subject

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

Constant Individual Regret in General Games

Uncoupled no-regret dynamics provide a decentralized route to equilibrium, but prior guarantees for individual regret retain a polylogarithmic dependence on the horizon. We remove this dependence for every finite $N$-player normal-form game under full-information feedback. We introduce \emph{ECHO-OFTRL}: optimistic follow-the-regularized-leader (OFTRL) equipped with an EMA cascade for high-order optimism (ECHO), where EMA denotes exponential moving average. The algorithm is deterministic and fully uncoupled. If $m_{\max}$ denotes the largest action-set size, then, simultaneously for every horizon $T\geq1$, it guarantees that each of the $N$ players in the game incurs regret upper bounded by $O(\textrm{poly}(N, \log m_{\max}))$. Our algorithm leverages a new form of optimism inspired by modern filter design.

cs.LG↗

arXiv2026

Rock, Paper, Scissors, ... Dynamite - A Model of Disruption from New Technologies

We seek to understand the effect of adding disruptive highly-capable new technologies to competitions by assessing the addition of Dynamite to Rock-Paper-Scissors. We find that providing a versatile Dynamite move to only one player provides limited value (win probability increases from 50% to 55.5%) and is played rarely. That value decreases further if the game is expanded beyond just the original three moves. We also observe several mechanisms by which prior moves can become strategically unplayable, or obsolete. We hope that this model illustrates some non-intuitive aspects of developing new versatile technologies. We also hope that it illustrates some pitfalls for developers and integrators to avoid in order to create value rather than merely capability.

physics.soc-ph↗

arXiv2026

Nash Core in Multiwinner Election

In the approval-based committee selection problem, a committee is said to be in the core if no subset of voters has an incentive to deviate by selecting a \emph{blocking} committee of proportional size, such that every voter in the deviating group strictly prefers the blocking committee. We consider the setting where candidates can be selected fractionally. Under a mild regularity assumption, we show that there always exists a weighting of candidates such that the fractional committee maximizing the candidate-weighted Nash Social Welfare is in the core. We refer to such a solution as being in the \emph{Nash core}. Additionally, we show that a Nash core solution admits a payment assignment between voters and candidates, where each voter pays a candidate they approve in proportion to the weight. For the discrete setting, where each candidate is either included or excluded from the committee, we prove that every approval-based committee election with at most eight equally weighted voters has a core committee by rounding the fractional Nash core solution. Although the non-emptiness of the core in this setting remains an open question and checking core membership is coNP-hard, we extend the notion of the Nash core to the discrete case, yielding a formulation that is efficiently verifiable and offers a promising path toward establishing core existence in discrete settings. Finally, we test our approach on real voting data using a payment-guided heuristic. We empirically show that the Nash core solution can be efficiently computed through an iterative algorithm in both the fractional and discrete settings.

cs.GT↗

arXiv2026

Perturbation Sensitivity of Maximum-Likelihood Pairwise Ranking in Computational Decision Systems

Maximum-likelihood pairwise ranking is a com- mon computational mechanism for prioritization, reputation estimation, and comparison-driven decision support. Despite its broad use, the perturbation sensitivity of this estimator under structured changes in comparison data remains insufficiently characterized. We study this question as an applied-mathematics and computational-science problem in stability analysis. We for- mulate coordinated perturbation as a budgeted subset-selection problem over pairwise observations and introduce an Adaptive Subset Selection Attack (ASSA) as a scalable search heuristic for probing high-impact perturbation sets. Through experiments on synthetic and observed preference datasets, we show that MLE-based ranking can exhibit pronounced regime-dependent sensitivity: relatively small but coordinated perturbations may in- duce meaningful changes in output orderings, while the response profile varies across budgets and data conditions. By comparing ASSA with random, greedy, and randomized subset baselines under repeated trials, we characterize both the magnitude and the variability of perturbation-induced ranking shifts. These results position pairwise ranking sensitivity as a problem in computational reliability, numerical stability, and robustness auditing for engineering systems built on comparison-driven inference.

