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arXiv2026

Games Over Observation Spaces in Multi-Agent Capture the Flag

We consider a multi-agent Capture the Flag (CtF) scenario in a graph-based environment, where a team of attackers seeks to reach designated flag vertices while a defending team attempts to intercept them. In our setting, both teams operate using decentralized heuristic policies. While the attacking team may choose its heuristic from a diverse library of policies, the defense is restricted to playing a single fixed policy. To overcome this limitation, a centralized defense oracle strategically restricts the portion of the graph visible to each of its agents in order to elicit a wider range of emergent behaviors from its fixed policy. We formalize this interaction as a two-player zero-sum game, where the attacker reasons over its library of heuristics and the defense reasons over the combinatorial space of visibility profiles. To solve this intractably large game, we propose a Double Oracle algorithm to find approximate empirical equilibria, and we empirically validate that observation manipulation can improve the defense's performance.

cs.GT↗

arXiv2026

Pairwise Maximin Share Allocations Need Not Exist

We study the fair allocation of indivisible goods among agents with strictly positive additive valuations. Pairwise maximin share fairness (PMMS) asks that, for every ordered pair of agents, the first agent value her own bundle at least as highly as the best worst-case share she could secure by repartitioning the two agents' combined bundles into two parts. Whether a PMMS allocation always exists for positive additive valuations has remained open since the notion was introduced. We resolve this question in the negative. We construct an instance with four agents and strictly positive additive valuations that admits no complete PMMS allocation.

cs.GT↗

arXiv2026

Antichains for Concurrent Parameterized Games (Long Version)

Concurrent parameterized games involve a fixed yet arbitrary number of players. They are described by finite arenas in which the edges are labeled with languages that describe the possible move combinations leading from one vertex to another (n players yield a word of length n). Previous work showed that, when edge labels are regular languages, one can decide whether a distinguished player, called Eve, has a strategy to ensure a reachability objective, against any strategy profile of her arbitrarily many opponents. This decision problem is known to be PSPACE-complete. A basic ingredient in the PSPACE-membership proof is the reduction to the exponential-size knowledge game, a 2-player game that reflects the knowledge Eve has on the number of opponents. In this paper, we provide a symbolic approach, based on antichains, to compute Eve's winning region in the knowledge game. In words, it gives the minimal knowledge Eve needs at every vertex to win the concurrent parameterized reachability game. More precisely, we propose two fixed-point algorithms that compute, as an antichain, the maximal elements of the winning region for Eve in the knowledge game. We implemented these two algorithms in C++, as well as the one initially proposed, and report on their relative performances on various benchmarks.

cs.LO↗

arXiv2026

The Popular Dimension of Matchings

We study popular matchings in three classical settings: the house allocation problem, the marriage problem, and the roommates problem. In the popular matching problem, (a subset of) the vertices in a graph have preference orderings over their potential matches. A matching is popular if it gets a plurality of votes in a pairwise election against any other matching. Unfortunately, popular matchings typically do not exist. So we study a natural relaxation, namely popular winning sets which are a set of matchings that collectively get a plurality of votes in a pairwise election against any other matching. The $\textit{popular dimension}$ is the minimum cardinality of a popular winning set, in the worst case over the problem class. We prove that the popular dimension is exactly $2$ in the house allocation problem, even if the voters are weighted and ties are allowed in their preference lists. For the marriage problem and the roommates problem, we prove that the popular dimension is between $2$ and $3$, when the agents are weighted and/or their preferences orderings allow ties. In the special case where the agents are unweighted and have strict preference orderings, the popular dimension of the marriage problem is known to be exactly $1$ and we prove the popular dimension of the roommates problem is exactly $2$.

