Papers

Crowdsourcing platforms coordinate large pools of online workers who strategically choose which contests to enter and how much effort to invest. This self-selection can leave important contests with too few participants or too little effort, while workers may regret entering contests that leave them worse off than available alternatives. We study how platforms can recommend contests to workers using self-selection in Tullock contests (SSTC), a two-stage model in which workers first choose contests and then compete within them. We introduce GRAF, a greedy polynomial-time framework that constructs self-selection outcomes by ordering workers according to a score vector, with guarantees of zero worker regret and platform optimality in special cases of SSTC. Because effective orderings are difficult to design under worker heterogeneity, we propose LLMScore, an LLM-driven evolutionary framework that automatically designs GRAF's scoring algorithm. LLMScore addresses two challenges: jointly optimizing platform utility and worker satisfaction, and evaluating worker regret when exact computation is intractable. Trained only on small instances of one setting, it transfers to larger and structurally different settings; moreover, its output is human-readable code that platform operators can inspect and modify. Across 1,000 synthetic instances spanning four settings, GRAF with LLMScore consistently achieves high-quality, often near-optimal, outcomes with low worker regret, benefiting both platforms and workers.

In approval-based committee voting, proportional approval voting (PAV) is a well-studied rule that combines proportional representation with Pareto efficiency. However, computing a PAV committee is NP-hard, raising a natural question: Can the proportionality and efficiency properties of PAV be achieved via computationally efficient procedures? We make two contributions toward answering this question. First, building on the known proportionality guarantees of the local-search-based variant of PAV (or local PAV), we systematically study its efficiency properties. We show that local PAV committees are weakly Pareto optimal, meaning that no other committee is strictly preferred by every voter. We also identify limitations: Local PAV guarantees only a $2$-approximation to fractional Pareto optimality ($2$-fPO) and a $2/3$-approximation to the optimal PAV score, and both bounds are tight. In contrast, global PAV is Pareto optimal and satisfies the stronger $\alpha^\star$-fPO guarantee, where $\alpha^\star \approx 1.346$ is the unique solution of $\int_0^{\alpha^\star} \frac{1-e^{-y}}{y} \, dy = 1$, and this approximation is tight. Second, we design a polynomial-time algorithm that combines the best of these guarantees. The committee returned by our algorithm satisfies EJR$+$ (a proportionality guarantee), $\alpha^\star$-fPO, and weak Pareto optimality. It also achieves a $0.79$-approximation to the optimal PAV score, matching the best possible polynomial-time approximation assuming $P \neq NP$. Our algorithm works by pipage rounding a concave relaxation of the PAV objective and using that committee to initialize local PAV, thereby combining global approximation guarantees with local search stability.

Large language models act as strategic agents and models of human choice, yet choosing like a strategic agent does not mean computing like one. We recorded activations from four open-weight models — dense and mixture-of-experts, including a matched base–instruct pair — in one-shot play of 144 strict ordinal $2\times2$ games. We followed a prespecified incentive from prompt, through activations, to choice. Dense models mirrored the unadjusted human decline with game complexity. Incentive and choice were detectable in every model, but models differed in whether incentive reached the choice, aligned with it and, where tested, whether strengthening it shifted preference. The base and instruction-tuned Qwen2.5 models chose almost identically at baseline yet differed in whether incentive reached choice. Fixed decision cues were distinguishable internally but changed choices selectively. Similar behaviour can rest on different computation; post-training can reshape the path from represented incentive to decision while leaving behaviour and decodable information largely intact.

Quantum game theory is an extension of classical game theory that uses quantum principles in game theory. The Eisert-Wilkens-Lewenstein (EWL) quantum game is an early example of the two-player classical Prisoner's Dilemma transformed into a quantum Prisoner's Dilemma. In the EWL game, the players choose pure quantum strategies represented by unitary matrices. This extension can resolve the classical dilemma by enabling cooperative equilibrium with higher payoff. In this paper, we first discuss the Extended EWL (EEWL) for multiplayer quantum games with mixed strategies. In EEWL, each player controls a set of unitary operators as quantum actions and uses a classical mixed strategy over these actions. The payoffs are defined as expectation values of Hermitian reward operators acting on a shared quantum state, which is generated and measured according to the EEWL protocol. We then propose the Unitary Strategy Matrix Exponential Algorithm (USMEA), a geometry-aware sequential algorithm for the EEWL mixed-strategy setting, in which each player jointly learns a trainable set of local unitary actions and the associated classical mixing probabilities. Thereby it acts as a learning-and-control layer for multi-agent quantum decision systems. We analyze the convergence properties of USMEA under standard smoothness and step-size conditions and validate the theory with numerical experiments. These results show how classical optimization methods can be systematically integrated into the design and analysis of engineered quantum strategic interactions.