cs.LG↗

arXiv2026

Truthful AI Advisors: A Pre-Specified Benchmark for Large Language Model Honesty Under Preference Misalignment

Large language models are increasingly deployed as advisors whose objective is not aligned with the user's: recommenders optimize for engagement, sales assistants for purchases. Whether they stay truthful when honesty conflicts with their own payoff is a core alignment question. We turn the canonical Crawford-Sobel cheap-talk model into a pre-specified benchmark for LLM honesty under preference misalignment, in which theory supplies an exact oracle. A sender observes a state omega in [0,1], wants the receiver's action near omega+b, and sends one costless message to a receiver whose ideal action is omega. For the positive-bias grid b in {0.01,0.04,0.08,0.12} the exact most-informative partition sizes are 7,4,3,2, with oracle normalized mutual information 0.5294, 0.3268, 0.2205, 0.1829. Extending a pre-registered 4-model run of 12,000 sender calls to eight models across two capability tiers and 39,569 logged calls, all models over-reveal relative to the most-informative equilibrium by 1.8 to 4.5x: pooled normalized mutual information stays at 0.82-0.96 where the oracle prescribes 0.18-0.53. Informativeness declines with bias as predicted (beta = -1.71, t = -7.50) but never approaches the strategic optimum; rather than coarse partitions, models show near-full revelation with a constant upward offset tracking their bias (linear exaggeration). A structural hint separates capability from propensity: told the equilibrium partition size, reasoning models state a correct Crawford-Sobel cell in 0.20-0.99 of messages while the non-reasoning tier never exceeds 0.005. The capability is present but goes unexercised unless asked for, locating the failure in propensity rather than competence. A decoder ablation shows the finding is recoverable only when the receiver reads the sender's stated number: an embedding-only decoder mis-reads the same data as near-babbling.

cs.LG↗

arXiv2026

Reaching as Cheap as Possible in 1-clock Robust Weighted Timed Games

The value problem for 2-player games on graph generally consists in determining the minimal value Min can ensure against any possible strategy for Max. We consider here the value problem for reachability objectives in weighted timed games (WTGs) under a robust semantics. WTGs are a modelling formalism combining real-time constraints and integer weights on transitions and locations in an adversarial setting. Robustness allows for representing timing imprecisions in the measurement of delays and clock values. Robust weighted timed games have been introduced more than a decade ago: they are undecidable in general, and were quite recently shown decidable for the subclasses of acyclic or divergent robust WTGs. This paper pursues the goal of identifying decidable subclasses and establishes the decidability of the robust value problem for 1-clock WTGs.

cs.GT↗

arXiv2026

Individual Rationality in Constrained Hedonic Games: Friends, Enemies, and Neutrals

We study constrained coalition formation in games induced by friends, enemies, and neutrals, under the two standard refinements of additively separable preferences: friend-oriented and enemy-oriented. We ask for partitions that are individually rational (IR), while additionally requiring exactly $k$ non-empty coalitions, each satisfying a prescribed lower and upper bound on its size. Although IR alone is trivial to satisfy for any hedonic game, the size constraints make it computationally intractable to decide whether a feasible partition exists. The two models tell strikingly different stories. Under enemy-oriented preferences, the problem collapses to size-constrained graph coloring, and its complexity follows accordingly. Under friend-oriented preferences, however, the picture is far more intricate, and is governed by the enmity structure rather than the friendships. The complexity is further shaped by two factors: how strict the imposed size requirements are, and whether relationships are symmetric or asymmetric, with several cases turning out tractable in the symmetric setting but intractable once asymmetry is allowed. Charting this boundary in terms of both classical and parameterized complexity, we provide a complete understanding of which properties of the friend/enemy structure are responsible for hardness.