cs.GT↗

arXiv2026

Enhancing Affine Maximizer Auctions with Correlation-Aware Payment

Affine Maximizer Auctions (AMAs), a generalized mechanism family from VCG, are widely used in automated mechanism design due to their inherent dominant-strategy incentive compatibility (DSIC) and individual rationality (IR). However, as the payment form is fixed, AMA's expressiveness is restricted, especially in distributions where bidders' valuations are correlated. In this paper, we propose Correlation-Aware AMA (CA-AMA), a novel framework that augments AMA with a new correlation-aware payment. We show that any CA-AMA preserves the DSIC property and formalize finding optimal CA-AMA as a constraint optimization problem subject to the IR constraint. Then, we theoretically characterize scenarios where classic AMAs can perform arbitrarily poorly compared to the optimal revenue, while the CA-AMA can reach the optimal revenue. For optimizing CA-AMA, we design a practical two-stage training algorithm. We derive that the target function's continuity and the generalization bound on the degree of deviation from strict IR. Finally, extensive experiments showcase that our algorithm can find an approximate optimal CA-AMA in various distributions with improved revenue and a low degree of violation of IR.

cs.GT↗

arXiv2026

Trusting AI in Competitive Markets

People's trust in AI advice diverges as they use it, deepening for some and eroding for others. We study this divergence in oligopoly pricing, where advice cannot prove itself: rivals' responses decide whether it pays off. In a laboratory experiment, 273 sellers compete across 91 three-seller markets over 30 rounds; we vary the presence of AI pricing recommendations and the gender composition of the market (female-only, male-only, or mixed). We find that the gender composition of the market shapes how sellers learn from the advice, and where prices settle as a result. In female-only markets, recommendations raise prices by 29% and profits by 39%; in male-only and mixed-gender markets, they have no significant effect. A Non-Homogeneous Hidden Markov Model reveals a composition-specific dynamic association: profitable rounds predict rising adherence to the AI in female-only markets and declining adherence otherwise, a pattern consistent with learned trust and self-serving attribution. The pattern reverses what recent evidence on gender and AI would predict. We discuss implications for platform governance and regulatory oversight, which should focus not only on the algorithm but on the human side that shapes its effects.

cs.GT↗

arXiv2026

Token-Level Advertising

Generative AI is transforming how people access information, challenging traditional advertising mechanisms built around predefined slots. Towards generation-native advertising, we propose the Latent Advertiser Mixture Auction (LAMA), a token-level advertising mechanism that embeds advertiser influence directly into the generation process. Advertisers report local continuation values that induce advertiser-specific next-token policies, from which the platform decodes through a latent mixture while updating an allocation posterior. We show that LAMA satisfies Markov DSIC and IR, and achieves near-optimal KL-regularized welfare. We further develop a learning-based implementation that reconstructs the required reports online from learned local advantages and root values. Proof-of-concept experiments on real-world commercial-search query splits show that LAMA improves platform welfare and revenue while maintaining user-facing response quality, providing initial evidence for the feasibility of generation-native advertising.

cs.GT↗

arXiv2026

Weighted Fair Division of Indivisible Mixed Manna

We study weighted fair division of indivisible mixed manna under additive valuations. First, we resolve the general existence open question for weighted envy-freeness up to one item (WEF1), and show that every instance with arbitrary positive entitlements admits a complete WEF1 allocation computable in polynomial time. We then show that existence does not imply any welfare guarantee, i.e., the utilitarian price of WEF1 is infinite, even for two unweighted agents with normalized valuations, common item signs, and singleton values in a fixed four-value set; a welfare-maximizing WEF1 allocation in the construction is fractionally Pareto optimal. Second, suppose each agent $i$ has a number $a_i>0$ such that their valuation for any item is $-a_i$, $0$, or $a_i$. Then, for arbitrary entitlements, a weighted maximin share (WMMS) allocation always exists, is computable in polynomial time, and can be chosen to be fractionally Pareto optimal. An exact formula for each WMMS value leads to a polynomial-time flow algorithm. In this class, every WEF1 allocation satisfies a best possible additive WMMS guarantee whose loss depends on the agent's entitlement relative to the largest entitlement. Thus maximum entitlement agents receive exact WMMS and, under equal entitlements, every WEF1 allocation is also MMS-fair. Allowing a second positive magnitude can violate exact WMMS, while unrestricted entitlement ratios rule out any fixed multiplicative WMMS guarantee compatible with WEF1 for chores.

