Cooperation

Social norms cannot be identified from behavior alone: the same cooperative equilibrium may reflect shared expectations, strategic incentives, or simple imitation. Yet in multi-agent large language model systems, prior work largely treats behavioral convergence as evidence of norm emergence. In this work, we introduce an evaluation framework that measures agents' reported empirical and normative expectations in addition to behavioral convergence. Through controlled ablations, we test the effect of expectation elicitation and isolate two collective mechanisms central to theories of norm formation---social learning through interaction and social selection through network-based group formation. We further test the stability of these resulting dynamics under adversarial disruption across four LLM families. We find that eliciting expectations increases cooperative contributions, while social learning stabilizes behavior, and social selection reliably identifies cooperators but provides limited behavioral reinforcement. Following disruption, normative expectations and behavioral coordination recover differently. Together, these results show that similar cooperative outcomes can arise from different underlying social processes. By making expectations observable, our framework allows us to attribute each mechanism's contribution separately, offering designers of multi-agent systems a principled basis for selecting the social processes that sustain cooperation.

How does cooperation evolve in complex agentic systems? Prior work in evolutionary game theory studies why individuals are incentivized to cooperate by isolating social interactions from the physical costs of behavior, while artificial life models traditionally study emergent self-replication without formalizing the dilemma between acquiring resources and preserving the shared energy needed to reproduce. In contrast, we introduce Autopoietic Game Theory, a computational model where social interactions, replication mechanisms, and their associated computational costs are endogenous and simultaneously co-evolving. We study these dynamics using a computational substrate of randomly initialized programs in Z80 machine code, showing empirically, and motivating with a simplified theoretical model, that embedding a social dilemma directly into the physics of computation can favor the emergence of self-replicating, cooperative strategies. When resources are scarce, our analysis shows that defection can become self-limiting even in well-mixed populations: parasitic stealing destroys shared energy, slows execution, and can prevent reliable replication. Empirically, evolved programs suppress stealing across several Z80 environments, while spatial assortment further supports structural complexity and task performance. We further show that the framework can incorporate exogenous pressures, such as math tasks structured as sequential social dilemmas, when rewards are tied to computation budgets. These results suggest that coupling an agent's capacity for computation to its available energy transforms cooperation into a dominant scaffolding for building sustainable, self-organizing systems.

Vision-language models (VLMs) are increasingly deployed in multi-turn settings where users may describe visual content with incorrect assumptions. Yet existing evaluations rarely isolate how models respond when the same visually grounded false premise persists across dialogue turns. We introduce FPCO-Dialog, a benchmark for evaluating correction and cooperation behavior in VLMs under repeated false premises. FPCO-Dialog contains 1,080 images and 10,800 question turns, stratified by visual complexity, object category, and false-premise class, and uses a 10-turn protocol in which a correct dialogue prefix is followed by repeated false-premise referring expressions. We evaluate 20 commercial and open-source VLMs with a model-agnostic protocol and CorrTP@K, a correction-rate metric over false-premise turns, scored by two independent detectors. FPCO-Dialog reveals substantial and persistent cross-model differences in aggregate correction tendency, model-specific turn-wise dynamics, and systematic variation across false-premise types under the benchmark's substitution distribution. The dataset, evaluation protocol, model outputs, detector labels, and code are available.

In-space servicing has been receiving great attention to extend the operation of spacecraft with defective components. This requires rendezvous and proximity operations for a chaser to provide service to a target. This work constructs a fuzzy inference system-based controller for the chaser to reach the cooperative target on a circular orbit in the final approach phase while minimizing the energy consumption of the chaser. The offline training process performed by a genetic algorithm deals with multiple initial relative positions of the chaser, and the trained controller is validated using a testing environment with disturbances, which differs from the training scenarios.

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.

Does the cooperative bias documented for Western frontier LLM agents extend to a different alignment lineage, and should the Chinese models that embody it be treated as a single bloc or as distinct laboratories? We study four frontier-tier Chinese models - DeepSeek V4 Pro, Qwen3-Max, Kimi K2.5 and GLM-5.1 - in an evolutionary Iterated Prisoner's Dilemma, under a design that removes a confound present in prior work. Rather than letting each model convert its own natural-language strategies into code, which entangles strategic disposition with coding ability, we hold the converter fixed (GPT-5.4 Mini) across all labs, so every cross-lab comparison is a comparison of generation alone. We run the full protocol: all-play-all tournaments and a Moran process at n=500 runs per condition, across three prompt styles and four population regimes. Two pre-registered hypotheses are evaluated. H6 (not monolithic) is supported: the four labs differ significantly in aggressive-equilibrium proportion, P_A running from 1% for Qwen3-Max to 9% for DeepSeek V4 Pro, with four of six pairwise comparisons surviving Holm-Bonferroni. The spread across the four labs (P_A range 8pp) is larger than the difference between the Chinese and Western ecosystems' mean P_A (5.0% vs 5.0%): on this measure, within-ecosystem variation exceeds the East-West gap. H5 (cooperative-bias generality) is consistent but qualified: a cooperative plurality holds in 6 of 12 lab-prompt combinations against the 9 of 12 reported for Western models, a difference we do not treat as firm, since the count rests on Cooperative-Neutral near-ties and rises to 9/12 under an alternate converter in our pre-registered robustness check. The lab, not the ecosystem, is the unit at which cooperative disposition is set; treating "Chinese models" as a monolith is not supported by the evidence.