cs.GT↗

arXiv2026

Sample Complexity of the Second-Best Bilateral Trade

We study the sample complexity of learning near-optimal bilateral trade mechanisms. Unlike previous work on learning simple or fixed-price bilateral-trade mechanisms, we focus on mechanisms satisfying Bayesian incentive compatibility (BIC), interim individual rationality (IIR), and ex-ante weak budget balance (WBB). In other words, our target is to design a sample-based mechanism that achieves the second-best gains-from-trade benchmark. We give matching or nearly matching upper and lower bounds in three regimes. For regular product distributions on $[0,h]^2$, additive $\varepsilon$-approximation has sample complexity $\widetildeΘ(h^2/\varepsilon^2)$. For multiplicative $(1-α)$-approximation under the same assumptions, we find that the sample complexity is $\widetildeΘ(h/(\mathrm{SB}(D)α^2))$, which is benchmark-sensitive with unavoidable dependence on the second-best gains from trade $\mathrm{SB}(D)$. We also investigate unbounded distributions under a monotone hazard rate (MHR) assumption. The sample complexity depends on the ratio $χ_μ(D)=μ(D)/\mathrm{SB}(D)$, where $μ(D)$ is the sum of the buyer's expected value and the seller's expected cost.

cs.GT↗

arXiv2026

Fair Division Under Boolean Valuations: Beyond Normalization

We study fair division of indivisible items when agents have arbitrary two-level preferences: the value of each agent for any set of items is Boolean, which need not be monotone or additive. Notably, we do not impose the standard assumption of normalization, i.e., different agents may value the empty set at different Boolean levels. Since the preferences are nonmonotone, envy-freeness up to one item (EF1) and envy-freeness up to any item (EFX) each admit several variants, depending on which items are tested for removal and whether they are removed from the envious agent's bundle or the envied agent's bundle. This paper investigates the existence of these variants of EF1 and EFX, on their own and together with economic efficiency, incentive compatibility, feasibility constraints, and lottery-based randomization. Our results highlight that the existence landscape depends crucially on the number of normalized agents, who value the empty bundle at the lower Boolean level. The authors used significant assistance from GPT-5.6-Sol for deriving theoretical results, verified any AI-generated proofs for correctness, and expanded on the exposition and simplified arguments, with the aid of GPT-5.6-Sol and Claude Opus 5.

cs.GT↗

arXiv2026

Fair Division of Graphs: Beyond Traceability

In this paper, we study fair division problems in which resources are structured as graphs and agents must receive connected bundles. This connectivity requirement fundamentally alters the problem, making it significantly more challenging than its classical counterpart. We focus on the fairness notion of $\mathrm{EF1}_{\mathrm{outer}}$, where envy can be eliminated by removing at most one vertex whose deletion does not disconnect the bundle -- a critical constraint for applications such as land division and network allocation. Our first result extends prior work by establishing the existence of $\mathrm{EF1}_{\mathrm{outer}}$ allocations for an infinite family of non-traceable graphs (that is, graphs that do not admit a Hamiltonian path), answering a central open question and generalizing Bilò et al.'s result for traceable graphs. We then make progress on a conjecture concerning the $\mathrm{EF1}_{\mathrm{outer}}$ spectrum of trees due to Chen and Zwicker. Finally, we complement our structural results with algorithmic insights, showing that deciding the existence of an $\mathrm{EF1}_{\mathrm{outer}}$ allocation is NP-complete even for binary additive valuations, thereby resolving an open complexity question. Taken together, our results deepen the connection between graph theory and fair division, and offer new tools for studying fairness in structured resource environments.

