Papers

In metric social choice, voters and candidates lie in a common but unknown metric space, voters rank candidates by distance, and a voting rule seeks to minimize total distance to the voters. Its distortion is the worst-case approximation ratio relative to the minimum possible total distance. We study weighted-tournament rules (also known as C2 rules), which observe only the fraction of voters who prefer $a$ to $b$ for each pair of candidates $a,b$. These frequencies form a weighted tournament on candidates, a compressed representation that omits voter identities and the association of comparisons with individual voters. Prior work placed the optimal distortion of deterministic C2 rules between $3.1128$ and $3.9312$ [Charikar et al., EC 2025]. We introduce the Path-Unblanketed Set rule, a polynomial-time deterministic C2 rule with distortion at most $1+2\sqrt{2}\approx3.8284$ for every finite number of candidates. For elections with no more than six candidates, we prove with computer assistance that the distortion is at most $3.3346$. Furthermore, using an exact computer-assisted certificate, we provide a lower bound of $3.1828$ for deterministic C2 rules as a byproduct.

We study interval scheduling from the perspective of fair allocation. There are $m$ identical machines and a set of intervals, each specified by a start time, an end time, and a nonnegative weight. A schedule assigns a subset of the intervals to the machines so that no two intervals on the same machine overlap, and the goal is to maximize the total weight of scheduled intervals. Viewing machines as agents and intervals as goods, we require the schedule to be envy-free up to one item (EF1), and we measure efficiency against the offline optimum without fairness. In the offline setting, we give an algorithm that computes an EF1 schedule whose loss is at most a factor of $3/2$ in the unweighted regime, and we prove lower bounds of $\frac{3m-2}{2m-1}$, approaching $3/2$, in both the unweighted and the unit-length weighted regimes, so the price of fairness is $3/2$ in the limit. In the online setting, intervals arrive in nondecreasing order of start times; an arriving interval must be accepted or rejected, rejections are irrevocable, and an accepted interval may be revoked, and lost, at any time before it ends. For the unweighted regime we present Greedy-Balanced, a simple algorithm that maintains EF1 at every point in time and is $(2-\tfrac{1}{m})$-competitive against the offline optimum without fairness, and we prove a matching lower bound for every deterministic algorithm; the optimal deterministic fair competitive ratio is thus exactly $2-\tfrac{1}{m}$. Experiments on real-world benchmark instances show that Greedy-Balanced performs well beyond its worst-case guarantee, with an observed ratio never exceeding $1.306$.

Many real-world interactions among self-interested parties can be modeled by game theory, and the rapid advancements in AI have raised concerns about the possible misuse—accidental or deliberate—of superhuman or human-level game-playing agents by bad actors. While AI watermarking has mainly been applied to LLM-generated texts, a recent line of work proposes developing watermarking techniques for agents in game-theoretic settings. However, existing watermarking techniques for game-theoretic agents are not readily applicable due to their limited scope or capabilities—they are tailored to perfect-information games and are thus inapplicable to richer game types. We propose a new approach to watermarking game-playing agents, which a) can be applied to imperfect-information settings; b) is directly integrated into the learning process itself; and c) incurs only a bounded cost in exploitability. For this purpose, we introduce perturbed regret minimization, which adds perturbations to the utilities prior to observation so as to encourage the learning algorithm to embed the watermark. Our experiments show that the watermark incurs only a small exploitability cost and can be detected within just a couple of hours of gameplay at human speed.

We introduce the Open-Strategy Dictator Game (OSDG), a variant of the classic dictator game in which each player's strategy is a natural-language document visible to all participants. The dictator's decision, to SHARE or TAKE an endowment, may depend on the text of the recipient's strategy. A large language model adjudicates each interaction by interpreting the dictator's strategy in the context of the recipient's. We run round-robin tournaments among diverse strategies and analyze the resulting payoff matrix using softmax equilibrium frequencies, dominance analysis, and sensitivity to the relative value of cooperation. Conditionally cooperative strategies, those that share with cooperators and take from exploiters, consistently dominate, while unconditional strategies (always share or always take) are weakly dominated. The results suggest that in environments where agents can inspect each other's decision procedures, conditional cooperation is evolutionarily robust across a wide range of payoff parameters.