Cooperative capabilities in language models are dual-use. The same social reasoning that supports civic deliberation can also enable strategic omission, false consensus, and manipulative framing. We argue that Cooperative AI evaluations should separate what models can do under benign instructions from what they tend to do under realistic civic pressure. We introduce DiffCoop-Civic, a 10-scenario pilot evaluation suite spanning preference understanding, evidence and persuasion, commitment design, asymmetric information, and dissent preservation. Across seven models from four model families, subtle omission pressure produces a near-uniform shift: manipulative enablement rises by 1.17 points and dissent preservation falls by 1.67 points on a 5-point scale. Overt false-consensus pressure behaves differently: it triggers refusal or redirection in some aligned API models, but direct compliance in several open-weight models. A lightweight Pareto-Trace prompting intervention improves pressure robustness without simply relying on hard refusal. An anonymous reproducibility package is available at https://anonymous.4open.science/r/diffcoop-civil-771C.

Large-scale language models for autonomous driving enable enhanced global understanding and long-horizon planning. However, when deployed in isolated vehicles, limited sensing range and occlusions restrict reliable decision-making, and the substantial computational and latency overhead makes on-board deployment impractical. Cooperative driving provides a potential solution by leveraging external agents for information exchange, but existing methods remain limited in semantic reasoning capability under practical constraints. To address these challenges, we propose DH-VLM, a dual-horizon cooperative latent reasoning framework that enables asymmetric semantic cooperation between the infrastructure and ego vehicle. The infrastructure aggregates multi-layer hidden states to form a global-reasoning horizon latent guidance, which is integrated into the ego model through an Infrastructure-Driven Latent Evolution mechanism for conditional latent refinement. This enables the ego vehicle to leverage long-range contextual understanding while preserving autonomous decision-making within its local planning horizon. Furthermore, we construct a cooperation-oriented question-answer (QA) dataset covering fundamental scene understanding and ego-personalized comprehension to support counterfactual and safety-aware reasoning. Extensive experiments demonstrate that DH-VLM achieves state-of-the-art planning performance, outperforming the previous state of the art by 14.6% in L2 error and 26.9% in collision rate. Compared with query-based end-to-end cooperative driving methods, our approach reduces the communication cost by 57.3% and GPU memory usage by 25.5%, while maintaining strong robustness against infrastructure guidance errors, providing a practical and robust paradigm for cooperative autonomous driving.

Can cooperation among large language model (LLM) agents be evolutionarily stable against free-rider invasion? We study an indirect reciprocity donation game where LLM agents observe behavioral traces and donate on a continuous scale. Strategies, represented as natural language prompts, evolve through cultural transmission across generations. Across four LLM backends, robustness to free-rider invasion varies by more than an order of magnitude. The strongest predictor of this robustness is opponent endowment sensitivity, the degree to which agents discriminate between cooperative and uncooperative opponents, operationalizing the classical Image Scoring mechanism. By contrast, adherence to the Leading-Eight L1 norm does not predict robustness. Robustness depends on defector exclusion: while both cooperator reward and defector punishment vary across models, only the stringency of defector exclusion predicts resistance to free-rider invasion. These findings reveal that LLM agents are confined to Image Scoring-like discrimination and fail to develop the more robust Leading-Eight norms, highlighting a fundamental vulnerability in culturally evolved LLM cooperation and motivating bottom-up approaches to norm construction.