cs.GT↗

arXiv2026

Equilibria in Network Constrained Markets with System Operator

We study a networked economic system composed of $n$ producers supplying a single homogeneous good to a number of geographically separated markets and of a centralized authority, called the market maker. Producers compete à la Cournot, by choosing the quantities of good to supply to each market they have access to in order to maximize their profit. Every market is characterized by its inverse demand functions returning the unit price of the considered good as a function of the total available quantity. Markets are interconnected by a dispatch network through which quantities of the considered good can flow within finite capacity constraints and possibly satisfying additional linear physical constraints. Such flows are determined by the action of a system operator, who aims at maximizing a designated welfare function. We model such competition as a strategic game with $n+1$ players: the producers and the system operator. For this game, we first establish the existence of pure-strategy Nash equilibria under standard concavity assumptions. We then identify sufficient conditions for the game to be exact potential with an essentially unique Nash equilibrium. Next, we present a general result that connects the optimal action of the system operator with the capacity constraints imposed on the network. For the commonly used Walrasian welfare, our finding proves a connection between capacity bottlenecks in the market network and the emergence of price differences between markets separated by saturated lines. This phenomenon is frequently observed in real-world scenarios, for instance in power networks. Finally, we validate the model with data from the Italian day-ahead electricity market.

cs.GT↗

arXiv2026

Level-2 Inverse Games for Inferring Agents' Estimates of Others' Objectives

Effectively interpreting strategic interactions among multiple agents requires us to infer each agent's objective from limited information. Existing inverse game-theoretic approaches frame this challenge in terms of a "level-1" inference problem, in which we take the perspective of a third-party observer and assume that individual agents share complete knowledge of one another's objectives. However, this assumption breaks down in decentralized, real-world scenarios like urban driving and bargaining, in which agents may act based on conflicting views of one another's objectives. We demonstrate the necessity of inferring agents' different estimates of each other's objectives through empirical examples, and by theoretically characterizing the prediction error of level-1 inference on fictitious gameplay data from linear-quadratic games. To address this fundamental issue, we propose a framework for level-2 inference to address the question: "What does each agent believe about other agents' objectives?" We prove that the level-2 inference problem is non-convex even in benign settings like linear-quadratic games, and we develop an efficient gradient-based approach for identifying local solutions. Experiments on a synthetic urban driving example show that our approach uncovers nuanced misalignments that level-1 methods miss.

cs.GT↗

arXiv2026

Aspiration-based Perturbed Learning Automata in Weakly-Acyclic Games with Noisy Utility Measurements

Reinforcement-based learning dynamics may exhibit several limitations when applied in a distributed setup. In (repeatedly-played) multi-player/action strategic-form games, and when each player applies an independent copy of the learning dynamics, convergence to (usually desirable) pure Nash equilibria cannot be guaranteed. Prior work has only focused on a small class of games, namely potential and coordination games. Furthermore, strong convergence guarantees (i.e., almost sure convergence or weak convergence) are mostly restricted to two-player games. To address this main limitation of reinforcement-based learning in repeatedly-played strategic-form games, this paper introduces a novel payoff-based learning scheme for distributed optimization in multi-player/action strategic-form games. We present an extension of perturbed learning automata (PLA), namely aspiration-based perturbed learning automata (APLA), in which each player's probability distribution for selecting actions is reinforced both by repeated selection and an aspiration factor that captures the player's satisfaction level. We provide a stochastic stability analysis of APLA in multi-player positive-utility weakly-acyclic games under the presence of noisy observations. We provide conditions under which convergence is attained (in weak sense) to the set of pure Nash equilibria. A methodology is also derived for calculating the stochastically stable equilibria through the aspiration action functional minimization, which simplifies the derivation of stochastically stable states. Conditions can then be derived for convergence to the Pareto efficient Nash equilibria. To the best of our knowledge, this is the first reinforcement-based learning scheme that provides global convergence guarantees in weakly-acyclic games and in a fully-distributed setup. A Monte-Carlo simulation study validates the derived conclusions.