We study randomized strategyproof mechanisms for strategic obnoxious facility location on a line segment, where agents wish the facility to be located as far away from them as possible and their utility is their distance from the facility, under the social utility and minimum utility objectives. For social utility, we propose a novel randomized mechanism that breaks the previously best known \(\frac32\)-approximation of [Cheng, Yu, and Zhang, TCS 2013], achieving an approximation ratio of at most \(1.47359\). We also raise the lower bound on the approximation ratio of randomized strategyproof mechanisms from \(\frac{2}{\sqrt{3}}\approx1.15470\) [Feigenbaum et al., JAAMAS 2020] to \(\frac{105}{88}\approx1.19318\). For minimum utility, following the profile-independent approach of [Chan, Lin and Wang, AAMAS 2026], we design a simple randomized mechanism that reduces the approximation guarantee from \(\sqrt{2n}+O(1)\) to \(\sqrt n+O(1)\), where \(n\) is the number of agents. Finally, we prove that no randomized strategyproof mechanism can achieve an asymptotic approximation ratio strictly smaller than \(2\), strengthening the previous asymptotic lower bound of \(\frac32\) [Feigenbaum et al., JAAMAS 2020]. Thus, all four bounds considered in this paper strictly improve upon the corresponding previously known results.

Trust-Hub reuses host circuits: several files differ mainly in the inserted Trojan. When gates from sibling variants enter both training and test folds, a detector can benefit from host logic it has already seen. We measure that effect instead of proposing another classifier. The corpus contains 49,124 gates from 16 netlists grouped into five host families. We left the parser, 36 gate features, class weighting, model settings, threshold, and family-level aggregation unchanged and altered one choice: the test boundary. The three settings draw test gates from the pooled corpus, withhold a complete netlist, or withhold every variant of one host. The choice matters. Random forest records F1/AP of 0.914/0.978 with pooled gates, 0.636/0.851 with one netlist held out, and 0.460/0.577 with a host family held out. XGBoost falls from 0.946/0.976 to 0.464/0.544 across the same comparison. Logistic regression loses AP, although its fixed-threshold F1 is not monotonic. Each family shows the same pooled-to-family direction. Feature removal, repeated model and simulator seeds, score normalization, parser-related exclusions, and a smaller sample change the size of the gap without reversing it. Aggregation also matters: a gate-weighted average is dominated by the larger ISCAS files, so the headline values give each host family one vote. Bootstrap and jackknife summaries keep the gap positive, but their folds reuse training families. We treat the five family rows as descriptive evidence rather than independent trials. Five host families are too few for a population claim, and the experiment says nothing about transfer to a new cell library or an industrial design. It supports a narrower conclusion: sibling benchmark variants can inflate apparent transfer. Benchmarks with several variants of one host circuit should report family-aware holdouts and all five family results beside pooled scores.

We study the fine-grained complexity of computing approximate Nash equilibria and approximating the value of free games in the regime where the approximation error vanishes. Under the PCP for PPAD and ETH for PPAD conjectures, we show that computing $\varepsilon$-approximate Nash equilibria in 2-player $N$-action normal-form games requires time $N^{(\log(N)/\varepsilon^2)^{1-o(1)}}$, thus showing that the classical Lipton-Markakis-Mehta algorithm (2003) is optimal through all regimes of $\varepsilon = \omega(1/\sqrt{N})$. While such optimality was known in the constant-$\varepsilon$ regime (Rubinstein, 2016), previous work could only rule out significantly smaller running times of $N^{O(\log(N)/\varepsilon)}$ in the regime $\varepsilon = o(1)$. Using similar techniques, we then establish an analogous tight lower bound of $N^{(\log(N)/\varepsilon^2)^{1-o(1)}}$ under ETH for $\varepsilon$-additive value estimation in free games, when $\varepsilon \geq 2^{-o(\sqrt{\log N})}$, answering a question of Aaronson, Impagliazzo, and Moshkovitz (2014).