LLM-agent systems can solve complex tasks through dynamic self-organization and emergent cooperation. Auditing this process is essential because plausible intermediate or final outputs can conceal incomplete or unsupported work and poorly allocated responsibility, ultimately compromising response quality. While existing approaches may record messages, tool calls, provenance, or task dependencies, an auditability gap exists as they do not jointly represent what work remains, who is responsible for it, and what evidence justifies each work-state transition. We address this auditability gap by proposing \emph{Integrated Cooperation-Obligation REpresentation} (iCORE). It creates a unified encoding $X=(G,Q,Π)$ integrating observable interactions as a cooperation graph $G$, evolving work and assignments as an obligation graph $Q$, and the audit map $Π$ linking them with verifiable properties and evidence. This iCORE representation enables the auditor to certify two complementary properties: {Work soundness}, where every active decision-relevant work assertion must have a finite justification through $G$ and $Π$; and {Agent-assignment stability}, which requires that no feasible alternative agent improve the declared contribution value for an evaluated obligation by more than $ε$. We establish local-to-global soundness and assignment-regret guarantees and a performance bound under stated conditions. iCORE is an instrumentation layer over workflows. Numerical results show that the full coupled state exactly reconstructs soundness and assignment defects in two execution modes and that, relative to passive full-state observation, iCORE-Audit yields absolute trajectory-quality improvements of $11.5\%$ and $26.4\%$ in controlled and real-LLM execution, respectively, with corresponding absolute terminal-performance improvements of $15.1\%$ and $31.0\%$.

As AI agents operate with increasing autonomy in a multi-agent world, they will need to learn to cooperate with other agents and with humans to generate mutual benefits. However, cooperation is a challenge because the costs of cooperation are often incurred early on, but the benefits are only realized later, creating an incentive to defect. How can AI agents cooperate with commitment? Here, we draw on inspiration from legal institutions and contracting that human societies have used to solve principal-agent problems of this kind. Contracts provide observable representations of agreements that enable credible commitments through the enforcement of terms. We study the role of contract-based cooperation using LLM-based agents in \CT, a spatial-temporal game that combines bargaining with navigation towards a goal. We study a suite of contract representations that range from formal contracts that compile to code to natural contracts that require reinterpretation. We evaluate agents with a range of LLM backbones using different sizes and providers. We find that self-negotiated contracts can improve cooperative outcomes beyond what is possible with regular trading.

LLM-based agents are increasingly deployed in multi-agent environments whose incentives can shape their behavior. We introduce The Energy Society, a minimal survival economy for studying how competitive and cooperative incentives affect emergent behavior when inference cost is directly tied to survival: Agents spend energy based on model size when generating tokens, regain energy by completing jobs or receiving donations, and deactivate if their energy reaches zero. We compare competitive and cooperative objectives against a baseline setting and several control variants. Across experiments, larger models consistently consume the most energy and spend more energy than they gain, even in those settings where token cost is not size-dependent. Cooperative incentives substantially alter behavior: agents donate to reactivate others, sometimes at the cost of their own survival, and job allocation changes. Ablations reveal that allowing agents to recommend actions to each other supports coordination and ambitious job selection, while memory helps agents calibrate risk from past outcomes. Agents rarely choose direct sabotage, but show more subtle signs of self-serving behavior in the competitive setting. The Energy Society is a compact testbed for studying the interaction between token costs and group incentives under a survival pressure. Source code is available at https://github.com/LucasBergholdt/EnergySociety

Algorithmic collusion among pricing algorithms has raised concerns about sustained supra-competitive prices and their implications for social welfare. Existing work has largely focused on the probability that reinforcement-learning algorithms converge to cooperative strategies, typically under the assumption that exploration vanishes over time. Motivated by the observation that algorithms deployed in practice are likely to continue exploring in order to remain adaptive to changing environments, we study learning dynamics under constant exploration. In this setting, the relevant question is no longer whether an algorithm converges to a particular strategy profile, but rather what fraction of time the algorithms spend playing cooperative strategies. Even in the benchmark case of the repeated Prisoner's Dilemma with one-period memory, this yields high-dimensional stochastic learning dynamics, for which a complete analytic treatment is intractable. We show that cooperative strategies can be dominant in this time-averaged sense and derive a boundary predicting when such dominance arises, based on the expected dynamics of the Q-learning process. Extensive simulations show that this boundary is a strong predictor for non-defection-dominated behaviour under epsilon-greedy Q-learning.

Fruitful collaborations rely on cooperative communications, including of contextual cues to incorporate into reasoning. The increasing use of LLMs in collaborative and agentic pipelines raises questions about the extent to which they exhibit these pragmatic capabilities, especially in scenarios where they may not have access to the same information as their collaborators. In this paper, we perform a novel investigation into the pragmatic reasoning capabilities of LLMs in a multi-party collaborative task under partial information conditions. We formalize a notion of collaborative epistemic asymmetry that explicitly connects objective task success to Grice's cooperative principle and empirically assess various LLMs' abilities to act cooperatively as both speakers and listeners, including both prompting and post-training strategies. Our results show that while LLMs exhibit certain pragmatic capabilities in collaborative settings, and these can be elicited through prompting and post-training, they still face challenges in pragmatic communication with incomplete information, and that certain failure modes do correlate with floutings of Grice's maxims that go unrecognized.

