arXiv subjects

Yanchen Jiang

Publications and source records attributed to Yanchen Jiang.

18 recordsLinked to original sources

arXiv2026

The Power of Recruiting the Smaller Side: Two Additional Traders Suffice in Two-Sided Markets

We study Bulow-Klemperer-style competition complexity in two-sided double auctions with $m$ unit-demand buyers drawn i.i.d. from $F_B$ and $n$ unit-supply sellers drawn i.i.d. from $F_S$. When $m \ge n$ and buyer valuations first-order stochastically dominate seller costs ($F_B \succeq_{\mathrm{FSD}} F_S$), we prove that recruiting just two additional sellers enables Seller Trade Reduction (STR), a prior-independent mechanism, to achieve expected Gains From Trade (GFT) at least the first-best GFT of the original market; symmetrically, when $m \le n$, Buyer Trade Reduction suffices with two additional buyers. This resolves open questions of Babaioff, Goldner, and Gonczarowski (SODA 2020) and Cai, Liaw, Mehta, and Zhao (STOC 2024). Moreover, this uniform bound is optimal: already for $m = n = 1$, no prior-independent mechanism (deterministic or randomized) that is dominant-strategy incentive-compatible (DSIC), individually rational (IR), and weakly budget-balanced (WBB) matches the first-best GFT with one additional seller. We further extend our characterization to $r$-dominance ($F_B \succeq_r F_S$), where $r \in (0, 1]$ and $1 - F_B(x) \ge r(1 - F_S(x))$ for all $x \in \mathbb{R}$ (recovering $F_B \succeq_{\mathrm{FSD}} F_S$ at $r = 1$). When $m \ge n \ge 1$, $c = \lceil 1/r \rceil + 1$ additional sellers suffice for STR to match or exceed the first-best GFT, while every prior-independent DSIC, IR, and WBB mechanism requires at least $\max(2, \lceil 1/r \rceil - 1)$ additional sellers even for $m = n = 1$, pinning down the optimal bound to within two traders. Finally, this $Θ(1/r)$ bound cannot be asymptotically improved even by recruiting on both sides: for $r < 1/64$ and $m = n = \lceil 2/(5r) \rceil$, every prior-independent DSIC, IR, and WBB mechanism requires $c \ge \lceil 1/(64r) \rceil = Ω(1/r)$ additional traders per side.

cs.GT↗

arXiv2026

Cogentic: Multi-Agent Orchestration for Automated Proof Discovery

We present Cogentic, a multi-agent harness for automated proof discovery on open research problems. While frontier language models can generate strong mathematical ideas in a single shot, single-shot generation is often insufficient for open problems that require exploring multiple competing conjectures, overcoming subtle technical obstructions, and retaining intermediate progress over a long horizon. Cogentic addresses these challenges through an iterative prove-verify loop in which an orchestrator allocates a population of independent provers across distinct proof directions, subjects their output to adversarial verification by several specialized components, and promotes confirmed intermediate results into a persistent verified ledger that later rounds build on. The harness is designed to be able to solve research-level math and theoretical computer science problems. Using either Gemini 3.1 Pro or an early version of Gemini 4 Argon as the base model, Cogentic produced novel results on open problems across online learning, auction theory, and mechanism design. Each result was independently verified by domain experts and is developed in full in companion papers. We list these results, and new ones as they are verified, at https://sites.google.com/view/cogentic .

cs.AI↗

arXiv2026

Efficiency of Generalized Proportional First-Price Auctions Under Auto-bidding

Auto-bidding is now widely adopted in online advertising platforms, allowing advertisers to specify high-level campaign objectives--such as maximizing total value subject to a return-on-spend (ROS) constraint--rather than manual per-query bids. A central question in algorithmic mechanism design is characterizing the worst-case efficiency loss, or Price of Anarchy (PoA), across auction formats in this prior-free setting. While randomized auctions are known to strictly improve efficiency over deterministic mechanisms for two bidders, two fundamental questions have remained open: (1) what is the optimal PoA for two bidders, and (2) can any mechanism beat the barrier of 2 for general $n \ge 3$ bidders? We resolve both questions using the family of $r$-proportional first-price auctions ($\text{pFPA}_r$), in which each bidder wins with probability proportional to their bid raised to an exponent $r > 0$ and pays their bid upon winning. First, for two bidders, we prove that the standard proportional first-price auction ($r = 1$) achieves a tight $\text{PoA} \le 1.5$, complemented by a matching lower bound showing that no anonymous, monotone mechanism can do better. Second, for general $n \ge 2$ bidders, setting $r = 2n$ achieves $\text{PoA} \le 2 - \frac{1}{4n+1} = 2 - Ω(1/n)$ across all undominated bid profiles, breaking the deterministic barrier of 2 for every finite $n$ and asymptotically matching the known $2 - Θ(1/n)$ lower bound.

