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cs.GT

cs.GT: explore 136 source-linked works published from 2026 to 2026, with original documents and citations.

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Includes records with this source-supplied label or an explicit phrase match in their metadata. Matches indicate a mention, not proof that a paper uses a method or tests a material. Source versions are consolidated by DOI.

Sources: arxiv. Collection updated 2026-09-16. Counts describe this index, not the complete source archives.

arXiv2026

Mechanism Design for Alignment and Control

We develop a framework for mechanism design with AI agents whose alignment (preferences) and capabilities (feasible actions and information) are unknown. We want such agents to act on our behalf so mechanisms must incentivize both honesty and obedience. A one-sided imitation structure---capabilities can be concealed but not counterfeited---yields a revelation principle, a characterization of implementable policies via nested cyclical monotonicity, and conditions under which eliciting higher-order beliefs can discipline multiple agents. We apply our framework to stylized examples of (i) sandbagging in which a more capable agent pretends to be less capable; (ii) an alignment--interpretability trade-off, where the two are substitutes in the instrument but complements in value; (iii) discipline via peer scoring; (iv) coupling rewards to induce competition among multiple agents; and (v) scalable oversight and reward shaping.

econ.TH↗

arXiv2026

When Does Information Sharing Improve Decentralized Discovery? Aggregation, Independent Rescue, and Equilibrium Selection

Information sharing can improve a pooled estimate while eliminating independent rescue actions. This paper separates those effects in exact finite discovery models. A centralized action-budget profile shows that equal one-person accuracy can coexist with different portfolio values. Under a registered incremental-sharing protocol, a sharing step improves discovery exactly when pooled residual error contracts faster than an independent rescue attempt. Exact bounded registries exhibit compression, aggregation, neutral curves, and a bounded zero mixed class. In a two-agent Bayesian game with a hidden mixture of common and independent signal sources, the registered selected equilibrium yields a strict positive sharing interval at signal accuracy 3/5, while alternative equilibria show that the result is selection-dependent rather than universal. The models are synthetic and finite; no human or organizational data are used.

cs.AI↗

arXiv2026

The Power of Static Pricing for Reusable Resources

We consider the problem of pricing a reusable resource service system. Potential customers arrive according to a Poisson process and purchase the service if their valuation exceeds the current price. If no units are available, customers immediately leave without service. Serving a customer corresponds to using one unit of the reusable resource, where the service time has a general distribution. The objective is to maximize the steady-state revenue rate. This system is equivalent to the classical Erlang loss model with price-sensitive customers, which has applications in vehicle sharing, cloud computing, and spare parts management. With general service times, the optimal pricing policy depends not only on the number of customers currently in the system but also on how long each unavailable unit has been in use. We prove several results that show a simple static policy is universally near-optimal for any service time distribution, arrival rate, and number of units in the system. When there are multiple classes of customers with regular valuation distributions, we prove that static pricing guarantees 78.9% of the revenue of the optimal dynamic policy, achieving the same guarantee known for a single class of customers with exponential service times. When there is one class of customers who have a monotone hazard rate valuation distribution, we prove that a static pricing policy guarantees 97.5% of the revenue from the optimal inventory-based policy. In addition, we prove that the optimal static policy can be easily computed, resulting in the first polynomial-time approximation algorithm for the multi-class problem. Finally, we consider the extensions to irregular valuation distributions and general multi-resource networks.

cs.GT↗

arXiv2026

Expected flow networks in stochastic environments and two-player zero-sum games

Generative flow networks (GFlowNets) are sequential sampling models trained to match a given distribution. GFlowNets have been successfully applied to various structured object generation tasks, sampling a diverse set of high-reward objects quickly. We propose expected flow networks (EFlowNets), which extend GFlowNets to stochastic environments. We show that EFlowNets outperform other GFlowNet formulations in stochastic tasks such as protein design. We then extend the concept of EFlowNets to adversarial environments, proposing adversarial flow networks (AFlowNets) for two-player zero-sum games. We show that AFlowNets learn to find above 80% of optimal moves in Connect-4 via self-play and outperform AlphaZero in tournaments.