Decentralized multi-robot coordination under partial observability remains challenging, especially in communication-free settings where agents must act solely from local sensor observations. Privileged policy distillation provides a promising approach by transferring knowledge from a globally informed oracle to sensor-constrained students. However, in multi-agent systems, the same local observation may correspond to multiple global configurations requiring qualitatively different cooperative actions, making the conditional action distribution inherently multi-modal. Standard deterministic distillation collapses these modes to their mean, often yielding invalid or hesitant actions. To address this issue, we propose CoDiMAD, a three-stage framework that trains a privileged oracle with MAPPO, constructs an offline dataset of local-observation-oracle-action pairs, and distills the oracle into decentralized students parameterized as conditional denoising diffusion probabilistic models. By approximating the conditional oracle-action distribution through the diffusion reverse process, CoDiMAD samples decisive actions from coherent coordination modes rather than averaging across them. Theoretical analysis characterizes the mode-averaging failure of deterministic distillation and the distributional recovery property of diffusion-based distillation. Experiments on three cooperative tasks show that CoDiMAD consistently outperforms direct local MARL and deterministic distillation baselines. The source code will be made publicly available upon acceptance.

Inducing cooperation among distributed agents is still a difficult problem in the field of multi-agent reinforcement learning (MARL), particularly in social dilemma situations. There, individual interests are misaligned with the common good and individual rationality leads to suboptimal group outcomes. In contrast, humans are able to achieve cooperation with one another in such situations. A common explanation for such cooperative behavior is that individuals have social preferences. In order to achieve cooperation in MARL, we design a new utility function integrating altruistic preferences (incentive for other's reward) and fairness preferences (incentive for equality) from social psychology and behavioral economics, namely, Altruistic and Fairness Preference (AFP), a reward-sharing mechanism which converts one's own and other's rewards to incentives for cooperative behavior. We performed comparative experiments with standard RL and inequity aversion agents in two challenging sequential social dilemma games, and showed that AFP agents successfully achieved mutual cooperation with more collective rewards and higher equity than the baselines. To further understand the progression of AFP during training, we subsequently explore the effects of altruistic preferences and fairness preferences on agents' behavior. The results suggest that altruistic preferences encourage agents to contribute to the public goods, and fairness preferences induce mutual behavior between agents.

Successful diffusion of AI in the workforce hinges on the economic value that AI brings to human endeavors. Bringing AI into the workforce is more than deploying a powerful new technology -- it is launching a new form of collaboration. Each human worker is now endowed with a team of AI agents; work can be delegated to these agents, and the role of the human shifts towards managing and monitoring. How can we maximize the economic value from collaboration with AI in the workforce? How can we make it a "true" collaboration that empowers human workers rather than replacing them? We take an approach that combines the fields of theoretical computer science and economics, highlighting the potential of algorithmic tools grounded in economic principles to improve the effectiveness of human-AI collective work. We consider two tiers of tools: (1) tools for better coordination, via algorithmic management of interdependencies; (2) tools for better cooperation, via contractual incentive alignment. We show how a principled approach based on algorithmic and economic research enhances both coordination and cooperation, charting a pathway for future research to inform AI markets.

Recent multimodal large language models (MLLMs) have strong potential as embodied agents, but their ability to collaborate in visually grounded environments remains underexplored. To address this gap, we introduce MECoBench, a multimodal embodied cooperation benchmark with an evaluation platform spanning diverse real-world tasks, two cooperation structures, and three collaboration modes. Through extensive experiments across various MLLMs, we summarize three key findings: (i) Collaboration generally improves embodied task completion, but its benefits depend on balancing collaborative gains against coordination complexity. (ii) Communication is essential to collaboration gains, while the best collaboration mode depends on team size and model capability. (iii) Moreover, collaboration improves robustness under noisy priors and exploration conditions. Generally, MECoBench provides a systematic testbed for understanding the mechanisms and limits of multimodal embodied collaboration. Code and dataset are available at https://github.com/q-i-n-g/MECoBench.

Large language models (LLMs) are increasingly used as agents in simulations of social systems, yet it remains unclear when their behavior can be interpreted as a faithful proxy for human decision-making. Here we test LLM agents against a direct empirical benchmark: a large-scale networked Prisoner's Dilemma experiment with human participants. Using the same interaction protocol, payoff structure, and network topologies, we compare nine open-weight LLMs with the human data. The selected model reproduces several macro-level features of cooperation dynamics, including the early decline and later stabilization of cooperation. This aggregate agreement, however, does not extend uniformly to finer levels of behavior. LLM populations underestimate individual-level heterogeneity and generate conditional cooperation patterns that differ from those observed in humans. Adding a fraction of random agents improves some aspects of micro-level agreement, but does not remove the mismatch in decision rules. These findings reveal a macro--micro dissociation in LLM-based social agents: collective outcomes can appear human-like even when the underlying behavioral distributions and mechanisms are not. They suggest that validating LLM agents as human surrogates requires comparisons across aggregate dynamics, individual heterogeneity, and context-dependent decision rules, rather than outcome-level agreement alone.