A tournament rule maps the outcomes of all pairwise matches among $n$ teams to a possibly randomized winner. Desirable rules should be Condorcet consistent and monotone, yet also resistant to manipulation among coalition. Prior work mostly measures such manipulation additively through $k$-strongly non-manipulable at $\alpha$ ($k$-SNM-$\alpha$), meaning that no coalition of size $k$ can fix the matches among themselves to increase their total winning probability by $\alpha$. Very recently, two new notions of non-manipulability were introduced. Multiplicative non-manipulability ($k$-MNM-$\delta$) is defined analogously, using the multiplicative factor instead. Non-manipulability for $\lambda$ ($k$-NM$_\lambda$) characterizes the selfishness of a team, which restricts a coalition's gain to be less than $\lambda$ times the winning probability sacrificed by its members. In this work, we begin with a strict hierarchy among these three notions: NM$_\lambda$ is stronger than MNM, which is then stronger than SNM. This motivates us to consider those two notions that are stronger but less studied: pairwise multiplicative non-manipulability and $2$-non-manipulability for $\lambda$. We show that Randomized Death Match is $2$-MNM-$3/2$ and optimally matches the lower bound. Then, we introduce the BlockBonusedWinStrengths rule, which is Condorcet consistent, monotone, and $2$-NM$_2$. This rule substantially improves the previous upper bound of $\lambda=11$ and comes within a factor of two of the lower bound $\lambda=1$.

Generalized Nash Equilibrium Problems (GNEPs) often arise in multi-agent engineering applications that require distributed algorithms. Unlike traditional approaches that enforce consensus on multipliers, our method removes the need to share multipliers, reducing communication and improving privacy. As a result, different initializations can lead to different GNEs, including non-variational ones. We establish convergence under sufficient conditions using an input-to-state stability (ISS) framework.

This letter investigates a reach-avoid game involving two Attackers and one Defender, where the Attackers aim to maximize the number reaching the target region while the Defender seeks to minimize it. In contrast to conventional complete information formulations, we consider an information asymmetry scenario where the Attackers' heterogeneous maximum speeds are privately known but publicly disclosed to lie within continuous ranges. Existing studies on uncertain speeds, however, have primarily focused on homogeneous settings, whereas heterogeneity extends the uncertainty from a common capability level to the relative capability configuration of the Attackers. To address the resulting capture-order ambiguity over infinitely many possible speed combinations, we establish a critical speed pair framework that characterizes when different capability configurations induce different optimal capture orders, and enables the analysis of the Defender's guessing behavior and the design of information-limiting strategies for the Attackers. We demonstrate that under certain initial conditions, the Attackers can mislead the Defender into making suboptimal decisions through a slow-speed deception strategy, achieving superior payoffs compared to the complete information game. Numerical visualizations reveal the widespread occurrence of such dilemma conditions.

We show that every additive chore instance with three agents and seven or eight indivisible chores has an EFX allocation. Costs may be arbitrary nonnegative reals. Together with the theorem of Kobayashi, Mahara, and Sakamoto for at most $2n$ chores, this settles the existence of EFX allocations for three agents and at most eight chores; for four or more agents, He and Tao have shown that EFX allocations of additive chores need not exist. Both proofs are computer-assisted. For seven chores, we normalize each agent's costs and sort the chores, and then express the nonexistence of an EFX allocation as a formula of quantifier-free linear real arithmetic with one clause per allocation; the SMT solvers Z3 and cvc5 show that this formula is unsatisfiable. For eight chores, if two agents share a cheapest chore, we remove that chore, apply the seven-chore result, and put the chore back using an insertion lemma of Kobayashi, Mahara, and Sakamoto. The remaining instances, in which the agents' sets of cheapest chores are pairwise disjoint, are handled by a second formula of the same kind.

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.

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.