cs.LG↗

arXiv2026

Algorithmic Collusion by Large Language Models

We conduct experiments with algorithmic pricing agents based on Large Language Models (LLMs). In oligopoly settings, LLM-based pricing agents quickly and autonomously reach supracompetitive prices and profits. Variation in seemingly innocuous phrases in LLM instructions ("prompts") substantially influence the degree of supracompetitive pricing. We develop novel techniques for behavioral analysis of LLMs and use them to uncover price-war concerns as a contributing factor. Our results extend to auction settings. Our findings uncover unique challenges to any future regulation of LLM-based pricing agents, and AI-based pricing agents more broadly.

econ.GN↗

arXiv2026

On the Equivalence of the Graph-Structural and Optimization-Based Characterizations of Popular Matchings

Popular matchings provide a model of matching under preferences in which a solution corresponds to a Condorcet winner in voting systems. In a bipartite graph in which the vertices have preferences over their neighbours, a matching is defined to be popular if it does not lose in a majority vote against any matching. In this paper, we study the following three primary problems: only the vertices on one side have preferences; a generalization of this problem allowing ties in the preferences; and the vertices on both sides have preferences. A principal issue in the algorithmic aspects of popular matchings is how to determine the popularity of a matching, because it requires exponential time if the definition is simply applied. In the literature, we have the following two types of characterizations: a graph-structural characterization; and an optimization-based characterization described by maximum-weight matchings. The graph-structural characterizations are specifically designed for each problem and provide a combinatorial structure of the popular matchings. The optimization-based characterizations work in the same manner for all problems, while they do not reveal the structure of the popular matchings. A main contribution of this paper is to provide a direct connection of the above two types of characterizations for all of the three problems. Specifically, we prove that each characterization can be derived from the other, without relying on the fact that they characterize popular matchings. Our proofs offer a comprehensive understanding of the equivalence of the two types of characterizations, and suggest a new interpretation of the graph-structural characterization in terms of the dual optimal solution for the maximum-weight matching problem.

cs.GT↗

arXiv2026

Make an Offer They Can't Refuse: Grounding Bayesian Persuasion in Real-World Dialogues without Pre-Commitment

Large language models (LLMs) still struggle with strategic persuasion, largely because existing approaches either neglect information asymmetry or rely on unrealistic pre-commitment assumptions. We introduce a type-induced commitment-communication mechanism that grounds Bayesian Persuasion (BP) in natural language dialogue without pre-commitment: the persuader narrates their potential types (e.g., honest vs. dishonest) to dynamically construct an information schema, enabling the persuadee to perform Bayesian belief updates within the conversation itself. We implement two variants: Semi-Formal-Natural-Language (SFNL) and Fully-Natural-Language (FNL), evaluating them against strong baselines across multiple LLMs and human judges. BP strategies consistently outperform baselines: SFNL excels in logical credibility, while FNL shows superior robustness and emotional resonance. We verify that gains stem from genuine Bayesian reasoning rather than superficial formatting, and we further show that supervised fine-tuning enables small models to match the persuasive performance of much larger ones.

cs.CL↗

arXiv2026

Individualized Algorithmic Advice as a Strategic Signal on Competitive Markets

As algorithms increasingly mediate competitive decision-making, their influence extends beyond individual outcomes to shaping strategic market dynamics. In our experiment, we examined how algorithmic advice affects human behavior in a classic economic game with a unique, non-collusive, and analytically traceable equilibrium. Participants (N = 129) played a Cournot quantity competition with equilibrium-aligned or strategically biased algorithmic recommendations. While individualized equilibrium advice supported stable convergence, collusively downward-biased advice led to sustained underproduction and supracompetitive profits - hallmarks of tacit collusion. Participants' quantities converged faster and more consistently toward individualized than collective equilibrium advice, potentially due to an objective quality advantage or greater perceived ownership of the former. These findings demonstrate that algorithmic advice can function as a strategic signal, shaping coordination even without explicit communication. The results echo real-world concerns about algorithmic collusion and underscore the need for careful design and oversight of algorithmic decision-support systems in competitive environments.