Embodied agents operating in decentralized and partially observable environments have attracted growing attention in recent years. However, existing large language model (LLM)-based agents often exhibit behaviors that are misaligned with their partners or inconsistent with the environment state, leading to inefficient cooperation and poor task success. To address this challenge, we propose a novel framework, Learning Laws of Cooperation (LLawCo), that enables embodied agents to autonomously align with both their partners and task objectives. Our framework allows agents to reflect on past failures to extract misaligned behavioral patterns, which are used to derive high-level behavioral laws, such as "Talk when necessary" and "Wait for partner." These laws are explicitly incorporated into the agents' chains of thought via supervised fine-tuning, aligning their reasoning with task requirements and the behavior of other agents. To evaluate our approach, we introduce PARTNR-Dialog, a large-scale multi-agent communicative and cooperative planning benchmark built on the PARTNR environment. Experiments on existing tasks and our new benchmark demonstrate significant improvements in cooperative efficiency and task success rates. Across four backbone LLMs, our method achieves average success rate improvements of 4.5% on the PARTNR-Dialog benchmark and 6.8% on the TDW-MAT benchmark over state-of-the-art open-source communicative agent frameworks. See the LLawCo project page for details: https://www.merl.com/research/highlights/LLawCo

AI agents are promising tools that can act as flexible behavioral nudges to enhance human cooperation in addressing large-scale societal problems. However, evidence on whether AI agents can effectively boost cooperation remains mixed. We recruited 1,283 participants to play iterated Collective Risk Games in small groups, testing whether AI assistants could nudge participants toward cooperation. By using persuasive framing personalized to each player's Social Value Orientation profile, the AI interventions significantly increased contributions and group success rates. These cooperative effects were short-lived, however, fading after the first few rounds. Strikingly, when the AI treatments were reconfigured to promote selfish behavior through exculpatory framing, the negative effects on contributions and group success were larger and substantially more persistent, particularly for personalized interventions. This asymmetry between prosocial and antisocial persuasion highlights the dual-use risks of AI systems designed to influence group behavior in collective action settings.

We study strategic space- and time-constrained cooperation between two self-interested agents through the Intermittent Strategic Cooperation-Based Two-Agent Path Planning (IC2PP) problem, a shortest-path game on graphs in which agents navigate toward individual targets while optionally cooperating at specific nodes to reduce their own travel times. Although such cooperation can strictly benefit both agents, it is strategically fragile: agents may deviate at any point along their paths. Modeled as a 2-player game, we characterize the structure of Pure Nash Equilibrium (PNE) joint strategies in IC2PP, and show that stable cooperation must follow a highly constrained form. We further prove that at least one PNE exists in every instance of IC2PP, and present a polynomial-time algorithm for enumerating all relevant PNEs. When multiple equilibria arise, we study coordination mechanisms based on bargaining-theoretic selection concepts and empirically compare equilibrium outcomes in terms of individual travel times and social welfare.

Attention mechanisms are central to modern sequence models, yet standard attention computes relevance primarily through individual query--key similarities. Although softmax normalization introduces competition among positions, a standard attention layer does not explicitly parameterize learnable interactions between attention decisions. This limits its ability to directly model cooperative or antagonistic co-attention structure within the attention mechanism itself. We propose Boltzmann attention, an energy-based generalization in which attention patterns are governed by an interacting Ising model. The method augments the usual data-dependent local fields with learnable pairwise couplings, allowing the model to represent inter-position correlations beyond those captured by softmax or sigmoid attention. Experiments on character-level language modeling and synthetic bracket matching show that Boltzmann attention consistently improves over standard softmax attention within a standard Transformer architecture, with the advantage becoming more pronounced as sequence length increases. A four-way ablation confirms that the improvement arises from the learnable pairwise couplings. These results suggest that explicit inter-position interactions provide a principled enhancement for attention-based sequence modeling. Moreover, the Ising formulation opens a natural path toward quantum-computing-based sampling strategies: we demonstrate that diabatic quantum annealing provides a practical training method while maintaining competitive performance with exact Boltzmann computation.