cs.GT↗

arXiv2026

LLM Bidders Preserve the Mechanism-Level Orderings of Human Bidders

Training on vast amounts of human-generated data has motivated growing interest in using large language models (LLMs) to simulate human behavior. We ask which features of human behavior general-purpose models preserve when used out of the box in auctions, where multiple bidders interact under explicit rules and incentives. We evaluate five LLMs across seven laboratory settings against human benchmarks reconstructed from published experiments, with uncertainty bands for the private-value comparisons. Our main focus is on three large models without extended test-time reasoning: GPT-4o, Claude~3.5 Haiku, and Gemini~2.0 Flash. LLM and human deviations from theory differ in magnitude and often in direction: humans overbid in second-price auctions, whereas most models that deviate underbid. Surprisingly, without task-specific fine-tuning or calibration to human bids, the three non-reasoning large models robustly preserve key orderings of auction formats by deviation from theory. First-price auctions are harder than second-price, and ascending clocks reduce deviations relative to sealed bids wherever data are adequate. Kendall's $τ_b$ between the human and GPT-4o difficulty rankings is $0.60$ and positive in every joint bootstrap draw. The reasoning model bids almost at equilibrium in the observed private-value settings, leaving little variation in errors to compare; the small model's large errors yield an inverted ranking. All five models nevertheless reproduce the stronger first-price winner's curse. Clock framing improves bidding for two of the three non-reasoning large models, and GPT-4o recovers the ordering of last-minute bidding across closing rules in an eBay-style marketplace.

cs.GT↗

arXiv2026

Improved Revenue Guarantees for Selling Separately and Bundling

We study how much revenue a seller can lose by restricting attention to selling separately or grand bundling, in the setting of a single additive buyer with independent item values. Although revenue-optimal mechanisms can require lotteries and infinite menus, Babaioff, Immorlica, Lucier, and Weinberg showed that the better of these two simple formats always achieves a constant fraction of optimal revenue. We prove that $\mathrm{OPT} \le 3.52 \max\{\mathrm{SREV}, \mathrm{BREV}\}$, where $\mathrm{SREV}$ and $\mathrm{BREV}$ are the optimal revenues from selling separately and grand bundling, respectively. This improves the previous best-known approximation factor of $5.2$ due to Ma and Simchi-Levi and narrows the gap to the known lower bound of $2$.

cs.GT↗

arXiv2026

Prediction with Expert Advice: Anytime Regret with Many Experts Matches the Fixed-Time Constant

Prediction with expert advice is a fundamental problem in online learning. When the time horizon $T$ is known in advance, the minimax cumulative regret over $n$ experts is asymptotically $\sqrt{\frac{T \ln n}{2}}$. This is achieved by the Multiplicative Weights Update algorithm with a learning rate tuned to $T$, and is known to be tight. If instead the regret bound is required to hold simultaneously at every time $t$, the best known guarantee has been $\sqrt{t \ln n}$---a factor of $\sqrt{2}$ worse---and it has remained unknown whether this factor of $\sqrt{2}$ is necessary. We show that it is not. We give an algorithm, requiring no knowledge of the horizon, whose cumulative regret satisfies $R_t \le \bigl(1 + O(\sqrt{\ln \ln n / \ln n})\bigr)\sqrt{t \ln n / 2}$ simultaneously for every $t \ge 1$.