cs.HC↗

arXiv2026

Learning Proportional Committees from Violation Feedback

We study violation-feedback learning of proportionally representative approval-based committees. In each round, a learner proposes a committee of size $k$. An oracle either accepts the proposal or adversarially selects a representation violation with respect to a single fixed hidden approval profile. We compare \emph{full-witness feedback}, which reveals the violation level, an omitted candidate, and the affected voter group, with \emph{candidate-only feedback}, which reveals only that candidate. The target notions are proportional justified representation plus (PJR+) and extended justified representation plus (EJR+). In every setting we study, the number of rejected proposals can be bounded solely in terms of $k$, with no dependence on the numbers of voters and candidates. For PJR+, the optimal deterministic and randomized rejection complexities equal $k$ under both feedback models. For EJR+, the picture is more nuanced. Under full-witness feedback, we prove an $Ω(k^{3/2})$ deterministic lower bound and give a deterministic polynomial-time algorithm using $O(k^2\log k)$ rejections. Under candidate-only feedback, randomization achieves $O(k^2\log k)$ expected rejections via uniform random deletion, while deterministic exhaustive branching gives a $2^{O(k^2(\log k)^2)}$ rejection bound. Even with full-witness feedback, randomized learners may require $k$ rejections.

cs.GT↗

arXiv2026

Rival-Injective Allocations: Support-List Structure and Maximum-Anchor EFX$_0$ Certificates

We study complete allocations under nonnegative additive valuations through the positive supports of goods, focusing on the all-good form of envy-freeness up to any good (EFX$_0$). We define rival-injective (RI) endpoint ownership: every good with nonempty positive support is assigned to an agent who values it positively, and every ordered observer--owner pair is used by at most one good. RI ownership is exactly proper list coloring of the graph joining goods whose positive supports overlap in at least two agents. For pair-supported goods with arbitrary exceptional goods, fixing the exceptional owners yields a necessary-and-sufficient pair-capacity criterion and an exact finite-domain owner constraint satisfaction problem (CSP). Every RI allocation in which each agent's own bundle is worth at least her maximum-valued singleton is all-good EFX$_0$. A specified injective choice of maximum-singleton anchors, together with residual support-list degeneracy, constructs such an allocation by reverse greedy coloring in $O(nm^2)$ time. We give two explicit witness families: a nonempty relatively open, 22-dimensional cone on a fixed $4\times10$ support face, and a family for every $n\ge4$ with two universal-support goods and $m=(n-1)(n-2)+2$ goods. Both fail unanchored list degeneracy and are not implied by the explicit pure-multigraph or published high-girth/controlled-multiplicity hypotheses compared here. We also study recognition of the maximum-anchor certificate class, leaving its general complexity unresolved. The exact list-coloring and pair-capacity results concern RI ownership, not general EFX$_0$ existence; unrestricted four-agent, ten-good all-good EFX$_0$ remains unresolved.

cs.GT↗

arXiv2026

Residual Maximin Share: Exact Finite-Agent Frontier, Sparse Extremizers, and Threshold Cuts