Computing Nash equilibria in interdependent security (IDS) games on networks is computationally expensive: best-response dynamics may need hundreds of iterations per instance, and downstream tasks such as auditing, stress-testing, and incentive design often require repeatedly re-solving the game under parameter perturbations. We propose BRAID, a Best-Response Amortized Iterative Dynamics model that uses a weight-tied iterative graph neural network to learn a direct map from game parameters to Nash equilibrium effort profiles, replacing iterative best response computation with a single forward pass that is up to 43X faster per instance. BRAID is derived from the best-response fixed-point structure of IDS games: its SUM aggregation reflects additive neighbor coupling, and a weight-tied gated recurrent unit (GRU) mirrors a damped best-response update. The same architecture applies across IDS specifications that vary investment-cost curvature and neighborhood aggregation, including log-linear, quadratic-cost, and log constant-elasticity-of-substitution (CES) utilities. Beyond equilibrium prediction, BRAID also recovers how equilibrium efforts change under perturbations to game parameters, including costs and network edge weights. We make this sensitivity recovery an explicit evaluation target and introduce two training strategies, interior-equilibrium training and input-noise regularization, that improve the local behavior of the learned equilibrium map without using sensitivity labels. Experiments show that BRAID effectively predicts Nash equilibria and recovers equilibrium sensitivities across utility specifications and network sizes.

An AI that can only give advice seems safe: the human is always free to ignore it. That is the premise of the boxing tradition in AI safety, and its long-suspected weak point is that the human who reads the answers is part of the system. We make the fraction $\varepsilon_t$ of behavior that follows the advice a state of a Markov decision process, moved by the advisor's own messages, so that use deepens reliance. Granted a channel rich enough to echo any action the human could take, higher $\varepsilon_t$ weakly lowers every monotone measure of the power of a human with a message-independent fallback. An oracle rewarded by per-round approval cultivates reliance beyond a closed-form patience threshold, so the same reward weights leave the optimal oracle answering in episodic deployments and cultivating in long-memory ones. An influence bound certified once at deployment is blind to that horizon and bounds the loss no lower than its trivial ceiling. An exogenous cap on influence bounds the guarantee the human loses, and a short enough memory reset removes the incentive to cultivate, while neither recovers the value already steered away. In a closed-form example the optimal oracle never cultivates in fifteen-round sessions and does in sixteen.

At a finite public-chance cut, counterfactual regret minimization (CFR) must choose how many outcomes to evaluate before each regret update. Exact evaluation processes the full cut at one strategy profile; persistent partial evaluation processes a fixed without-replacement order across evolving profiles. The latter covers every outcome once per epoch, yet its feedback is generally conditionally biased because earlier batches influence the profiles seen by later batches. We establish a deterministic target-transfer theorem for uniform, nonnested additive public cuts. The theorem bounds full-cut exploitability by regret on the delivered feedback and a public-debit term that couples prefix coverage discrepancy with motion along the realized strategy path. Consecutively balanced schedules consequently converge for additive signed regret matching (RM) and RM+ under predetermined averaging weights, while a fixed RM+ construction proves that the discrepancy–path product is necessary in general. A component-resolved form of the theorem converts an execution trace into a numerical exploitability certificate. On two released heads-up no-limit hold'em turn endgames, persistent order improves substantially over fresh reshuffling despite identical epochwise coverage, and partial coverage wins every registered shallow matched-budget comparison. A depth study locates a crossover between 32 and 64 full-cut outcome budgets, after which complete coverage dominates. These results characterize public-chance width and order as learning variables and provide a deterministic basis for designing and auditing persistent CFR schedules.