stat.ML↗

arXiv2026

Efficient Online Inverse Optimization with $O(d)$ Regret

We give a deterministic algorithm for online inverse linear optimization with regret $O(d)$, uniform in the horizon and $O(d^{2})$ time per round. A bound of this order was obtained recently by Dewasurendra, settling a question of Gollapudi et al.\ and of Oki and Sakaue, but by an improper rule that enumerates covers at every scale and costs $T^{Θ(d)}$ a round; ours is the first efficient such bound and the first proper one. We build on the variable-metric framework of Sakaue et al., adding a self-normalized rank-one update, and we replace the $\log\det$ potential by the trace power $\tr(H^{-1/2})$, which is bounded outright and removes the $\ln T$. The bound also holds against an expert that does not optimize, and we give corruption-robust and rank-adaptive variants, and an application to convex minimization.

cs.LG↗

arXiv2026

Data Market Design through Deep Learning

The data market design problem is a problem in economic theory to find a set of signaling schemes (statistical experiments) to maximize expected revenue to the information seller, where each experiment reveals some of the information known to a seller and has a corresponding price [Bergemann et al., 2018]. Each buyer has their own decision to make in a world environment, and their subjective expected value for the information associated with a particular experiment comes from the improvement in this decision and depends on their prior and value for different outcomes. In a setting with multiple buyers, a buyer's expected value for an experiment may also depend on the information sold to others [Bonatti et al., 2022]. We introduce the application of deep learning for the design of revenue-optimal data markets, looking to expand the frontiers of what can be understood and achieved. Relative to earlier work on deep learning for auction design [Dütting et al., 2023], we must learn signaling schemes rather than allocation rules and handle obedience constraints $-$ these arising from modeling the downstream actions of buyers $-$ in addition to incentive constraints on bids. Our experiments demonstrate that this new deep learning framework can almost precisely replicate all known solutions from theory, expand to more complex settings, and be used to establish the optimality of new designs for data markets and make conjectures in regard to the structure of optimal designs.

cs.GT↗

arXiv2026

The Prosocial Ranking Challenge: Reducing Polarization on Social Media without Sacrificing Engagement

We report the first direct comparisons of multiple alternative social media algorithms on multiple platforms on outcomes of societal interest. We used a browser extension to modify which posts were shown to desktop social media users, randomly assigning 9,386 users to a control group or one of five alternative ranking algorithms which simultaneously altered content across three platforms for six months during the US 2024 presidential election. This reduced our preregistered index of affective polarization by an average of 0.03 standard deviations (p < 0.05), including a 1.5 degree decrease in differences between the 100 point inparty and outparty feeling thermometers. We saw reductions in active use time for Facebook (-0.37 min/day) and Reddit (-0.2 min/day), but an increase of 0.32 min/day (p < 0.01) for X/Twitter. We saw an increase in reports of negative social media experiences but found no effects on well-being, news knowledge, outgroup empathy, perceptions of and support for partisan violence. This implies that bridging content can improve some societal outcomes without necessarily conflicting with the engagement-driven business model of social media.

cs.SI↗

arXiv2026

Duality for Optimal Multi-Item, Multi-Bidder Auction Design: Revenue Certificates through Deep Learning

Characterizing revenue-optimal auctions for multi-item, multi-bidder settings remains a fundamental open problem, with no known closed-form solution existing beyond restrictive binary-type instances. This has motivated interest in computational approaches to optimal auction design. In this paper, we introduce the first computational framework that directly tackles the dual problem for multi-item, multi-bidder auctions and dominant-strategy incentive compatibility (DSIC), generating certified revenue upper bounds. Our approach parametrizes Lagrange multipliers with a structurally guaranteed strict flow-conservation property using neural networks, enabling efficient optimization over feasible dual solutions via gradient descent. To bridge the gap between discrete computational methods and theoretical guarantees for continuous types, we develop a novel lifting technique that maps dual certificates from coarse discretizations to fine refinements. We prove that lifting gives valid revenue upper bounds for multi-item, multi-bidder auctions with continuous uniform valuations. Furthermore, we give a generalized lifting construction for arbitrary continuous distributions and demonstrate that these lifted duals converge to the revenue of the original continuous problem in the discrete limit. We validate this computational framework for the dual auction design problem by recovering known analytical mechanisms for canonical instances. For multi-item multi-bidder problems, our framework establishes a small gap between the optimal revenue and best-known DSIC mechanisms, providing computational certificates of near-optimality.