Residual maximin share (RMMS) is the largest share threshold that remains guaranteeable throughout dynamic allocation processes, even after previously allocated, lower-valued bundles are removed from the item pool. For additive valuations, recent density-balance analyses established finite-agent lower bounds comparing RMMS with the classical maximin share (MMS). In this paper, we prove that these finite-agent lower bounds are exact. Specifically, if $d_n$ denotes the largest odd integer at most $n$, the worst-case ratio satisfies $\inf_{M,v:\operatorname{MMS}>0}\frac{\operatorname{RMMS}(M,v,n)}{\operatorname{MMS}(M,v,n)}=\frac{2d_n}{3d_n-1}$. Consequently, the exact additive frontier forms consecutive odd-even plateaus and converges monotonically to $2/3$. We then investigate the combinatorial structure of extremal instances. While naive witnesses require $Θ(n^2)$ items, we construct an explicit three-valued family achieving the exact boundary with only linear support: $(5n-3)/2$ items for odd $n$ and $(5n-4)/2$ items for even $n$. Its low-valued block supports two exact partitions that simultaneously certify the MMS benchmark and the residual obstruction. By modeling these dual partitions as a bipartite transportation graph, we prove that this block attains the absolute minimum support $q+d-1=3q$. At minimum support, any two-valued filler is uniquely rigid up to relabeling. Finally, we establish structural characterizations of RMMS. A general min--max representation applies to all finite monotone valuations. For integer additive valuations, we prove that a threshold $T$ is residual self-feasible if and only if every subset cut satisfies a packing-covering condition. Because RMMS is pointwise maximal among residual self-feasible shares, these exact constants establish a tight limitation on the fairness guarantees achievable by share-based lone-divider algorithms.

cs.GT↗

arXiv2026

The Exact MMS Guarantees of EFX and PMMS

Envy-freeness up to any good (EFX) and pairwise maximin share (PMMS) are standard local fairness criteria for indivisible goods, whereas maximin share (MMS) is a global benchmark. We determine the exact quantitative relationship between these local fairness notions and the global MMS guarantee under nonnegative additive valuations. We show that the optimal universal factor for both notions is $ρ^{\mathrm{EFX}\to\mathrm{MMS}}=ρ^{\mathrm{PMMS}\to\mathrm{MMS}}=\frac{10}{17}$. We prove the lower bound by a combinatorial charging argument. After an initial reduction, both EFX and PMMS imply the same local condition on every foreign bundle from the perspective of a focal agent: deleting its least valuable good leaves value at most the focal bundle. A three-piece concave weight function translates this local condition into the global $10/17$ guarantee. We then construct an explicit family of complete allocations that are simultaneously PMMS and EFX$_0$, whose MMS ratios converge to $10/17$, showing that both constants are tight even in the presence of zero-valued goods. The argument also gives $α$-EFX $\Rightarrow (10α/17)$-MMS. Finally, we establish an exact correspondence between these fair-division guarantees and scheduling equilibria. For every fixed number of agents $n$, the EFX-to-MMS extremal ratio equals the reciprocal of the pure price of anarchy for selfish identical-machine covering. Similarly, the PMMS-to-MMS ratio equals the reciprocal of a locality gap based on exact pairwise machine repartition. These correspondences explain why the constant $10/17$ governs both problems.

cs.GT↗

arXiv2026

Mechanism Design for Facility Location Games Under a Prelocated Facility

We study the problem of locating a new homogeneous facility under a prelocated facility. Here, a set of $n$ agents is located on a real line or a circle, each of whom has her location as private information, and her cost is the (expected) distance from her location to the nearest facility. Our goal is to design mechanisms which can approximately minimize the maximum cost or the social cost while eliciting agents' private information truthfully (i.e., strategy-proof). Based on real-life scenarios, we consider the problem in two settings: the general setting where each agent can be located at both sides of the prelocated facility, and the special setting where all the agents are located at the same side of the prelocated facility. For agents on a line, in the general setting, we design the best possible deterministic strategy-proof mechanism with $2$-approximation and provide a lower bound of $1.5-ε\textbf{ }(ε>0)$ for any randomized strategy-proof mechanism under the maximum cost objective. For the social cost, we obtain an upper bound of $n$ for deterministic strategy-proof mechanisms and lower bounds of $1.5$ and $1.0425$ for any deterministic strategy-proof mechanism and any randomized strategy-proof mechanism, respectively. In the special setting, we further provide a randomized strategy-proof $5/3$-approximation mechanism for the maximum cost and a deterministic strategy-proof $(n-1)$-approximation mechanism for the social cost. For agents on a circle, we provide a deterministic strategy-proof 2-approximation mechanism under the maximum cost objective.