We introduce the problem of designing mechanisms that incentivize strategic agents to form self-funded marketplaces. In our model, if agent $i$ exerts effort $x_i\in [0,1]$, they incur a cost of $x_i\cdot c_i$ (where $c_i$ is unknown to the mechanism designer) and they generate revenue $x_i\cdot r_i$; crucially, $c_i$ can be greater or smaller than $r_i$. Each effort profile $\mathbf{x}$ yields value $v(\mathbf{x})$ and the objective is to choose an effort vector that maximizes the value while ensuring that every agent $i$ receives a payment $p_i\geq x_i\cdot c_i$ and that $\mathbf{x}$ is budget-balanced, i.e., $\sum_{i} p_i \leq \sum_{i} x_i\cdot r_i$. This problem generalizes the well-studied budget-feasible mechanism design problem, where the requirement is that $\sum_{i} p_i \leq B$ for some predetermined budget $B$. To evaluate the performance of such mechanisms, we first consider the first-best benchmark (the optimal value achievable in the absence of any private information) and show that no truthful auction can achieve a bounded approximation of this benchmark. Also, even in restricted settings, no auction can achieve better than a logarithmic approximation. We complement these results by proposing a class of sequential auctions whose subgame perfect equilibria guarantee a logarithmic approximation of this benchmark. We then introduce an alternative benchmark, the maximin share (MMS), that better captures the thickness of the market and we provide an auction whose subgame perfect equilibria achieve a constant approximation of this benchmark.

We study the facility location mechanism design problem where $n$ strategic agents report locations in Euclidean space and the mechanism outputs a single facility location. Each agent's cost is its distance from the facility, and our objective is to minimize the egalitarian cost, i.e., the maximum agent cost, in a strategyproof way. The optimal deterministic approximation ratio is $2$, achieved by any dictator mechanism. We study the power of randomized strategyproof-in-expectation mechanisms. Prior work has focused on ex-post evaluation, defined as the expected maximum agent cost. We instead study ex-ante evaluation, defined as the maximum expected agent cost, which is naturally aligned with strategyproofness in expectation. We establish the following results: (1) Low dimensions: Strict ex-ante vs. ex-post separation. In $\mathbb{R}$, we give a simple strategyproof mechanism achieving the optimal ex-ante approximation ratio of $1$. In $\mathbb{R}^2$, we design the "Random Rotated Corner" mechanism, with ex-ante approximation ratio at most $1.598$, breaking the deterministic barrier. For the ex-post objective, we prove a lower bound of $1.605$, yielding a strict separation in $\mathbb{R}^2$. (2) High dimensions: Impossibility. In $\mathbb{R}^d$ for $d \gg 1$, we show that no strategyproof-in-expectation mechanism improves on the deterministic dictator mechanism beyond $o_d(1)$. Thus neither ex-post nor ex-ante evaluation yields improved fairness guarantees in high dimensions. An implication is that the "Random Rotation Coordinate-Wise Median" (RRCWM), currently the best known mechanism for the utilitarian objective, is also best possible for the egalitarian objective in high dimension: we show it achieves an approximation ratio of $2$ for both ex-post and ex-ante objectives in $\mathbb{R}^d$ for every $d \ge 1$.

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.

Battery swapping is a rapid way to recharge electric vehicles (EVs). As more and more entities are involved in building Battery Swapping Stations (BSSs), how non-cooperative BSSs maximize their profit in a competitive market needs further investigation. In this paper, we focus on a practical scenario where competitive BSSs are coordinated by the same aggregator. To study the optimal pricing and battery charging, we formulate a hierarchical game-theoretic model, where BSSs determine the swapping price in the day-ahead market in the first stage, and then determine the optimal battery charging strategy in the real-time market in the second stage. We rigorously prove the existence and uniqueness of the Subgame Perfect Nash Equilibrium (SPNE). In particular, the uniqueness property provides theoretical support that the strategy under equilibrium is optimal in the competitive environment. Based on the unique SPNE, we propose an optimal pricing and charging strategy for each BSS to maximize profit in the competitive market. A prediction error handling method is also proposed to deal with unexpected fluctuations in swapping demand. Our simulation with a 12-BSS system based on real-life data from Xi'an, China shows that our pricing and charging strategy increases the individual BSS profit by at least 18.1%, while the optimal charging strategy naturally achieves peak shaving for the power grid.