cs.GT↗

arXiv2026

Strategic Facility Location in Euclidean Spaces

The strategic facility location problem is defined as follows: $n$ agents report their location in a metric space, and the objective is to design a \emph{mechanism} deciding the (possibly randomized) location of a facility such that agents have no incentive to lie about their position. We focus on the egalitarian cost, which means that the goal of the mechanism is to minimize the expected maximal facility-agent distance. Meanwhile, mechanisms must be \emph{truthful} (or \emph{strategyproof}): no agent may decrease their expected distance to the facility via lying on their location. Designing truthful mechanisms minimizing the approximation ratio is a well-studied problem, and the optimal solution is known for the real line. We focus in this paper on higher dimension Euclidean spaces, for which gaps remain between the best known lower and upper bounds. We first show that, maybe counter-intuitively, the problem is easier for two agents on the plane rather than on the line: the mechanism can exploit the additional dimension to prevent more efficiently agent lies. Based on this intuition, we devise lower bounds for $\mathbb R^d$ asymptotically matching the best known approximation factor of $2$ for large $d$. We also provide novel mechanism ideas, improving over the best known algorithms on the plane, and when the agents belong to $\mathbb R^d$ but the facility may use an additional dimension.

cs.GT↗

arXiv2026

Cutting Down the Tower: Single-Exponential Envy-Free Cake Cutting

Envy-free cake cutting is a central problem in fair division with a striking divide between existence and computation. Classical topology guarantees that envy-free allocations exist, yet finding one efficiently turned out to be much harder, and this problem has resisted decades of work. A well-known result by Aziz and Mackenzie established the existence of a bounded protocol for every $n$, but its query bound is $n^{n^{n^{n^{n^n}}}}$. A tighter analysis by Sokolov subsequently reduced this upper bound to $n^{8n^2(1+o(1))}$, the best known prior to this work. In contrast, the general lower bound, due to Procaccia, is merely $Ω(n^2)$. We close much of this massive gap with a protocol using at most $n^{O(1)}2^n$ queries. At a high level, our protocol repeatedly allocates some cake without creating envy until the remaining problem involves fewer agents. The main difficulty is to ensure that, when we later put these allocations together, we neither assign any cake twice nor create envy. To overcome this difficulty, we develop a new construction using only polynomially many partial allocations, replacing the $n^{n^{n^n}}$ partial allocations used in previous work. Overall, our protocol gives the first single-exponential query bound for finding a complete envy-free allocation with arbitrary nonatomic, additive valuations.

cs.GT↗

arXiv2026

Optimal Rates for Agentic Networked Information Aggregation

Building on the pioneering paper of Kearns, Roth, and Ryu (SODA'26), we study information aggregation in a networked learning model. The model captures a central pattern in agentic AI: each agent sees only part of the data and passes on only its own conclusion. Their model considers a linear regression problem with the mean squared error (MSE) loss. Agents sit in a DAG and each sees only a subset of the features and its parents' predictions, fits a linear predictor, and passes only its prediction forward. The benchmark is the full-feature learner that sees all raw features. A path of depth $D$ is $M$-covered if every block of $M$ consecutive agents collectively sees all raw features. Kearns, Roth, and Ryu proved that the excess mean squared error of the last agent on such a path is $O(M/\sqrt D)$, and gave a cyclic instance with excess error $Ω(M/D)$ for $D<M^2$. We close this gap: the correct rate is constant up to depth $M^2$, and $Θ(M^2/D)$ beyond it. We first give a sharper analysis of the cyclic instance and improve its lower bound to $Ω(\sqrt{M/D})$ for $D<M^2$. We then construct, for every depth $D\ge M^2$, an $M$-covered path of depth $D$ with excess error $Ω(M^2/D)$. The same instance gives the constant lower bound for all $D < M^2$. We also show that for any fixed distribution the excess error contracts geometrically along the path, ruling out any single instance that witnesses any polynomial lower bound at every depth. Finally, we prove the same optimal rate for logistic classification in the logit-passing model of Bateni et al., which considers the binary cross-entropy (BCE) loss. The same improved upper bound of $O(M^2/D)$ holds, and we transfer all the regression lower bounds by showing that on those examples the logistic path follows the least-squares path up to rescaling.