cs.GT↗

arXiv2026

One Model, Two Markets: Bid-Aware Generative Recommendation

Generative Recommender Systems using semantic ids, such as TIGER (Rajput et al., 2023), have emerged as a widely adopted competitive paradigm in sequential recommendation. However, existing architectures are designed solely for semantic retrieval and do not address concerns such as monetization via ad revenue and incorporation of bids for commercial retrieval. We propose GEM-Rec, a unified framework that integrates commercial relevance and monetization objectives directly into the generative sequence. We introduce control tokens to decouple the decision of whether to show an ad from which item to show. This allows the model to learn valid placement patterns directly from interaction logs, which inherently reflect past successful ad placements. Complementing this, we devise a Bid-Aware Decoding mechanism that handles real-time pricing, injecting bids directly into the inference process to steer the generation toward high-value items. We prove that this approach guarantees allocation monotonicity, ensuring that higher bids weakly increase an ad's likelihood of being shown without requiring model retraining. Experiments demonstrate that GEM-Rec allows platforms to dynamically optimize for semantic relevance and platform revenue.

cs.IR↗

arXiv2026

Incentive-Aligned Multi-Source LLM Summaries

Large language models (LLMs) are increasingly used in modern search and answer systems to synthesize multiple, sometimes conflicting, texts into a single response, yet current pipelines offer weak incentives for sources to be accurate and are vulnerable to adversarial content. We introduce Truthful Text Summarization (TTS), an incentive-aligned framework that improves factual robustness without ground-truth labels. TTS (i) decomposes a draft synthesis into atomic claims, (ii) elicits each source's stance on every claim, (iii) scores sources with an adapted multi-task peer-prediction mechanism that rewards informative agreement, and (iv) filters unreliable sources before re-summarizing. We establish formal guarantees that align a source's incentives with informative honesty, making truthful reporting the utility-maximizing strategy. Experiments show that TTS improves factual accuracy and robustness while preserving fluency, aligning exposure with informative corroboration and disincentivizing manipulation.

cs.CL↗

arXiv2026

LLM Active Alignment: A Nash Equilibrium Perspective

We develop a game-theoretic framework for predicting and steering the behavior of populations of large language models (LLMs) through Nash equilibrium (NE) analysis. To avoid the intractability of equilibrium computation in open-ended text spaces, we model each agent's action as a mixture over human subpopulations. Agents choose actively and strategically which groups to align with, yielding an interpretable and behaviorally substantive policy class. We derive closed-form NE characterizations, adopting standard concave-utility assumptions to enable analytical system-level predictions and give explicit, actionable guidance for shifting alignment targets toward socially desirable outcomes. The method functions as an active alignment layer on top of existing alignment pipelines such as RLHF. In a social-media setting, we show that a population of LLMs, especially reasoning-based models, may exhibit political exclusion, pathologies where some subpopulations are ignored by all LLM agents, which can be avoided by our method, illustrating the promise of applying the method to regulate multi-agent LLM dynamics across domains.

cs.AI↗

arXiv2025

Charting the Shapes of Stories with Game Theory

Stories are records of our experiences and their analysis reveals insights into the nature of being human. Successful analyses are often interdisciplinary, leveraging mathematical tools to extract structure from stories and insights from structure. Historically, these tools have been restricted to one dimensional charts and dynamic social networks; however, modern AI offers the possibility of identifying more fully the plot structure, character incentives, and, importantly, counterfactual plot lines that the story could have taken but did not take. In this work, we use AI to model the structure of stories as game-theoretic objects, amenable to quantitative analysis. This allows us to not only interrogate each character's decision making, but also possibly peer into the original author's conception of the characters' world. We demonstrate our proposed technique on Shakespeare's famous Romeo and Juliet. We conclude with a discussion of how our analysis could be replicated in broader contexts, including real-life scenarios.

cs.GT↗

arXiv2025

BundleFlow: Deep Menus for Combinatorial Auctions by Diffusion-Based Optimization