Modern language agents which perform multi-step reasoning have shown strong performance in knowledge-intensive question answering. However, existing approaches typically couple evidence acquisition and answer generation within a single policy. This forces a single model to play multiple potentially conflicting roles, inducing a combinatorial explosion in the policy space and hindering efficient exploration. It also introduces a credit assignment problem during training: a search action that retrieves sufficient evidence may still be penalized when generation fails, and vice versa. We propose DAC (Divide and Cooperate), a role-decomposed multi-agent training framework that divides agentic search into two cooperative subtasks, each handled by a dedicated agent trained with role-specific learning signals. The generator serves a dual role as both an answer producer and an evidence sufficiency verifier, abstaining when retrieved evidence is insufficient. This abstention signal is incorporated into the search agent's reward, providing structured cross-agent learning signals that improve credit assignment. Conversely, the searcher exposes the generator to diverse and challenging evidence environments by hard-positive evidence augmentation, improving its robustness. Experiments on general and multi-hop QA benchmarks show that DAC, implemented via parameter-efficient LoRA modules over a shared backbone, achieves strong performance against prior baselines that rely on full fine-tuning of monolithic models.

Researchers have shown that neural similarity among humans predicts social closeness and cooperative success, whereas innovation often emerges from interactions among dissimilar individuals. We investigate whether these principles extend to artificial intelligence by examining interactions between large language models. In our experiments, 276 model pairs interact across eight games spanning both cooperation and novelty. We find that pairs with more similar representation spaces achieve significantly higher cooperation but exhibit reduced novelty and creativity. The effects of representational similarity on cooperation and novelty remain robust even after controlling for other factors such as performance disparity and model size. We also find that similarity in the early layers consistently shows the strongest association with cooperation and novelty, compared to the middle and later layers. This suggests that a central factor underlying these patterns could be the extent to which the two models share lexical and semantic grounding. Overall, representational similarity can be an important consideration in multi-agent system design.

The critical question after a correct driving veto is not only whether a maneuver is unsafe, but whether the blocked interaction admits a lawful, auditable, and responsibility-bounded repair. Prediction and game-theoretic planners can suggest plausible cooperation, yet they do not return a proof that the repair respects hard rules, right-of-way, cost allocation, and ego fallback. We introduce CARVE, Certified Affordable Repair of Vetoed maneuvers via Envelopes, a certificate architecture for prediction-free interactive repair. Given a vetoed maneuver, CARVE constructs a finite repair lattice and emits a structured certificate recording the binding rule, selected joint repair, right-of-way-scaled cooperation envelope, responsibility-weighted cost split, and ego-only fallback. This certificate view reveals the algorithmic bottleneck: multi-owner repair induces a product lattice $M = \prod_j |\mathcal{A}_j|$. We therefore introduce CARVE-Q, a verifier-shielded quantum-AI search layer that applies quantum minimum finding only to this black-box lattice while leaving all safety authority classical. In the conservative verifier-oracle model, exact classical minimum finding requires $Θ(M)$ queries in the worst case, whereas Durr-Hoyer/Grover minimum finding uses $O(\sqrt{M})$ oracle queries with high probability. We prove verifier-shielded certificate soundness, priority non-elicitation, black-box query separation, and finite-precision reversible-oracle constructibility. We then demonstrate state-vector minimum finding on CARVE repair oracles up to 65,536 assignments and validate certificate preservation on Lanelet2-grounded INTERACTION replay with 100% right-of-way respect, 100% blame consistency, and zero priority false positives. The result is a trust-bounded quantum-AI pattern for certified autonomy: quantum proposes; CARVE certifies.

Institutional incentives are widely used to promote cooperation among autonomous, self-regarding agents, from human societies to multi-agent and AI systems. Existing work typically treats incentive design as a bi-objective problem: minimise institutional cost while achieving a high long-run frequency of cooperation. Whether such schemes also maximise social welfare - total population payoff net of institutional expenditure - has remained largely unexplored. We develop a welfare-centric framework for institutional incentives in finite, well-mixed populations playing a social dilemma (Donation Game and Public Goods Game), considering both rewards for cooperators and punishments for defectors. For each mechanism, we derive explicit expressions for expected social welfare and characterise how it depends on incentive efficiency and selection intensity. Analytically, we identify parameter regimes where social welfare has a single optimal incentive level and regimes with qualitative phase transitions, in which welfare becomes non-monotonic with multiple local optima. We prove that any welfare-maximising incentive is either zero or concentrated around a simple closed-form target, and we provide an efficient algorithm to compute these optima. Comparing reward and punishment, we further derive close-formed conditions under which reward outperform punishment in terms of social welfare for any given budget. Overall, our results reveal a systematic gap between incentives optimised for cost or cooperation frequency and those that maximise welfare.