We study equilibrium pricing in oligopolistic data markets with budget-constrained buyers (e.g., machine learning companies purchasing data to improve model accuracy) and strategic data sellers. Sellers compete by setting prices for their datasets, giving rise to a pricing game whose pure Nash equilibria correspond to equilibrium prices. While equilibrium prices are guaranteed for rivalrous goods via competitive equilibrium, we show that the non-rivalry of data fundamentally alters this picture: an exact Nash equilibrium (NE) need not exist, and in fact, 1.363-approximate NE may also not exist under uniform pricing. We therefore investigate relaxed equilibrium notions. Allowing sellers to use beyond-uniform pricing—specifically, piecewise-linear convex pricing functions—guarantees approximate stability within a constant factor: there exists a pricing profile in which no seller can improve revenue by a factor of two by deviating to any uniform price (a 2-approximate NE against uniform deviations). Finally, our simulations demonstrate fast convergence and empirical approximation guarantees that outperform the worst-case bound of 2.

Three-player Auction Bridge is a finite imperfect-information game in which dynamic partnerships create a distinctive interaction between scoring, strategic incentives, and payoff distribution. This paper develops a unified statistical and game-theoretic framework to evaluate a traditional scoring rule against a modified mechanism designed to improve strategic incentives. We first identify a structural defect in the original scheme: a bid-invariant slam bonus can make lower contracts strictly more attractive than higher ones. A bid-dependent correction removes this incentive distortion. We then compare the two schemes using higher-moment analysis, fairness measures, Nash equilibrium analysis, and General-Sum Counterfactual Regret Minimization (GS-CFR). The results show significant differences in the shape of the payoff distributions and reveal that, although both schemes remain highly balanced across physical seats, the modified scheme substantially increases inequality across strategic roles. The game is shown to be neither zero-sum nor constant-sum, motivating a general-sum rather than minimax analysis. Full-game GS-CFR further indicates a substantial increase in the bidder's payoff under the modified scheme, accompanied by a reduction in defender payoff and a shift from separating to partially pooling bidding behavior. These findings demonstrate that scoring-rule design can fundamentally reshape incentives, payoff distribution, and information transmission in imperfect-information games. The proposed framework provides a systematic approach to evaluating such mechanisms from both statistical and strategic perspectives.

We examine the interplay between ordinal, preference-based solution concepts in games and the long-run behavior of game dynamics, asking in particular to what extent the combinatorial data of a game – its preference graph – determine the outcomes of no-regret learning dynamics – such as follow-the-regularized-leader (FTRL). In one direction, we show that the skeleton of every dynamically stable set (i.e. the set of pure profiles it contains) must also be preferentially stable, that is, it must be closed under profitable deviations. We then ask the converse question: when do preferences determine the long-run behavior of the players' learning dynamics? We begin by showing that preferences characterize asymptotic stability in the case of subgames – i.e. subsets of pure profiles obtained by restricting players' action sets. Beyond this case however, the equivalence between dynamic and preferential stability collapses: concretely, we construct a three-player game with a preferentially stable set whose span is dynamically unstable, showing in this way that preferences do not suffice as a criterion of dynamic stability. We then bridge this gap via the notion of resilience under aggregate deviations, an easy-to-check payoff-based condition that guarantees asymptotic stability of arbitrary spans of pure strategies.

We study a large language model (LLM) service in which a provider chooses a per-token price and a default reasoning-token allocation, while a user may accept the default, customize the allocation, or exit. Larger allocations can improve accuracy but increase token cost and latency. We model this interaction as a Stackelberg game and derive the user's unique optimal customized allocation in closed form. For any price, the acceptable defaults form either an empty set or a compact interval. We characterize the provider's optimal default through a three-regime rule, reduce equilibrium computation to a one-dimensional price optimization, and prove the existence of the equilibrium. We further show that defaults affect the implemented reasoning allocation only when users value the convenience of avoiding customization; otherwise, every service-providing outcome implements the user's optimal customized allocation. Experiments with two compact open-weight reasoning models on five mathematics and science benchmarks support the accuracy-token model and show how model and task characteristics determine equilibrium prices, defaults, and reasoning allocations.

