization as a generative task, learning direct mappings between perspectives without relying on dense satellite image databases. We evaluate these models across two real-world environments: a university campus navigated by a Jackal robot and an urban downtown area navigated by a Tesla sedan. The VAE-Transformer achieves impressive precision, with median deviations of 2.29m (1.37% of environment size) and 4.45m (0.35% of environment size) respectively, outperforming both VAE-RNN and prior cross-view geo-localization approaches. Our comprehensive Localization Performance Characteristics (LPC) analysis demonstrates superior performance with the VAE-Transformer achieving an AUC of 0.777 compared to 0.295 for VIGOR 200 and 0.225 for Tra

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level automated reasoning. The introduction of AlphaGeometry, a neuro-symbolic model trained with 100 million synthetic samples, marked a major breakthrough. It solved 25 of 30 International Mathematical Olympiad (IMO) problems whereas the reported baseline based on Wu's method solved only ten. In this note, we revisit the IMO-AG-30 Challenge introduced with AlphaGeometry, and find that Wu's method is surprisingly strong. Wu's method alone can solve 15 problems, and some of them are not solved by any of the other methods. This leads to two key findings: (i) Combining Wu's method with the classic synthetic methods of deductive databases and angle, ratio, and distance chasing solves 21 out of 30 methods by just using a CPU-only laptop with a time limit of 5 minutes per problem. Essentially, this classic method solves just 4 problems less than AlphaGeometry and establishes the first fully symbolic baseline strong enough to rival the performance of an IMO sil

The projected belief network (PBN) is a generative stochastic network with tractable likelihood function based on a feed-forward neural network (FFNN). The generative function operates by "backing up" through the FFNN. The PBN is two networks in one, a FFNN that operates in the forward direction, and a generative network that operates in the backward direction. Both networks co-exist based on the same parameter set, have their own cost functions, and can be separately or jointly trained. The PBN therefore has the potential to possess the best qualities of both discriminative and generative classifiers. To realize this potential, a separate PBN is trained on each class, maximizing the generative likelihood function for the given class, while minimizing the discriminative cost for the FFNN against "all other classes". This technique, called discriminative alignment (PBN-DA), aligns the contours of the likelihood function to the decision boundaries and attains vastly improved classification performance, rivaling that of state of the art discriminative networks. The method may be further improved using a hidden Markov model (HMM) as a component of the PBN, called PBN-DA-HMM. This paper