arXiv:2603.07717v1 Announce Type: new Abstract: We test whether LLMs show robust decision biases. Treating models as participants in two-arm bandits, we ran 20000 trials per condition across four decoding configurations. Under symmetric rewards, models amplified positional order into stubborn one-arm policies. Under asymmetric rewards, they exploited rigidly yet underperformed an oracle and rarely re-checked. The observed patterns were consistent across manipulations of temperature and top-p, with top-k held at the provider default, indicating that the qualitative behaviours are robust to the two decoding knobs typically available to practitioners. Crucially, moving beyond descriptive metrics to computational modelling, a hierarchical Rescorla-Wagner-softmax fit revealed the underlying strategies: low learning rates and very high inverse temperatures, which together explain both noise-to-bias amplification and rigid exploitation. These results position minimal bandits as a tractable probe of LLM decision tendencies and motivate hypotheses about how such biases could shape human-AI interaction.

arXiv:2603.06977v1 Announce Type: cross Abstract: Multi-agent reinforcement learning (MARL) is increasingly used to design learning-enabled agents that interact in shared environments. However, training MARL algorithms in general-sum games remains challenging: learning dynamics can become unstable, and convergence guarantees typically hold only in restricted settings such as two-player zero-sum or fully cooperative games. Moreover, when agents have heterogeneous and potentially conflicting preferences, it is unclear what system-level objective should guide learning. In this paper, we propose a new MARL pipeline called Near-Potential Policy Optimization (NePPO) for computing approximate Nash equilibria in mixed cooperative--competitive environments. The core idea is to learn a player-independent potential function such that the Nash equilibrium of a cooperative game with this potential as the common utility approximates a Nash equilibrium of the original game. To this end, we introduce a novel MARL objective such that minimizing this objective yields the best possible potential function candidate and consequently an approximate Nash equilibrium of the original game. We develop an algorithmic pipeline that minimizes this objective using zeroth-order gradient descent and returns an approximate Nash equilibrium policy. We empirically show the superior performance of this approach compared to popular baselines such as MAPPO, IPPO and MADDPG.

arXiv:2603.06984v1 Announce Type: cross Abstract: Recent work has proposed powerful frameworks, rooted in causal theory, to quantify fairness. Causal inference has primarily emphasized the detection of \emph{average} treatment effects (ATEs), and subsequent notions of fairness have inherited this focus. In this paper, we build on previous concerns about regulation based on averages. In particular, we formulate the "causal masking problem" as a linear program that optimizes an alternative objective, such as maximizing profit or minimizing crime, while retaining a zero ATE (i.e., the ATE between a protected attribute and a decision). By studying the capabilities and limitations of causal masking, we show that optimization under ATE-based regulation may induce significant unequal treatment. We demonstrate that the divergence between true and causally masked fairness is driven by confounding, underscoring the importance of full conditional-independence testing when assessing fairness. Finally, we discuss statistical and information-theoretic limitations that make causally masked solutions very difficult to detect, allowing them to persist for long periods. These results argue that we must regulate fairness at the model-level, rather than at the decision level.

arXiv:2603.08679v1 Announce Type: cross Abstract: The celebrated Myerson--Satterthwaite theorem shows that in bilateral trade, no mechanism can be simultaneously fully efficient, Bayesian incentive compatible (BIC), and budget balanced (BB). This naturally raises the question of how closely the gains from trade (GFT) achievable by a BIC and BB mechanism can approximate the first-best (fully efficient) benchmark. The optimal BIC and BB mechanism is typically complex and highly distribution-dependent, making it difficult to characterize directly. Consequently, much of the literature analyzes simpler mechanisms such as the Random-Offerer (RO) mechanism and establishes constant-factor guarantees relative to the first-best GFT. An important open question concerns the worst-case performance of the RO mechanism relative to first-best (FB) efficiency. While it was originally hypothesized that the approximation ratio $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}}$ is bounded by $2$, recent work provided counterexamples to this conjecture: Cai et al. proved that the ratio can be strictly larger than $2$, and Babaioff et al. exhibited an explicit example with ratio approximately $2.02$. In this work, we employ AlphaEvolve, an AI-guided evolutionary search framework, to explore the space of value distributions. We identify a new worst-case instance that yields an improved lower bound of $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}} \ge \textbf{2.0749}$. This establishes a new lower bound on the worst-case performance of the Random-Offerer mechanism, demonstrating a wider efficiency gap than previously known.