Differentiable economics -- the use of deep learning for auction design -- has driven progress in the automated design of multi-item auctions with additive or unit-demand valuations. However, little progress has been made for optimal combinatorial auctions (CAs), even for the single bidder case, because we need to overcome the challenge of the bundle space growing exponentially with the number of items. For example, when learning a menu of allocation-price choices for a bidder in a CA, each menu element needs to efficiently and flexibly specify a probability distribution on bundles. In this paper, we solve this problem in the single-bidder CA setting by generating a bundle distribution through an ordinary differential equation (ODE) applied to a tractable initial distribution, drawing inspiration from generative models, especially score-based diffusion models and continuous normalizing flow. Our method, BundleFlow, uses deep learning to find suitable ODE-based transforms of initial distributions, one transform for each menu element, so that the overall menu achieves high expected revenue. Our method achieves 1.11$-$2.23$\times$ higher revenue compared with automated mechanism design baselines on the single-bidder version of CATS, a standard CA testbed, and scales to problems with up to 150 items. Relative to a baseline that also learns allocations in menu elements, our method reduces the training iterations by 3.6$-$9.5$\times$ and cuts training time by about 80% in settings with 50 and 100 items.

cs.GT↗

arXiv2025

On Diffusion Models for Multi-Agent Partial Observability: Shared Attractors, Error Bounds, and Composite Flow

Multiagent systems grapple with partial observability (PO), and the decentralized POMDP (Dec-POMDP) model highlights the fundamental nature of this challenge. Whereas recent approaches to addressing PO have appealed to deep learning models, providing a rigorous understanding of how these models and their approximation errors affect agents' handling of PO and their interactions remain a challenge. In addressing this challenge, we investigate reconstructing global states from local action-observation histories in Dec-POMDPs using diffusion models. We first find that diffusion models conditioned on local history represent possible states as stable fixed points. In collectively observable (CO) Dec-POMDPs, individual diffusion models conditioned on agents' local histories share a unique fixed point corresponding to the global state, while in non-CO settings, shared fixed points yield a distribution of possible states given joint history. We further find that, with deep learning approximation errors, fixed points can deviate from true states and the deviation is negatively correlated to the Jacobian rank. Inspired by this low-rank property, we bound a deviation by constructing a surrogate linear regression model that approximates the local behavior of a diffusion model. With this bound, we propose a \emph{composite diffusion process} iterating over agents with theoretical convergence guarantees to the true state.

cs.LG↗

arXiv2025

LLM-Powered Preference Elicitation in Combinatorial Assignment

We study the potential of large language models (LLMs) as proxies for humans to simplify preference elicitation (PE) in combinatorial assignment. While traditional PE methods rely on iterative queries to capture preferences, LLMs offer a one-shot alternative with reduced human effort. We propose a framework for LLM proxies that can work in tandem with SOTA ML-powered preference elicitation schemes. Our framework handles the novel challenges introduced by LLMs, such as response variability and increased computational costs. We experimentally evaluate the efficiency of LLM proxies against human queries in the well-studied course allocation domain, and we investigate the model capabilities required for success. We find that our approach improves allocative efficiency by up to 20%, and these results are robust across different LLMs and to differences in quality and accuracy of reporting.

cs.AI↗

arXiv2024

GemNet: Menu-Based, Strategy-Proof Multi-Bidder Auctions Through Deep Learning

Automated mechanism design (AMD) uses computational methods for mechanism design. Differentiable economics is a form of AMD that uses deep learning to learn mechanism designs and has enabled strong progress in AMD in recent years. Nevertheless, a major open problem has been to learn multi-bidder, general, and fully strategy-proof (SP) auctions. We introduce GEneral Menu-based NETwork (GemNet), which significantly extends the menu-based approach of the single-bidder RochetNet (Dütting et al., 2024) to the multi-bidder setting. The challenge in achieving SP is to learn bidder-independent menus that are feasible, so that the optimal menu choices for each bidder do not over-allocate items when taken together (we call this menu compatibility). GemNet penalizes the failure of menu compatibility during training, and transforms learned menus after training through price changes, by considering a set of discretized bidder values and reasoning about Lipschitz smoothness to guarantee menu compatibility on the entire value space. This approach is general, leaving trained menus that already satisfy menu compatibility undisturbed and reducing to RochetNet for a single bidder. Mixed-integer linear programs are used for menu transforms, and through a number of optimizations enabled by deep learning, including adaptive grids and methods to skip menu elements, we scale to large auction design problems. GemNet learns auctions with better revenue than affine maximization methods, achieves exact SP whereas previous general multi-bidder methods are approximately SP, and offers greatly enhanced interpretability.

cs.GT↗