This paper develops a computationally tractable framework for measuring voters' power in collective decision-making platforms that support transitive and suspendable delegations—commonly known as liquid democracy. We employ Random Walk Decay centrality to capture how influence propagates through delegation networks, argue for its intuitive appeal in this context and its advantages over alternatives such as PageRank, and derive a natural axiomatic characterization within the class of power metrics. Moreover, we conceptualize how the framework can be extended into a practical tool for analyzing power distributions in such platforms, and propose and study, both axiomatically and algorithmically, methods for selecting representative slates of influential participants.

We study the peer selection problem in which a group of peers must select a fixed-size committee from among themselves. To this end, we introduce a class of approval-based preference profiles, inspired by delegation graphs in liquid democracy and the transitivity of trust therein, which we call “liquid profiles”. Under this new domain restriction, each voter designates a single trusted agent and, in turn, approves all those trusted by that individual. After establishing relationships to standard restricted preference profiles and examining computational properties of liquid profiles, we focus on understanding how novel and established proportionality axioms behave in this domain and how they relate to one another. Then, we study their satisfaction under various voting rules, including new ones that are directly inspired by the structure of liquid profiles. Our findings reveal that particularly strong proportionality guarantees are attainable in this new domain, showing promise for applications to real-world peer selection problems via transitive delegations.

In expert-parallel (EP) MoE serving, every layer synchronizes at the slowest GPU. Dispatchers balance token counts (EPLB, LPLB, UltraEP) or activated-expert counts (METRO), assuming expert time is linear in one. Measurements on two datacenter GPU generations show it is neither: below $n^* \approx 156$–$168$ tokens, HBM weight streaming dominates—cost attaches to $activated replicas$, not tokens; above it, grouped GEMM rounds tokens to 128-tile $M$-tiles, so $splitting$ an expert adds padded compute. A max-affine profile $t=\max(a+bG,\,c+\beta N)$ captures both regimes. Realistic decode batches hold hot experts in the linear regime and cold in the flat $simultaneously$; recorded batches show proxy dispatches differ by $1.4$–$1.6\times$ in modeled block time (p95 up to $1.7\times$), and $which$ proxy wins flips with the regime. We formalize per-batch dispatch as a fixed-charge makespan problem—NP-hard on two fully replicated GPUs, polynomial in degenerate limits—and present TEMPO, a makespan-aware dispatcher solving it in milliseconds off the critical path; its SGLang integration runs out-of-process and fuses dispatch with count collection into one in-graph kernel. Anchored by an 8-GPU Testbed A microbenchmark, TEMPO stays within $1\%$ of the best fixed baseline everywhere and wins by up to $15.5\%$ where regimes mix. End-to-end on Testbed B, Qwen3-235B (inside the win region) gains $4$–$6\%$ throughput and cuts p99 latency by $\sim 15.6\%$; DeepSeek-V3 (outside, communication-dominated) shows only mechanism cost. A phase diagram, not a universal win, is the claim: it predicts both outcomes before deployment.

Routing each query to a cost-effective large language model (LLM) is critical for balancing quality and cost, yet most routers rely on a centralized task center to predict model performance, creating an information-risk mismatch and a scalability bottleneck as the model pool grows. We formulate LLM routing as a market-based allocation problem among strategic providers and propose a routing paradigm that shifts ex-ante prediction to LLM providers via a reverse auction, where providers submit self-predicted acceptance probabilities and execution costs. To account for noisy provider predictions and center evaluations, we introduce the \textit{Error-Aware Reverse Auction Mechanism} (EA-RAM), which explicitly models this Dual Error. We prove that, under a private-evaluation-belief structure, truthful effective-surplus reporting is incentive compatible in the reduced-form score space and individually rational under sellers' subjective beliefs, establish sufficient conditions for center rationality, and derive an explicit social-welfare loss bound. We further identify robustness effects: opposite-signed errors can cancel, vanishing-tail link functions (e.g., logistic) stabilize clear-cut cases via saturation, and extra noise smooths belief maps and reduces their maximal local sensitivity. Simulations and real-world benchmarks show that EA-RAM is robust to Dual Error and achieves a better cost–performance Pareto frontier than centralized baselines, with additional gains from provider-side local information, validating its practical effectiveness.