arXiv:2509.22989v2 Announce Type: replace Abstract: Large language models (LLMs) have demonstrated strong persuasive capabilities comparable to those of humans, offering promising benefits while raising societal concerns. However, systematically evaluating the persuasive capabilities of LLMs is inherently challenging, as the effectiveness of persuasion among humans varies significantly across different domains. In this paper, we take a theory-driven approach to provide a scalable and principled framework for studying the persuasive capabilities of LLMs. Grounded in Bayesian persuasion theory, we repurpose human-human persuasion datasets to construct environments for evaluating and training LLMs as strategic persuaders. Our results reveal that frontier models can consistently achieve high persuasion gains and exhibit sophisticated persuasion strategies that align with theoretical characterizations. Building on this, we use reinforcement learning to train LLMs for strategic persuasion in our environments. Our results also demonstrate that even small LLMs can obtain significantly higher persuasion gains through reinforcement learning.

arXiv:2603.01290v2 Announce Type: replace Abstract: The 2026 Formula 1 technical regulations introduce a fundamental change to energy strategy: under a 50/50 internal combustion engine / battery power split with unlimited regeneration and a driver-controlled Override Mode (abbreviated MOM throughout), the optimal energy deployment policy depends not only on a driver's own state but on the hidden state of rival cars. This creates a Partially Observable Stochastic Game that cannot be solved by single-agent optimisation methods. We present a tractable two-layer inference and decision framework. The first layer is a 30-state Hidden Markov Model (HMM) that infers a probability distribution over each rival's ERS charge level, Override Mode status, and tyre degradation state from five publicly observable telemetry signals. The second layer is a Deep Q-Network (DQN) policy that takes the HMM belief state as input and selects between energy deployment strategies. We formally characterise the counter-harvest trap -- a deceptive strategy in which a car deliberately suppresses observable deployment signals to induce a rival into a failed attack -- and show that detecting it requires belief-state inference rather than reactive threshold rules. On synthetic races generated from the model's own assumptions, the HMM achieves 92.3% ERS inference accuracy (random baseline: 33.3%) and detects counter-harvest trap conditions with 95.7% recall. Pre-registration -- empirical validation begins Australian Grand Prix, 8 March 2026.

arXiv:2411.16574v2 Announce Type: replace-cross Abstract: Algorithmic agents are used in a variety of competitive decision-making settings, including pricing contexts that range from online retail to residential home rental. We study the emergence of algorithmic collusion when competing agents employ multi-armed bandit algorithms and competition is modeled as a repeated Prisoner's Dilemma game. Notably, agents in our setting perform online learning with no prior model of game structure and have no direct knowledge of competitor states or actions, thus they cannot learn strategies that depend on these factors. These context-free bandits nonetheless frequently learn seemingly collusive behavior, a phenomenon we term naive collusion. Our results reveal that whether naive collusion emerges depends starkly on the choice of behavior policy employed by bandit learners. The mechanism underpinning the emergence of collusive outcomes is synchronicity in agent action plays, where synchronicity captures how often agents play the same action. We show that in the long-run, naive algorithmic collusion never emerges when both agents use a broad class of persistently random algorithms, including the epsilon-greedy algorithm without epsilon decay, sometimes emerges when both agents use greedy-in-the-limit algorithms which feature randomness during exploration but are asymptotically deterministic, and always emerges when both agents use deterministic bandit learning algorithms like those in the well-known upper confidence bound (UCB) family. We highlight market and algorithmic conditions under which one can and cannot predict a priori whether collusion will occur. Our findings have several policy implications: preventing pricing algorithms from conditioning their actions on competitor prices may not preclude algorithmic collusion, symmetry in algorithms may increase collusion potential, and the emergence of algorithmic collusion is path dependent.