cs.GT↗

arXiv2026

LangBP: Language-Guided Reasoning and Acting for Joint Bidding and Pricing

Auto-bidding is a long-horizon sequential decision problem for maximizing conversion value under budget and key performance indicator (KPI) constraints. Recent work extends this task from bidding alone to joint bidding and pricing, where a policy controls bidding decisions and pricing corrections. Existing methods mainly rely on numerical trajectory modeling, which offers limited support for interpreting campaign context and expressing high-level strategies. Large language models (LLMs) can complement this paradigm with their reasoning capabilities. However, existing language-guided methods have two limitations. First, they condition actions on language strategies without modeling the corresponding state changes, making it difficult to distinguish errors in strategy understanding from errors in action generation. Second, different instructions can produce similar execution effects, leading to imbalanced policy updates across effects. We propose LangBP, a hierarchical framework for language-guided joint bidding and pricing. LangBP's Semantic Decision Transformer (S-DT) predicts target states from the instruction and the trajectory history, then recovers the joint action via inverse dynamics. We further propose Execution-Grouped Policy Optimization (EGPO), which scores candidate effects with a Context--Effect Verifier (CEV) and balances policy updates across effect groups. Experiments on AuctionNet show that LangBP outperforms strong baselines, and online A/B tests further demonstrate business gains in real-world deployment on a large-scale e-commerce platform.

cs.GT↗

arXiv2026

Test-time Reinforcement Learning in Imperfect Information Games

Test-time reasoning has significantly improved performance in domains ranging from games to language models. However, test-time policy changes with formal guarantees on the performance of the resulting strategy remain a challenge in two-player zero-sum imperfect-information games. Existing solutions are limited to tabular methods or single gradient step updates. In this work, we investigate policy-gradient algorithms as a method for scalable test-time reasoning. We extend the concept of gadget game, tabular technique for test-time search, to the reinforcement learning setting. Unlike prior approaches, we represent the gadget game implicitly by modified sampling and neural policy rather then explicitly by constructing it, thereby removing constraints on subgame size. Furthermore, we formally prove that, unlike prior tabular algorithms, regularized policy-gradient algorithms limit possible strategy degradation caused by test-time reasoning, even without the gadget games. Our evaluation across small- and large-scale games confirms that additional test-time training often substantially improves performance relative to the blueprint strategy.

cs.GT↗

arXiv2026

Reaching Fairness by Reallocating Goods

Fair allocation of indivisible goods has largely been studied under the assumption that no prior allocation exists. Motivated by practical settings with pre-existing (and possibly unfair) allocations, we study how to achieve fairness through limited reallocations. Building on recent work on reformability/reallocations, we consider three fairness notions---envy-freeness (EF), envy-freeness up to one good (EF1), and envy-freeness up to any good (EFX)---and optimize the number of goods reallocated. We analyze both the classical and parameterized complexity of these problems, providing a comprehensive analysis across multiple fairness notions.

cs.GT↗

arXiv2026

Bidding Games with Rewards: Taming Infinite Configuration Space

Bidding games are graph games in which a token is placed on a vertex, each player starts with an initial budget, and a simultaneous auction determines which player moves the token; the players' budgets are then updated accordingly. Motivated by scenarios such as resource-allocation systems in which agents receive periodic rewards (e.g., credits, energy) while competing for control, we introduce and study bidding games with rewards, in which, at each vertex, players may receive additional budget, incentivizing desired behaviors. We focus on reachability discrete poorman bidding games with rewards (DPBGr). The main challenge when compared to discrete bidding games without rewards is that the configuration graph is infinite. To this end we introduce a novel technique to eliminate plays with suboptimal infixes. This enables focusing on a finite part of the infinite configuration graph in order to solve the game via approximation to continuous bidding games with overall complexity in EXP. Finally, we discuss a new type of strategy, usable on a subclass of DPBGr, which guarantee a winning strategy for the reachability player. Membership in this subclass is shown to be in NP.