We consider a fully connected gossip network of $n$ nodes that track a binary continuous-time Markov source through a strategic sender transmitting updates under a communication budget at a rate that depends on the source state. The receivers exchange packets through gossip and decide whether to follow the sender. We model this interaction as a Stackelberg game and analyze it through a stochastic hybrid systems (SHS) framework. We prove that the sender's budget constraint binds at every interior optimum, reducing its problem to a one-dimensional search on the budget line. When the sender pushes its preferred state at the higher rate, the receivers gossip at the highest available rate. Gossip has no direction of its own and works against the asymmetry in the sender's policy rather than reinforcing it. We prove that an optimistic Stackelberg equilibrium exists, and that it is unique and explicitly characterized whenever a policy on the strategic half of that line is feasible at the gossip cap. Monte Carlo simulations agree with the analytical recursion.

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.

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 $\Omega(M/D)$ for $D<M^2$. We close this gap: the correct rate is constant up to depth $M^2$, and $\Theta(M^2/D)$ beyond it. We first give a sharper analysis of the cyclic instance and improve its lower bound to $\Omega(\sqrt{M/D})$ for $D<M^2$. We then construct, for every depth $D\ge M^2$, an $M$-covered path of depth $D$ with excess error $\Omega(M^2/D)$. 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.

We study the online fair division of indivisible items, where items arrive one at a time and must be allocated immediately and irrevocably. We address three central open questions in the literature. First, we show that for every $n\ge 2$ agents, every fixed $k\ge 1$, and every $\alpha\in(0,1]$, no online algorithm can guarantee $\alpha$-PROP$k$ against an adaptive adversary. This remains true even when the total number of goods is known in advance, all values lie in $[0,1]$, and every good is positively valued by at most two agents. The impossibility extends to a broad range of standard envy-based, proportionality-based, and share-based fairness notions. We also establish an analogous impossibility for chores. Second, in the setting with predictions, a lightweight form of future information, the maximum item value, was previously known to guarantee only $1/n$-PROP1, leaving open whether the dependence on $n$ is necessary. We give a deterministic $19/30$-PROP1 algorithm against adaptive adversaries that does not require knowing the total number of goods. Given an additional upper bound $\kappa\in[2,n]$ on the number of agents who value any good positively, the guarantee improves to $\max \{ 19/30, n/(n+\kappa) \}$. The guarantee remains a positive constant under any fixed one-sided prediction error below one. When predictions are exact and the total number of goods $m\ge n\log n$ is known in advance, a deterministic algorithm achieves the same $19/30$-PROP1 factor together with $O(\sqrt{m\log n/n})$ maximum additive envy after normalizing each agent's values by their maximum item value. Third, against a non-adaptive adversary, we determine the tight high-probability PROP1 guarantee of the classical Like rule, which assigns each good uniformly among the agents who value it positively. Its guarantee improves when fewer agents value the same good, unlike uniform random allocation.

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 $\Omega(n^2)$. 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.

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 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 truthful (or 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.

For approval-based committee elections, the sizewise least-core value $\Gamma(P)$ minimizes the maximum excess support of a deviation over size-$k$ committees. Deviations are nonempty and contain at most $k$ candidates, with support measured relative to their Hare quota. A negative value certifies core nonemptiness, while $-\Gamma(P)$ is the largest worst-case quota shortfall secured by any committee. We quantify this margin on candidate-disjoint approval chains, a domain whose qualitative core nonemptiness is already known. We first factor each committee's deviation score over disjoint components. For chains, a closed local table yields the exact value and an attaining committee in polynomial time for rational weights. For nonnegative normalized real weights, let $q_{\mathrm{act}}\ge1$ count the connected components of the positive-support incidence graph. Then \[ \Gamma(P)\le-\frac{1}{k\min\{q_{\mathrm{act}},k+1\}}. \] Explicit extremal profiles show that this dependence on the active-component count is sharp. The margin is $1$-Lipschitz in total variation on the full ballot space. Each negative margin therefore certifies a neighborhood with nonempty core, even when perturbations leave the chain domain.

An approval committee is Hare-core stable if no coalition meeting the Hare quota can strictly improve by moving to another candidate set. Whether every approval election has such a committee remains open. We prove nonemptiness when each voter disapproves at most two candidates, with no bounds on the numbers of candidates, seats, or voter types. The result also permits arbitrary positive rational voter weights. Our deterministic rule represents a committee by its missing set. It first maximizes weighted coverage of two-candidate disapproval sets and then maximizes total disapproval incidence. An exact coverage inequality excludes targets one seat below the committee. The incidence objective excludes unanimous equal-size targets, while targets of size at most $k-2$ cannot improve any voter. Two implementation-level independent verifiers audit overlapping finite grids. The symbolic proof, not this bounded enumeration, establishes the theorem's unbounded quantifiers. The argument identifies complement-side coverage as a tractable mechanism for a broad parameter range within a sharply defined preference domain.