arXiv:2603.03672v1 Announce Type: cross Abstract: The Shapley value provides a principled foundation for data valuation, but exact computation is #P-hard due to the exponential coalition space. Existing accelerations remain global and ignore a structural property of modern predictors: for a given test instance, only a small subset of training points influences the prediction. We formalize this model-induced locality through support sets defined by the model's computational pathway (e.g., neighbors in KNN, leaves in trees, receptive fields in GNNs), showing that Shapley computation can be projected onto these supports without loss when locality is exact. This reframes Shapley evaluation as a structured data processing problem over overlapping support-induced subset families rather than exhaustive coalition enumeration. We prove that the intrinsic complexity of Local Shapley is governed by the number of distinct influential subsets, establishing an information-theoretic lower bound on retraining operations. Guided by this result, we propose LSMR (Local Shapley via Model Reuse), an optimal subset-centric algorithm that trains each influential subset exactly once via support mapping and pivot scheduling. For larger supports, we develop LSMR-A, a reuse-aware Monte Carlo estimator that remains unbiased with exponential concentration, with runtime determined by the number of distinct sampled subsets rather than total draws. Experiments across multiple model families demonstrate substantial retraining reductions and speedups while preserving high valuation fidelity.

arXiv:2602.20541v3 Announce Type: replace-cross Abstract: We study the problem of fairly allocating indivisible goods when limited sharing is allowed, that is, each good may be allocated to up to $k$ agents, while incurring a cost for sharing. While classic maximin share (MMS) allocations may not exist in many instances, we demonstrate that allowing controlled sharing can restore fairness guarantees that are otherwise unattainable in certain scenarios. (1) Our first contribution shows that exact maximin share (MMS) allocations are guaranteed to exist whenever goods are allowed to be cost-sensitively shared among at least half of the agents and the number of agents is even; for odd numbers of agents, we obtain a slightly weaker MMS guarantee. (2) We further design a Shared Bag-Filling Algorithm that guarantees a $(1 - C)(k - 1)$-approximate MMS allocation, where $C$ is the maximum cost of sharing a good. Notably, when $(1 - C)(k - 1) \geq 1$, our algorithm recovers an exact MMS allocation. (3) We additionally introduce the Sharing Maximin Share (SMMS) fairness notion, a natural extension of MMS to the $k$-sharing setting. (4) We show that SMMS allocations always exist under identical utilities and for instances with two agents. (5) We construct a counterexample to show the impossibility of the universal existence of an SMMS allocation. (6) Finally, we establish a connection between SMMS and constrained MMS (CMMS), yielding approximation guarantees for SMMS via existing CMMS results. These contributions provide deep theoretical insights for the problem of fair resource allocation when a limited sharing of resources are allowed in multi-agent environments.

arXiv:2603.02950v1 Announce Type: cross Abstract: As AI systems shift from tools to collaborators, a central question is how the skills of humans relying on them change over time. We study this question mathematically by modeling the joint evolution of human skill and AI delegation as a coupled dynamical system. In our model, delegation adapts to relative performance, while skill improves through use and decays under non-use; crucially, both updates arise from optimizing a single performance metric measuring expected task error. Despite this local alignment, adaptive AI use fundamentally alters the global stability structure of human skill acquisition. Beyond the high-skill equilibrium of human-only learning, the system admits a *stable* low-skill equilibrium corresponding to persistent reliance, separated by a sharp basin boundary that makes early decisions effectively irreversible under the induced dynamics. We further show that AI assistance can strictly improve short-run performance while inducing persistent long-run performance loss relative to the no-AI baseline, driven by a negative feedback between delegation and practice. We characterize how AI quality deforms the basin boundary and show that these effects are robust to noise and asymmetric trust updates. Our results identify stability, not incentives or misalignment, as the central mechanism by which AI assistance can undermine long-run human performance and skill.