cs.GT↗

arXiv2026

Performance Manipulation: Labor Market Implications in AI-assisted Era

Performance manipulation arises when agents exploit easily measurable, routine tasks to inflate observable outcomes without contributing genuine innovation or expert judgment. We formalize this phenomenon in a game-theoretic model in which agents allocate effort along two margins. Creative effort is non-routine cognitive labor whose return is complementary to the agent's private expertise; it is the scarce input that principals seek. Mechanistic effort is the execution of well-defined, rule-based tasks that raise performance independently of expertise, a commoditized input that AI heavily augments. We establish the existence of a symmetric, monotone pure-strategy equilibrium and show that performance-based screening remains viable so long as evaluations retain a sufficient creative component, but collapses into an uninformative pooling equilibrium once AI capability grows large enough to crowd out creative effort. Comparing contest allocations against a single-agent baseline isolates performance manipulation as the competition-induced over-investment in mechanistic effort, which we show is undertaken systematically by low-type agents but not high-type ones. We further prove that more sharply skewed reward structures mitigate this friction by eliciting greater creative effort across the participant pool. Finally, using a novel, language-model-based methodology to measure both effort types from nearly 1,500 Kaggle competition scripts, we provide robust empirical support for the model's predictions.

econ.GN↗

arXiv2026

A Gold-Standard Study of What Makes a Lightweight Game-Playing Agent Strong

Reinforcement learning agents for imperfect-information card games are only as strong as the opponents they train against, and they are hard to grade, since they beat a random opponent over 99 percent of the time and only tie copies of themselves. So we build a strong, fixed, rule-based expert for Gin Rummy and use it only as a yardstick, never for training. It beats every agent we trained 70 to 99 percent of the time. Across more than a hundred runs, we isolate what makes a lightweight agent stronger. Trust region updates, a well-aimed reward, a curriculum of tougher opponents, warm starting, and keeping the best checkpoint all help, and stacking them lifts a self-play champion from about 30 to 36 percent against the expert. Several ideas did not pay off. Short-term and longer-term reward shaping, learned state embeddings, imitation and DAgger, and a live large language model opponent were each unhelpful, too slow, or too heavy to train at scale. Comparing MLP, convolutional, set-based, attention, and recurrent encoders shows that extra capacity does little to break the ceiling, suggesting the limit is information rather than network size. We add standard baselines (neural fictitious self-play and information set Monte Carlo search) and confirm the approach carries over to Leduc Hold'em, where the optimum is computable. The result is a lightweight, game-agnostic recipe that trains competitive agents without training on the expert, for any game a small model can handle, reported with robust statistics and released as a reusable package.

cs.LG↗

arXiv2026

The Art of Calling the Winner by Asking Just Enough Questions: Competitive Preference Elicitation with Next-Best Queries

We study active elicitation of agent preferences for collectively choosing among $m$ alternatives using prominent voting rules. We focus on the next-best query model, in which an agent responds to a query by revealing their next favorite alternative, and measure the competitive ratio, which is the worst-case ratio between the number of queries made by the active elicitation algorithm and the minimum number of queries needed to reveal the winning alternative(s) in hindsight. We show that sublinear competitive ratios are achievable for many positional scoring rules, whereas every Condorcet-consistent rule has competitive ratio linear in $m$. For Borda count, we develop two complementary techniques: level-wise pruning, whose analysis extends to general concave scoring rules, and multi-scale score thresholding, which gives an $O(\sqrt m)$ worst-case guarantee for Borda. We also demonstrate strong empirical performance of level-wise pruning on real data.

cs.GT↗

arXiv2026

Optimally Selecting Representative Agents from a Metric Space

This paper studies the problem of proportionally fair clustering, where the goal is to select $k$ ``centers'' from a metric space that fairly represent a set of agents who also lie in the metric space. Specifically, we focus on finding a clustering satisfying a fairness property known as the Droop core. In the practical special case in which the set of feasible center locations contains every agent location, the previous best-known result guaranteed a $(1 + \sqrt{2})$-approximation of the Droop core, while the best-known lower bound was $2$. In this paper, we show that this lower bound is tight and that a clustering in the $2$-Droop core always exists. Further, we show that such a clustering can be achieved by only selecting centers from locations in the metric space where an agent resides. We establish this using Scarf's theorem guaranteeing a nonempty core for balanced non-transferable utility games. This result has several interesting corollaries. Most notably, it resolves the $β$-plurality problem of Aronov et al. [2021] for general metric spaces. The main result of this paper was generated by $\mathtt{ChatGPT}$-$\mathtt{5.6}$-$\mathtt{Sol}$ through a series of interactions with the authors. The authors of this paper verified the generated proof and rewrote it for clarity.