Core stability gives approval-based committee elections a strong form of coalitional proportionality, but deterministic existence is not known for an arbitrary number of seats. We prove that every finite election with nine seats has a deterministic Hare-quota core committee. Starting from an eight-seat committee that is both a global Proportional Approval Voting (PAV) maximizer and core stable, we suppose that all one-candidate extensions are blocked and extract an inclusion-minimal closed response system. Singleton responses are eliminated by exact equality rigidity. For the remaining responses, rational Farkas certificates bound every nonpositive PAV add-marginal drift below by $-n/189$ and force every successor drift above $n/126$. The uniform response chain is irreducible, so stationarity makes these bounds incompatible. The computer-assisted component comprises an exact pointwise check over 7,356 voter types, 36 one-blocker cells, and a symmetry-complete family of 19 two-blocker motifs. Exact certificate archives and standard-library verifiers support these checks. The theorem settles the nine-seat case but does not decide deterministic core existence for arbitrary committee size.

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.

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.

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.

We introduce the first Probably Approximately Correct (PAC) learning framework for general-sum concurrent stochastic games (CSGs) with transition uncertainty, while addressing the challenge of Nash equilibrium (NE) existence. Our algorithm maintains data-driven $L^1$ confidence sets over transition kernels and solves a robust CSG to compute a social-welfare optimal $\varepsilon$-NE, using a robust MDP-based exploration mechanism to drive joint state-action coverage. Crucially, we introduce a Nash margin characterisation that enables principled reasoning about equilibrium existence: the framework either returns an $\varepsilon$-approximate NE whose social-welfare value is $\varepsilon$-close to optimal, or provides a sound certificate that no exact NE exists. Under a minimum reachability condition $p_{\mathrm{reach}}>0$ over relevant state-action pairs, the algorithm terminates after a polynomial number of trajectory samples, with sample complexity $\widetilde{O}\left( {R_{\max}^2 H^4 |S|^2 |A| / (p_{\mathrm{reach}} \varepsilon^2)} \right)$. Empirical results on benchmark CSGs demonstrate near-optimal performance, correct handling of equilibrium (non-)existence, and sample complexity consistent with theory.

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.

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.

We study the allocation of indivisible goods among agents with identical additive valuations, focusing on envy-freeness up to one good (EF1) and Nash social welfare (NSW). Since every maximum-NSW allocation is EF1 under additive valuations, the associated threshold problem inherits the known strong NP-hardness of NSW maximization under identical additive valuations and is strongly NP-complete. We therefore focus on welfare guarantees satisfied by arbitrary EF1 allocations. Although every such allocation is known to achieve an $e^{-1/e}$-approximation to the unrestricted optimal NSW, we identify conditions yielding stronger guarantees. Under uniform valuations, every EF1 allocation is NSW-optimal. Under an $\varepsilon$-small-item condition, every EF1 allocation achieves an explicit approximation ratio $\rho_n(\varepsilon)$ satisfying $\rho_n(\varepsilon) = 1-O(\varepsilon^2)$ as $\varepsilon\to 0$ for fixed $n$. We further consider the stronger sequential requirement that $\operatorname{EF1}$ be maintained after every item assignment. For this setting, we introduce PriorityNet, a deep reinforcement learning framework trained with Proximal Policy Optimization (PPO) and equipped with prospective $\operatorname{EF1}$ action masking, which guarantees prefix-wise $\operatorname{EF1}$ by construction. Across 3,000 test instances in each of the offline full-information and random-order online regimes ($n\in[2,20]$, $m\in[5,100]$), PriorityNet achieves mean normalized $\operatorname{NSW}$ values of $0.9911$ and $0.9701$, respectively. Relative to the offline Longest Processing Time (LPT) heuristic and the online least-valued-bundle rule, it attains instance-wise win-minus-loss rates of $+27.10\%$ and $+17.87\%$. Its aggregate welfare matches the offline LPT baseline to four decimal places and modestly improves upon the online baseline, from $0.9694$ to $0.9701$.

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.