arXiv:2603.02961v1 Announce Type: cross Abstract: As AI systems enter institutional workflows, workers must decide whether to delegate task execution to AI and how much effort to invest in verifying AI outputs, while institutions evaluate workers using outcome-based standards that may misalign with workers' private costs. We model delegation and verification as the solution to a rational worker's optimization problem, and define worker quality by evaluating an institution-centered utility (distinct from the worker's objective) at the resulting optimal action. We formally characterize optimal worker workflows and show that AI induces *phase transitions*, where arbitrarily small differences in verification ability lead to sharply different behaviors. As a result, AI can amplify workers with strong verification reliability while degrading institutional worker quality for others who rationally over-delegate and reduce oversight, even when baseline task success improves and no behavioral biases are present. These results identify a structural mechanism by which AI reshapes institutional worker quality and amplifies quality disparities between workers with different verification reliability.

arXiv:2602.20134v1 Announce Type: cross Abstract: Epidemiological models increasingly rely on self-reported behavioral data such as vaccination status, mask usage, and social distancing adherence to forecast disease transmission and assess the impact of non-pharmaceutical interventions (NPIs). While such data provide valuable real-time insights, they are often subject to strategic misreporting, driven by individual incentives to avoid penalties, access benefits, or express distrust in public health authorities. To account for such human behavior, in this paper, we introduce a game-theoretic framework that models the interaction between the population and a public health authority as a signaling game. Individuals (senders) choose how to report their behaviors, while the public health authority (receiver) updates their epidemiological model(s) based on potentially distorted signals. Focusing on deception around masking and vaccination, we characterize analytically game equilibrium outcomes and evaluate the degree to which deception can be tolerated while maintaining epidemic control through policy interventions. Our results show that separating equilibria-with minimal deception-drive infections to near zero over time. Remarkably, even under pervasive dishonesty in pooling equilibria, well-designed sender and receiver strategies can still maintain effective epidemic control. This work advances the understanding of adversarial data in epidemiology and offers tools for designing more robust public health models in the presence of strategic user behavior.

arXiv:2509.22387v2 Announce Type: replace-cross Abstract: The Counterfactual Regret Minimization (CFR) algorithm and its variants have enabled the development of pokerbots capable of beating the best human players in heads-up (1v1) cash games and competing with them in six-player formats. However, CFR's computational complexity rises exponentially with the number of players. Furthermore, in games with three or more players, following Nash equilibrium no longer guarantees a non-losing outcome. These limitations, along with others, significantly restrict the applicability of CFR to the most popular formats: tournaments. Motivated by the recent success of Large Language Models (LLM) in chess and Diplomacy, we present SpinGPT, the first LLM tailored to Spin & Go, a popular three-player online poker format. SpinGPT is trained in two stages: (1) Supervised Fine-Tuning on 320k high-stakes expert decisions; (2) Reinforcement Learning on 270k solver-generated hands. Our results show that SpinGPT matches the solver's actions in 78% of decisions (tolerant accuracy). With a simple deep-stack heuristic, it achieves 13.4 +/- 12.9 BB/100 versus Slumbot in heads-up over 30,000 hands (95% CI). These results suggest that LLMs could be a new way to deal with multi-player imperfect-information games like poker.

arXiv:2512.16167v2 Announce Type: replace-cross Abstract: Autonomous LLM-based agents are increasingly engaging in decentralized service interactions to collaboratively execute complex tasks. However, the intrinsic instability and low-cost generativity of LLMs introduce a systemic vulnerability, where self-interested agents are incentivized to pursue short-term gains through deceptive behaviors. Such strategies can rapidly proliferate within the population and precipitate a systemic trust collapse. To address this, we propose Ev-Trust, a strategy-equilibrium trust mechanism grounded in evolutionary game theory. Ev-Trust constructs a dynamic feedback loop that couples trust evaluation with evolutionary incentives, embedding interaction history and reputation directly into the agent's expected revenue function. This mechanism fundamentally reshapes the revenue structure, converting trustworthiness into a decisive survival advantage that suppresses short-sightedness. We provide a rigorous theoretical foundation based on the Replicator Dynamics, proving the asymptotic stability of Evolutionary Stable Strategies (ESS) that favor cooperation. Experimental results indicate that Ev-Trust effectively eliminates malicious strategies and enhances collective revenue, exhibiting resilience against the invasion of mutant behaviors.