cs.LG↗

arXiv2026

Utility-Driven Spatial Data Sampling for UAV-Assisted Scientific Smart Farming

Large smart-farming deployments generate continuous scientific data from spatially distributed sensors, including soil, humidity, temperature, crop-health, and pest-related measurements. In vast agricultural fields, however, an energy-constrained unmanned aerial vehicle (UAV) often cannot collect data from every sensor during each mission. Existing UAV-assisted collection methods typically optimize coverage, route length, data volume, or freshness, but they do not always distinguish between data that is merely available and data that is scientifically valuable. This poster introduces a utility-driven spatial sampling framework for UAV-assisted smart farming. The field is partitioned into grid cells, each sized according to the UAV ground coverage range. After an initial exploration phase, each cell receives a scientific utility score based on freshness, redundancy, anomaly likelihood, and model uncertainty. The UAV then selects and visits a subset of high-utility cells under battery and return-to-base constraints. The proposed framework reframes UAV-based collection as adaptive scientific data management rather than exhaustive sensing.

cs.GT↗

arXiv2026

Otter: A Provably MEV-Resilient Automated Market Maker via Surplus Redistribution

Miner extractable value (MEV) in automated market makers allows block builders to profit from transaction ordering and injected trades, imposing costs on users and contributing to builder centralization. We introduce Otter (Optimal Truthful Trading with Excess Redistribution), a two-asset batch AMM that achieves provable MEV resilience when the consensus layer provides censorship resilience and block space is uncongested. Otter makes truthful behavior a dominant strategy for both users and builders. Consequently, a builder cannot profit from strategic deviations, including reordering bids or injecting sybil bids, even when the builder is itself a trader with intrinsic value. Moreover, we show that Otter maximizes social welfare, in a strong sense, within a natural class of mechanisms satisfying the desired game-theoretic properties. To achieve these guarantees, we introduce a new paradigm called surplus redistribution, which provably prevents residual surplus from being captured as MEV by redirecting it to the broader community. Specifically, the pool's output tokens need not be distributed entirely among users in the current batch. Instead, residual surplus may be transferred to a smart contract governed by the decentralized community. The accumulated surplus can be used to benefit community members --- for example, by subsidizing transaction fees, rewarding liquidity providers, or returning assets to the pool. Our approach relies on the underlying consensus layer to provide censorship resilience. We motivate its necessity through an impossibility result showing that the desired game-theoretic guarantees become unattainable when the builder is additionally allowed to censor transactions. Thus, our results also provide a mathematically formal demonstration of how consensus-level security guarantees can fundamentally expand what is achievable at the application layer.

cs.GT↗

arXiv2026

Batched Pandora's Box

Motivated by numerous parallelizable stochastic search problems, most notable and timely among them being LLM inference-time scaling, we propose and study batched versions of the Pandora's Box problem of Weitzman. In particular, boxes are opened in capacity-constrained batches, each batch has a setup cost, and all rewards in a batch are revealed together. We consider two different variants, motivated by different application environments: one where boxes are reusable (i.e., can provide multiple i.i.d.~samples) and another where they are not. For both variants we rule out most ``simple'' natural heuristics, and also formally prove NP-hardness of approximation in the traditional sense. We then relax the problem to allow bi-criteria approximations, with respect to both rewards and setup costs, where we exhibit constant approximation algorithms for both the reusable and non-reusable settings. This is obtained through a linear-programming relaxation of Pandora's Box problem, followed by randomized or Pipage rounding.

cs.DS↗

arXiv2026

Constant regret in general games via higher-order optimism

We introduce an uncoupled learning algorithm which, when employed by all players of an arbitrary $N$-player normal form game with up to $K$ actions per player, guarantees $O(N^3\log^2 K)$ individual regret, uniformly over the horizon of play. The proposed algorithm - which we call higher-order optimism with discounting (HOOD) is a variant of optimistic follow-the-regularized-leader (OptFTRL) that combines a discounted $(N+1)$-th order predictor with entropic regularization over a suitable "lifting" of the game's strategy space. This combination of ingredients is purposefully designed to dampen large oscillations of the induced sequence of play in a controlled manner, removing in this way a key stumbling block of previous attempts to achieve constant regret in general games. Our approach bears several striking similarities to the concurrent - and completely independent - work of Liu, Farina, and Ozdaglar (arXiv:2608.31166), who very recently derived an $O(N^{21}\log^{4} K)$ regret bound through the use of higher-order optimism and an exponential moving average estimator.