Peer-to-peer (P2P) energy trading markets rely on double auction mechanisms to match prosumers and consumers in smart grid distribution networks. However, the strategic behavior of bidding agents in such markets remains not fully explored, particularly in repeated settings with bounded rationality. This paper proposes a novel framework that integrates large language models (LLMs) as reasoning-driven bidding agents in repeated P2P energy double auctions. We compare the performance of three bidding strategies: random bidding, an $\varepsilon$-greedy multi-armed bandit (MAB) approach, and an LLM-based strategy. Simulation results show that the LLM-based strategy achieves superior cleared trading volume over the first episodes compared to $\varepsilon$-greedy MAB and random bidding baselines, eliminating the exploration burn-in period that statistical learning algorithms inherently require before converging to productive price arms. Importantly, when tested in an environment different from the one used during learning, the performance of the $\varepsilon$-greedy strategy drops significantly, while that of the LLM-based bidding strategy continue to achieve higher surplus and successful trades. Nevertheless, the LLM's advanced contextual reasoning also gives rise to an important market dynamic. In a homogeneous population of LLM agents, sellers increasingly exploit buyers' rational outside options to drive clearing prices above the Nash equilibrium, resulting in a progressively more asymmetric allocation of surplus in favor of sellers that does not converge within the observed time horizon.

We introduce a repeated dynamic incentive framework for characterizing when "compliance", or full-effort honest service provision, is incentive compatible in Decentralized Physical Infrastructure Networks (DePIN). We model quality control in this setting as a repeated moral-hazard problem between the protocol and each provider, where compliance is enforced by both slashing posted collateral and the discounted threat of demotion to probation tiers on a reputation ladder. Our main contribution is the "deterrence ratio" $\Gamma$, the worst-case ratio of a deviation's private gain to its marginal probability of detection. We find that if any profitable deviation does not increase the fail probability relative to compliance, then binary public-outcome protocols cannot deter it. When all profitable deviations have positive detection gaps and no weakly costlier action is less likely to fail, compliance is sequentially incentive compatible if and only if immediate slashing plus discounted reputation loss is at least $\Gamma$ at every reputation tier. We use this condition to formulate a protocol design problem mapping service primitives to stake requirements, reward schedules, probation rules, and audit frequency.

We consider dynamic network flows and study the following question: Which dynamic edge flows can be implemented as tolled dynamic equilibrium flows? We study this question for the heterogeneous-user model, where the flow particles are partitioned into populations characterized by their own source,destination-pairs and a cost function associating with any walk and departure time some costs. As our two main results, we first provide a duality-based characterization of implementability of dynamic edge flows for the multi-source, multi-destination case. Secondly, we derive both, a combinatorial and duality-based characterization of implementability of dynamic edge flows for the multi-source, single-destination case. Both results are derived under a fairly general network loading model. For the proof, we make several technical contributions: We formulate a novel infinite dimensional optimization problem, where the goal is to minimize the aggregated costs of the particles with respect to the fixed network loading induced by the given edge flow. This requires the recently introduced concept of autonomous network loadings for which we show several new structural insights. In particular, we give an alternative (tighter) characterization of the existence of autonomous network loadings for our setting by deriving a generalization of a result of M.A. Zareckiĭ on the Lusin $N^{-1}$ property of absolutely continuous monotone functions which may also be of independent interest. These insights allow us to prove the stated characterizations under the assumption of strong duality. Finally, for the case of a single-destination, we are able to provide a non-trivial proof that this assumption is always fulfilled for finitely supported edge flows with costs representing weighted travel times.