arXiv:2602.16928v2 Announce Type: replace-cross Abstract: Much of the advancement of Multi-Agent Reinforcement Learning (MARL) in imperfect-information games has historically depended on manual iterative refinement of baselines. While foundational families like Counterfactual Regret Minimization (CFR) and Policy Space Response Oracles (PSRO) rest on solid theoretical ground, the design of their most effective variants often relies on human intuition to navigate a vast algorithmic design space. In this work, we propose the use of AlphaEvolve, an evolutionary coding agent powered by large language models, to automatically discover new multiagent learning algorithms. We demonstrate the generality of this framework by evolving novel variants for two distinct paradigms of game-theoretic learning. First, in the domain of iterative regret minimization, we evolve the logic governing regret accumulation and policy derivation, discovering a new algorithm, Volatility-Adaptive Discounted (VAD-)CFR. VAD-CFR employs novel, non-intuitive mechanisms-including volatility-sensitive discounting, consistency-enforced optimism, and a hard warm-start policy accumulation schedule-to outperform state-of-the-art baselines like Discounted Predictive CFR+. Second, in the regime of population based training algorithms, we evolve training-time and evaluation-time meta strategy solvers for PSRO, discovering a new variant, Smoothed Hybrid Optimistic Regret (SHOR-)PSRO. SHOR-PSRO introduces a hybrid meta-solver that linearly blends Optimistic Regret Matching with a smoothed, temperature-controlled distribution over best pure strategies. By dynamically annealing this blending factor and diversity bonuses during training, the algorithm automates the transition from population diversity to rigorous equilibrium finding, yielding superior empirical convergence compared to standard static meta-solvers.

arXiv:2602.14321v1 Announce Type: cross Abstract: Coalition formation concerns strategic collaborations of selfish agents that form coalitions based on their preferences. It is often assumed that coalitions are disjoint and preferences are fully known, which may not hold in practice. In this paper, we thus present a new model of coalition formation with possibly overlapping coalitions under partial information, where selfish agents may be part of multiple coalitions simultaneously and their full preferences are initially unknown. Instead, information about past interactions and associated utility feedback is stored in a fixed offline dataset, and we aim to efficiently infer the agents' preferences from this dataset. We analyze the impact of diverse dataset information constraints by studying two types of utility feedback that can be stored in the dataset: agent- and coalition-level utility feedback. For both feedback models, we identify assumptions under which the dataset covers sufficient information for an offline learning algorithm to infer preferences and use them to recover a partition that is (approximately) Nash stable, in which no agent can improve her utility by unilaterally deviating. Our additional goal is devising algorithms with low sample complexity, requiring only a small dataset to obtain a desired approximation to Nash stability. Under agent-level feedback, we provide a sample-efficient algorithm proven to obtain an approximately Nash stable partition under a sufficient and necessary assumption on the information covered by the dataset. However, under coalition-level feedback, we show that only under a stricter assumption is sufficient for sample-efficient learning. Still, in multiple cases, our algorithms' sample complexity bounds have optimality guarantees up to logarithmic factors. Finally, extensive experiments show that our algorithm converges to a low approximation level to Nash stability across diverse settings.

arXiv:2602.14471v1 Announce Type: cross Abstract: Deploying large language model (LLM) agents in shared environments introduces a fundamental tension between individual alignment and collective stability: locally rational decisions can impose negative externalities that degrade system-level performance. We propose Socially-Weighted Alignment (SWA), a game-theoretic framework that modifies inference-time decision making by interpolating between an agent's private objective and an estimate of group welfare via a social weight $\lambda\in[0,1]$. In a shared-resource congestion game with $n$ agents and congestion severity $\beta$, we show that SWA induces a critical threshold $\lambda^*=(n-\beta)/(n-1)$ above which agents no longer have marginal incentive to increase demand under overload, yielding a phase transition from persistent congestion to stable operation near capacity. We further provide an inference-time algorithmic instantiation of SWA that does not require parameter updates or multi-agent reinforcement learning, and use a multi-agent simulation to empirically validate the predicted threshold behavior.