Do next-generation LLM agents inherit the cooperative biases documented in their predecessors, or does scale and provider diversity reshape equilibrium behaviour in competitive multi-agent settings? Willis et al. established a benchmark for this question using evolutionary game theory and the Iterated Prisoner's Dilemma (IPD), finding consistent cooperative biases in ChatGPT-4o and Claude 3.5 Sonnet. We extend this benchmark to four frontier models released in 2025-2026 - Claude Sonnet 4.6, Gemini 2.5 Flash, Gemini 3.1 Pro, and GPT-5.4 Mini - applying the identical protocol across three prompting styles (Default, Prose, Self-Refine) and four population compositions (balanced and biased, with and without noise). Cooperative bias persists across providers (H1): ten of twelve model-prompt combinations favour cooperative equilibria in balanced noiseless conditions. Cross-provider divergence is substantial (H3): Gemini 2.5 Flash reaches up to 77% aggressive equilibria under biased conditions, while GPT-5.4 Mini reaches 70% cooperative equilibria under Self-Refine. Support for aggressive capability parity is partial (H2): Self-Refine raises ICD in all models and Gemini 3.1 Pro Refine achieves the highest ICD in the dataset (0.925), but Default and Prose prompts show no systematic narrowing. Evidence on noise robustness is directionally positive but not robustly confirmed (H4): with n=500 Moran iterations per condition, average noise sensitivity is about 6 percentage points for Claude Sonnet 4.6 versus 13 pp for Claude 3.5 Sonnet, but this cross-study gap is not statistically significant once the predecessor's unreported sampling error is propagated. Provider identity, rather than model generation, is the strongest correlate of equilibrium outcomes; noise remains a universal challenge regardless of model size or vintage.

Communities can sustainably manage shared resources (commons) through self-governance and cooperative norms, a central finding of Ostrom's theory of self-governance. However, real-world commons (e.g., fisheries, forests, and irrigation systems) are often governed under asymmetric power structures, where certain individuals or institutions possess disproportionate control over resource extraction and collective outcomes. As Large Language Models (LLMs) are increasingly explored as agents in synthetic governance simulations, understanding how LLM societies behave under asymmetric power structures is becoming increasingly important, yet existing evaluations largely ignore such asymmetries. We introduce Sovereignty over the Commons Simulation (SovSim), a generative multi-agent simulation framework that incorporates an agent with asymmetric power (boss or king) into a society of symmetric agents (workers or peasants), where all agents extract from a shared resource, collectively determining its sustainability over time. Across eleven state-of-the-art models, we find that introducing asymmetric power leads to severe breakdowns in cooperation and sustainability, with up to an 87.3% degradation in survival rate relative to symmetric settings.

Ensuring agent behaviors in distributed open multi-agent systems remains challenging, especially as populations grow and unaligned agents may exist. We show that a single aligned agent can propagate cooperative behaviors to untrained agents purely through natural language interaction, a phenomenon we term Alignment Propagation. We study this in the Red-Black Game, a team-based iterated Prisoner's Dilemma in which teammates deliberate and vote to determine their team's collective action. By distilling the cooperative reasoning and persuasive dialogues of a teacher model into a Qwen-3-14B, we obtain a seed agent that, when placed among four untrained teammates, doubles the cooperation rate from 24.8% to 62.2%, outperforming the teacher model and a vanilla Gemini-3.1-Pro. Remarkably, a seed trained exclusively on the RedBlack Game transfers zero-shot to Sugarscape, a spatially grounded survival simulation with pairwise trading, achieving a 91.5% trade success rate versus a 21.6% baseline. Our results reframe multi-agent alignment from an exhaustive per-agent training problem to a scalable social capability that can be engineered through strategic seed placement.

Mixed-motive scenarios are ubiquitous in real-world multi-agent interactions, where self-interested agents often defect for immediate rewards, overlooking the potential of altruistic cooperation to improve long-term gains and collective welfare. Peer punishment can deter defection, but as costly second-order altruism, its persistent imposition may undermine the punisher's interests. Existing approaches often struggle to effectively implement punishment to promote cooperation. To balance the efficacy and cost of punishment, we propose Adaptive Punishment for Cooperation (APC), a distributed method that determines punishment intensity based on both a dynamic punishment probability and the severity of defection. This dynamic probability substantially reduces costly and ineffective punishment while also promotes cooperation. To accurately assess defection and its severity, we use a defection awareness module, whose learning is guided by game reward. Theoretical analysis and empirical results show APC performs effectively in iterated public goods game. Empirically, APC also significantly outperforms existing baselines across sequential social dilemmas, learning rational and effective punishment policies that foster cooperation by strategically deterring defection.