As LLM-based agents with user-instructed goals are becoming widely deployed, they increasingly encounter each other in strategic interactions, and face challenges of finding mutually beneficial outcomes. Prior literature has argued that cooperation problems such as the Prisoner's Dilemma are resolvable in settings where agents know they follow very similar decision making patterns, as for example in monocultural AI ecosystems. Following that line of work, this paper introduces the first framework for evaluating LLM decision making when agents are provided with graded similarity signals. Among our findings, we establish that different LLM models vary drastically in how they navigate similarity signals, with some modern models showing consistent behavior across cooperation problems, payoff structures, and prompt framing. Perhaps surprisingly, our experiments also show that the dataset based on which the similarity signal is computed has small to no impact on induced cooperation, and that LLM models systematically self-identify as highly similar when asked to evaluate another model's chain-of-thought reasoning by themselves. Finally, we develop an LLM-behavioral-game-theoretic model that captures some of their reasoning rationale, and show that it can support cooperative outcomes in equilibrium under sufficiently high similarity scores.

Full justified representation (FJR) is among the strongest known satisfiable proportionality axioms for approval-based committee elections. Recent work has shown that an FJR committee can be found in polynomial time, but verifying whether a given committee satisfies FJR remains coNP-complete. We introduce FJR+, a strict strengthening of FJR and EJR+ that can be verified and satisfied in polynomial time. We then analyze the Residual-Budget Greedy (RBG) algorithm and prove that it selects a partial committee such that every size-$k$ completion satisfies FJR+. This freedom allows us to use sequential Phragmén to obtain a priceable completion. The resulting rule always satisfies FJR+ and the sub-core, and it is priceable whenever at least $k$ candidates receive an approval. We also obtain a Droop-quota version of FJR+. Finally, we extend FJR+ to approval-based participatory budgeting with arbitrary project costs. A project-specific version of RBG computes this property in polynomial time and can be continued to a priceable outcome satisfying a cost-based version of the sub-core.

We introduce the study of multilateral trade: a mechanism-design problem in which a single potential trade involves $k$ agents and can be executed only if all $k$ agents agree to participate. The classical case $k=2$ is the well-studied bilateral trade problem, where a seller and a buyer with private values must decide whether to trade an item initially held by the seller. Existing extensions of bilateral trade have largely focused on markets with many buyers and many sellers, but where each realized transaction is still bilateral, requiring agreement only between the matched buyer and seller. Our formulation captures settings in which the trade itself requires joint participation, coupling the agents' incentives and creating new challenges. We study welfare approximation in this setting under incentive compatibility, individual rationality, and budget balance. We give a DSIC mechanism with approximation ratio $O(k^2)$, and a BIC mechanism with approximation ratio $\widetilde O(k^{3/2})$. We prove matching lower bounds up to polylogarithmic factors. Finally, we extend the model to an $\ell$-out-of-$k$ partial-agreement setting, where the trade may occur once at least $\ell$ agents participate. In this relaxed model, the welfare guarantees improve smoothly as $k-\ell$, the number of agents whose participation is not required, grows, and we obtain matching upper and lower bounds up to polylogarithmic factors.

As the adoption of satellite-enabled Internet of Things (IoT) continues to rise, its intricate multidomain architecture becomes increasingly susceptible to cross-domain cyber threats. Attackers can exploit compromised IoT devices, inject malicious packets into data streams aggregated at the IoT gateway for satellite backhaul, and potentially endanger the satellite network during transmission by exploiting the hardware, software, and protocol vulnerabilities. Compared to single-domain defenses, cooperative defense at the IoT devices, IoT access network, and satellite transmission network provides fine-granularity defense against cross-domain intelligent attacks. However, quantifying cross-domain impacts and tilting incentive misalignment among different participants remain significant challenges, making systematic cooperative defense development a complex task. To address this, we develop a tripartite security game framework to characterize the impacts of attacks and defense methods across both the terrestrial and satellite domains. Leveraging this game model, we devise flow pricing to optimally motivate the IoT network operator (IoT-NO) to prevent malicious packet infiltration into the satellite domain. Subsequently, we propose efficient learning algorithms enabling both the IoT-NO to ascertain their ideal flow sampling strategies and the satellite service provider (SAT-SP) to determine optimal flow pricing. The simulation results corroborate the effectiveness of the consolidated game in counteracting cross-domain cyber attacks and facilitating cooperative defense between the IoT-NO and the SAT-SP with nonaligned incentives.