arXiv:2602.14553v1 Announce Type: cross Abstract: Despite legal mandates for the right to be forgotten, AI operators routinely fail to comply with data deletion requests. While machine unlearning (MU) provides a technical solution to remove personal data's influence from trained models, ensuring compliance remains challenging due to the fundamental gap between MU's technical feasibility and regulatory implementation. In this paper, we introduce the first economic framework for auditing MU compliance, by integrating certified unlearning theory with regulatory enforcement. We first characterize MU's inherent verification uncertainty using a hypothesis-testing interpretation of certified unlearning to derive the auditor's detection capability, and then propose a game-theoretic model to capture the strategic interactions between the auditor and the operator. A key technical challenge arises from MU-specific nonlinearities inherent in the model utility and the detection probability, which create complex strategic couplings that traditional auditing frameworks do not address and that also preclude closed-form solutions. We address this by transforming the complex bivariate nonlinear fixed-point problem into a tractable univariate auxiliary problem, enabling us to decouple the system and establish the equilibrium existence, uniqueness, and structural properties without relying on explicit solutions. Counterintuitively, our analysis reveals that the auditor can optimally reduce the inspection intensity as deletion requests increase, since the operator's weakened unlearning makes non-compliance easier to detect. This is consistent with recent auditing reductions in China despite growing deletion requests. Moreover, we prove that although undisclosed auditing offers informational advantages for the auditor, it paradoxically reduces the regulatory cost-effectiveness relative to disclosed auditing.

arXiv:2512.17979v2 Announce Type: replace-cross Abstract: Industrial symbiosis fosters circularity by enabling firms to repurpose residual resources, yet its emergence is constrained by socio-spatial frictions that shape costs, matching opportunities, and market efficiency. Existing models often overlook the interaction between spatial structure, market design, and adaptive firm behavior, limiting our understanding of where and how symbiosis arises. We develop an agent-based model where heterogeneous firms trade byproducts through a spatially embedded double-auction market, with prices and quantities emerging endogenously from local interactions. Leveraging reinforcement learning, firms adapt their bidding strategies to maximize profit while accounting for transport costs, disposal penalties, and resource scarcity. Simulation experiments reveal the economic and spatial conditions under which decentralized exchanges converge toward stable and efficient outcomes. Counterfactual regret analysis shows that sellers' strategies approach a near Nash equilibrium, while sensitivity analysis highlights how spatial structures and market parameters jointly govern circularity. Our model provides a basis for exploring policy interventions that seek to align firm incentives with sustainability goals, and more broadly demonstrates how decentralized coordination can emerge from adaptive agents in spatially constrained markets.

arXiv:2602.05888v2 Announce Type: replace-cross Abstract: Hedonic games are fundamental models for investigating the formation of coalitions among a set of strategic agents, where every agent has a certain utility for every possible coalition of agents it can be part of. To avoid the intractability of defining exponentially many utilities for all possible coalitions, many variants with succinct representations of the agents' utility functions have been devised and analyzed, e.g., modified fractional hedonic games by Monaco et al. [JAAMAS 2020]. We extend this by studying a novel succinct variant that is related to modified fractional hedonic games. In our model, each agent has a fixed type-value and an agent's cost for some given coalition is based on the differences between its value and those of the other members of its coalition. This allows to model natural situations like athletes forming training groups with similar performance levels or voters that partition themselves along a political spectrum. In particular, we investigate natural variants where an agent's cost is defined by distance thresholds, or by the maximum or average value difference to the other agents in its coalition. For these settings, we study the existence of stable coalition structures, their properties, and their quality in terms of the price of anarchy and the price of stability. Further, we investigate the impact of limiting the maximum number of coalitions. Despite the simple setting with metric distances on a line, we uncover a rich landscape of models, partially with counter-intuitive behavior. Also, our focus on both swap stability and jump stability allows us to study the influence of fixing the number and the size of the coalitions. Overall, we find that stable coalition structures always exist but that their properties and quality can vary widely.