cs.GT↗

arXiv2026

Constrained Fair Allocations via Partition Matroid Reductions

We study fair allocation of indivisible goods under additive valuations and matroid constraints. A challenging open question is whether a complete and feasible envy-free up to one good (EF1) allocation exists under every matroid that admits a complete and feasible allocation. The state-of-the-art result by Biswas and Barman [2018] positively resolves this question for partition matroids. Our first result positively resolves it for laminar matroids, which generalize partition matroids, when there are three agents. Our technique reduces this general existence question to finding an EF1 allocation satisfying a mild additional condition under a single finite-sized key laminar matroid, and we establish the required allocation by case analysis. We show that our technique somewhat extends to four agents, reducing the analogous problem to finding EF1 allocations under two finite-sized laminar matroids, although we are unable to establish their existence. We also use recent matroid decomposition results to establish EF1 existence under broader classes of matroids. Specifically, we show that EF1 allocations always exist under transversal matroids whenever a complete allocation is feasible, and obtain existence results for graphic matroids and gammoids under stronger assumptions.

cs.GT↗

Compare source metadata on this page

Work	Published	Source identifier	Source
Mechanism Design for Alignment and Control	2026-09-01	2609.01595	arxiv
When Does Information Sharing Improve Decentralized Discovery? Aggregation, Independent Rescue, and Equilibrium Selection	2026-09-01	2609.01814	arxiv
The Power of Static Pricing for Reusable Resources	2026-08-31	2302.11723	arxiv
Expected flow networks in stochastic environments and two-player zero-sum games	2026-08-31	2310.02779	arxiv
Algorithmic Collusion by Large Language Models	2026-08-31	2404.00806	arxiv
On the Equivalence of the Graph-Structural and Optimization-Based Characterizations of Popular Matchings	2026-08-31	2508.00349	arxiv
Make an Offer They Can't Refuse: Grounding Bayesian Persuasion in Real-World Dialogues without Pre-Commitment	2026-08-31	2510.13387	arxiv
Individualized Algorithmic Advice as a Strategic Signal on Competitive Markets	2026-08-31	2511.09454	arxiv
Learning Proportional Committees from Violation Feedback	2026-08-31	2608.30111	arxiv
Rival-Injective Allocations: Support-List Structure and Maximum-Anchor EFX$_0$ Certificates	2026-08-31	2608.30203	arxiv
Residual Maximin Share: Exact Finite-Agent Frontier, Sparse Extremizers, and Threshold Cuts	2026-08-31	2608.30257	arxiv
The Exact MMS Guarantees of EFX and PMMS	2026-08-31	2608.30267	arxiv
Mechanism Design for Facility Location Games Under a Prelocated Facility	2026-08-31	2608.30292	arxiv
LangBP: Language-Guided Reasoning and Acting for Joint Bidding and Pricing	2026-08-31	2608.30343	arxiv
Test-time Reinforcement Learning in Imperfect Information Games	2026-08-31	2608.30635	arxiv
Reaching Fairness by Reallocating Goods	2026-08-31	2608.30669	arxiv
Bidding Games with Rewards: Taming Infinite Configuration Space	2026-08-31	2608.30862	arxiv
Constrained Fair Allocations via Partition Matroid Reductions	2026-08-31	2608.31121	arxiv

These are bibliographic comparisons, not experimental rankings. Follow the original document for methods and conditions.