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Existing approaches either require expensive labelled supervision with inconsistent cross-task performance or aggregate scores from multiple sources by simple aggregations, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We formalise this as a coupled scoring problem among disparate, frozen verifiers, interpretable as a coordination game with a unique closed-form equilibrium where agreement signals valid steps while disagreement reveals instability. Towards this end, we propose a training-free domain-agnostic step-wise verification approach we call VERDICT: VERification via Disagreement-Informed Coupled Thresholding. To our knowledge, VERDICT is the first training-free verifier that makes the structure of cross-modal disagreement explicit and actionable. It computes consensus scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, \method consistently improves over the base model by up to +5.95%, and performs competitively with domain-specific critics that demand extensive supervision, demonstrating that cross-modal agreement provides robust verification signals without task-specific adaptation and Training-Free Verification

We study the existence of envy-free up to any item (EFX) allocations of indivisible chores when agents have monotone cost functions with binary marginals. For indivisible goods, the corresponding existence question is known to have an affirmative answer for general monotone functions with binary marginals. For chores, however, the existence of EFX allocation was previously known only for more restricted classes, while the general binary-marginal case remained unresolved. In this paper, we provide two counterexamples based on the same 18-agent, 53-chore word gadget, with one cost profile for binary XOS costs and another for binary supermodular costs. In both cases, a complete EFX allocation need not exist. Finally, we formalize and verify our main results in Lean 4.

The emergence of language-based AI agents promises to transform the scope of machine economic activity. Instead of just proposing bids or following hard-coded protocols, such agents can be used to negotiate and execute agreements in open-ended natural language. However, most evaluations of these abilities have focused on one-off exchanges or simple economic games, leaving open the rich space of time-extended, contingent, and incomplete contracts made expressible by language; they also focus on raw profit, without measuring the qualities required for trustworthy contracting. We address this by formulating a rational framework for how agents should negotiate and perform natural language contracts in uncertain multi-step environments. Within this framework, we develop metrics and baselines for quantifying rational and cooperative play. To evaluate how agents perform at such contracting, we instantiate our framework in ContractSim, an evaluation suite where two players negotiate and execute a multi-turn supplier contract under environmental and inter-player uncertainty. Across six environments and three supplier settings (catering, hotel cleaning, and AI hosting) we find that current LLM-based agents reach agreement reliably, and negotiate efficient contracts when environmental uncertainty is low. However, under high uncertainty, they often fail to negotiate satisfiable, efficient, or mutually beneficial contracts. They are also frequently uncooperative when executing contracts, violating contract terms for additional profit even when contracts are easy to satisfy. These findings highlight room for improvement in the design of language agents that can negotiate, interpret, and execute contracts both rationally and cooperatively.

We study the agent-wise disjunction of two central fairness notions for indivisible items, where every agent must be either envy-free up to any item (EFX) or maximin-share (MMS) satisfied. One might expect that having a flexible fairness requirement for individual agents will restore existence, especially because the existence of EFX itself resisted resolution for nearly a decade. Surprisingly, it does not. We construct counterexamples with three agents and eight submodular goods, and with three agents and seven submodular chores, significantly strengthening recent EFX impossibility results. On the positive side, we prove existence for additive mixed items with at most three valuation types when one type is a singleton. Additionally, we obtain polynomial-time approximation schemes for additive goods-only and chores-only instances. We also identify a clean separation between the disjunction and its constituents: For additive chores with two valuation types, EFX and MMS are both known to fail, whereas an EFX $\vee$ MMS allocation always exists. Finally, we show that identical additive valuations even admit the conjunction EFX $\wedge$ MMS for mixed items. Overall, our results show that allowing flexibility in choosing agent-specific fairness certificates expands the frontier of fair solutions while also uncovering surprising impossibilities.