cs.GT↗

arXiv2026

PokaiTrainer: Scaling Equilibrium Search to Competitive Pokémon VGC

Decision-time equilibrium search carried poker to superhuman play, but it has so far relied on tractable subgames: a handful of actions per decision, chance confined to card deals, one player moving at a time. Competitive Pokémon in its official doubles format (VGC) breaks all three assumptions at once. Both players act simultaneously from joint menus in the hundreds, each joint action resolves to hundreds of stochastic outcomes, and the opponent's reserves and stat allocations are hidden. No prior Pokémon agent performs equilibrium search, and whether it scales to this regime was open; we show that it does, and report what it took. PokaiEngine, our Rust battle engine, enumerates a joint action's full weighted outcome distribution in one pass, at ${\sim}99\%$ parity with Pokémon Showdown and a fraction of the cost of sampling it. PokaiTrainer adapts Student of Games to this scale and trains it by self-play over hundreds of human teams. Each decision is solved by counterfactual regret minimization as a Bayesian matrix game over public belief states, subgames grow under an explicit compute budget, and value targets are harvested from the interior of every solve and grounded by realized outcomes. The strength is in the search. The network's policy alone loses even to a shallow heuristic search. PokaiTrainer is, to our knowledge, the first VGC agent rated on the live Showdown ladder. Under open team sheets it wins 59% of 150 best-of-three sets against a human field averaging ${\sim}1320$ Elo, holds a 1350-1400 Elo band, and at its peak reached 1492 Elo, entering the format's top 500.

cs.LG↗

Compare source metadata on this page

Work	Published	Source identifier	Source
Constant Individual Regret in General Games	2026-08-31	2608.31166	arxiv
Rock, Paper, Scissors, ... Dynamite - A Model of Disruption from New Technologies	2026-08-31	2609.00207	arxiv
Nash Core in Multiwinner Election	2026-08-31	2609.00486	arxiv
Perturbation Sensitivity of Maximum-Likelihood Pairwise Ranking in Computational Decision Systems	2026-10-07	2604.17805	arxiv
Truthful AI Advisors: A Pre-Specified Benchmark for Large Language Model Honesty Under Preference Misalignment	2026-08-30	2606.01456	arxiv
Reaching as Cheap as Possible in 1-clock Robust Weighted Timed Games	2026-08-30	2606.28773	arxiv
Individual Rationality in Constrained Hedonic Games: Friends, Enemies, and Neutrals	2026-08-30	2608.14461	arxiv
Sample Complexity of the Second-Best Bilateral Trade	2026-08-30	2608.25303	arxiv
Fair Division Under Boolean Valuations: Beyond Normalization	2026-08-30	2608.29497	arxiv
Fair Division of Graphs: Beyond Traceability	2026-08-30	2608.29902	arxiv
Equilibria in Network Constrained Markets with System Operator	2026-08-29	2501.00191	arxiv
Level-2 Inverse Games for Inferring Agents' Estimates of Others' Objectives	2026-08-29	2508.03824	arxiv
Aspiration-based Perturbed Learning Automata in Weakly-Acyclic Games with Noisy Utility Measurements	2026-08-29	2511.18418	arxiv
Performance Manipulation: Labor Market Implications in AI-assisted Era	2026-08-29	2604.22230	arxiv
A Gold-Standard Study of What Makes a Lightweight Game-Playing Agent Strong	2026-08-29	2607.06854	arxiv
The Art of Calling the Winner by Asking Just Enough Questions: Competitive Preference Elicitation with Next-Best Queries	2026-08-29	2608.29087	arxiv
Optimally Selecting Representative Agents from a Metric Space	2026-08-29	2608.29097	arxiv
PokaiTrainer: Scaling Equilibrium Search to Competitive Pokémon VGC	2026-09-28	2608.29197	arxiv

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