cs.LG↗

arXiv2026

Abstraction Agent

Information abstraction, which groups strategically similar private states into a tractable number of buckets, is essential for scaling game-solving algorithms to large imperfect-information games. Constructing effective abstractions, however, has traditionally required domain-specific evaluators such as hand-strength calculators or equity estimators, which demand expert knowledge and engineering effort and are unavailable for most less-studied games. We propose the Abstraction Agent, a zero-shot pipeline that uses a large language model (LLM) to discover continuous strategic features from a natural-language game description, score private states on these features, and cluster them into abstraction buckets, without any game-specific evaluator, training data, or game-tree traversal during abstraction construction. The pipeline runs in four phases: feature discovery with calibration anchors, batched private-state scoring, correlation-based feature selection, and $k$-means clustering. The resulting abstractions reduce lifted-strategy exploitability by up to 62% relative to an expected-hand-strength baseline on heads-up no-limit Texas hold'em (HUNL) turn endgames, and beat a scalar rank baseline at every granularity on ROVER Trials, an original game absent from any pretraining corpus. Beyond these quantitative benchmarks, the pipeline transfers with unchanged prompts to four-card Pot-Limit Omaha, HUNL preflop and flop, and Riichi Mahjong, where the discovered features track each game's recognized strategic concepts. This is structured knowledge elicitation: converting implicit strategic knowledge in LLM parameters into explicit numerical features for downstream algorithmic computation. The code is available at https://github.com/lbn187/AbstractionAgent.

cs.MA↗

arXiv2026

Game-Theoretic Drone Swarm Defense: A Case Study in Applied Differential Game Theory

This technical report is a study of the use of differential game (DG) theory to solve the target-assignment and midcourse guidance problems of drone swarms tasked with intercepting opposing swarms in defense of high-value assets. The game-theoretic tactics---which treat the intruder swarm as a rational agent and seek a Nash equilibrium between defenders and intruders---are compared against baseline tactics that model the defense problem as a unilateral optimization of the defenders' maneuvers. Monte Carlo simulation and Bayesian analysis show that the game-theoretic approach has a higher probability of successfully intercepting all intruders than the baseline techniques. This improvement in successful defense probability is most pronounced when the intruder swarm is capable of evasive maneuvers: relative to baseline optimization tactics, differential-game tactics increase estimated defense success from 94.6% to 96.8%, closing approximately 41% of the remaining gap to perfect defense. To add statistical credibility to this result, a paired-trial Bayesian analysis assigns a 99.9% posterior probability that differential-game tactics have a higher probability of successful asset defense than baseline tactics in this scenario.

cs.GT↗

arXiv2026

A Numerical Approach to the Realizability Problems for Memoryless Nash and Epsilon Equilibria in Concurrent Multiplayer Reachability Games

The existence of equilibria, which is called the realizability problem in the formal methods community, for probabilistic undiscounted state-based systems has proven to be an incredibly challenging research setting. In this paper, we consider a restricted version of the classic realizability problem by focusing on equilibria that are both memoryless and numerically constrained. While the restriction to memoryless strategies is relatively common in the literature, numerical constraints, to the best of our knowledge, represent a new and powerful approach. First, we consider the existence of memoryless equilibria when all numbers involved must be rational numbers of a pre-defined limited size. Then, we extend this analysis to field extensions of the rational numbers created through radical algebraic generators. When the basis is provided for the latter, both realizability problems are NP-complete for both exact and epsilon Nash equilibria. Finally, we consider an unconstrained numerical setting. While the characterization of the exact Nash equilibria realizability problem as ETR-complete is one of the most celebrated results in the literature, we demonstrate that the constructions underlying this result are flawed as presented. We then mend said constructions to preserve the ETR upper bound, and note that the lower bound in the literature does not apply to the epsilon-equilibrium setting. Overall, this paper demonstrates an interesting relationship between the complexity of the realizability problem and the "complexity" of the numbers involved in the representations of strategies.

cs.GT↗