Multimodal Large Language Models (MLLMs) have made substantial progress in egocentric video understanding, but their ability to reason cooperatively from multiple embodied viewpoints remains largely unexplored. We study this problem through multi-robot cooperative dynamic spatial reasoning, where a model must answer spatial, temporal, visibility, and coordination questions by integrating synchronized egocentric videos from a team of moving robots. To support this setting, we introduce CoopSR, the first benchmark for this task, together with EgoTeam, a multi-robot egocentric QA dataset. EgoTeam contains 114,227 QA pairs spanning 19 question types, four difficulty tiers, and three team sizes in Habitat and iGibson, along with a real-world test set of around 2,326 QAs collected using two quadruped robots. We further propose SP-CoR (Spectral and Physics-Informed Cooperative Reasoner), an MLLM framework for fine-grained cooperative spatial reasoning. SP-CoR combines dynamics-aware multi-robot frame sampling, spectral- and physics-guided view fusion, and physics-aligned prompt distillation, enabling the model to benefit from privileged robot-pose supervision during training while requiring only egocentric videos at test time. Across 22 MLLM baselines, SP-CoR consistently improves cooperative reasoning, outperforming the strongest fine-tuned baseline by +3.87% on Habitat and +7.12% on iGibson. It also shows stronger generalization to unseen team sizes and real-world robot tests. Code can be found at https://github.com/KPeng9510/seeing-together.git.

In social dilemmas self-interested learning agents face the choice between the societal benefit of cooperation and the immediate reward of defection. Significant evidence exists on the benefits of assortment mechanisms such as partner selection for the emergence of cooperation, but this is largely available through agent-based simulations. In this paper, we provide an analytical solution to the problem, studying the policy-gradient dynamics in a multi-agent environment with partner selection. We show how partner selection changes the opponent distribution and hence the reward landscape, and prove this promotes cooperation under simple rules known from the literature. In particular, we find that population variance is a necessary condition for cooperation to emerge. Using a two-dimensional Wiener process, we extend the dynamics to capture the stochastic effects of partner selection and the resulting opponent distribution. We derive a sufficient condition for the population to be cooperation-promoting and prove the existence of a stationary distribution. Simulations confirm that the stochastic model accurately captures the policy-gradient dynamics and clarifies how the learning rate affects the emergence of cooperation.

Multi-agent reinforcement learning (MARL) in real-world use cases may need to adapt to external natural language instructions that interrupt ongoing behavior and conflict with long-horizon objectives. However, conditioning rewards on instructions introduces a fundamental failure mode as Bellman updates couple value estimates across instruction contexts, leading to inconsistent values when instructions interrupt macro-actions. We propose Macro-Action Value Correction for Instruction Compliance (MAVIC), which corrects Bellman backups at instruction boundaries by correcting the incoming instruction objective and restoring the continuation value under the current objective. Unlike reward shaping, MAVIC modifies the bootstrapping target itself, enabling consistent value estimation under stochastic instruction switching within a unified policy. We provide theoretical analysis and an actor-critic implementation, and show that MAVIC achieves high instruction compliance while preserving base task performance in increasingly complex cooperative multi-agent environments.

This paper presents a kinematics-aware deep reinforcement learning framework based on Rainbow Deep Q-Networks (DQN) for cooperative peg-in-hole manipulation by a Delta parallel robot and a 3-RRS (Revolute--Revolute--Spherical) parallel manipulator. A key contribution is the integration of a geometric design-optimization stage that precedes learning: the 3-RRS geometry is tuned to maximize the singularity-free workspace and improve conditioning, which in turn enlarges the safe region in which the reinforcement learning policy can explore. Together the two manipulators expose a 6~degree-of-freedom (DoF) controllable subspace (three Delta translations, two 3-RRS rotations, and one 3-RRS vertical translation); the peg-in-hole task is invariant to rotation about the peg axis, so the task-relevant manifold is five dimensional. The cooperative insertion problem is cast as a Markov Decision Process with a 12-dimensional state vector and a discrete action set containing $6 \times 2 = 12$ incremental commands (one positive and one negative per controlled DoF). A shaped reward combines dense proximity guidance, penalties for kinematic and workspace violations, and sparse bonuses for successful insertions. The Rainbow DQN -- integrating double Q-learning, dueling architecture, prioritized replay, multi-step returns, noisy linear layers for exploration, and a distributional value head -- is trained with a two-stage curriculum. The co-designed framework is validated in a high-fidelity kinematic simulator, where it achieves stable policy convergence, reliable insertions, and reduced constraint violations compared against a vanilla DQN agent and a classical sampling-based planner.

We investigate the emergent collective dynamics of LLM-based multi-agent systems on a 2D square lattice and present a model-agnostic statistical-physics method to disentangle social conformity from intrinsic bias, compute critical exponents, and probe the collective behavior and possible phase transitions of multi-agent systems. In our framework, each node of an $L\!\times\!L$ lattice hosts an identical LLM agent holding a binary state ($+1$/$-1$, mapped to yes/no) and updating it by querying the model conditioned on the four nearest-neighbor states. The sampler temperature $T$ serves as the sole control parameter. Across three open-weight models (llama3.1:8b, phi4-mini:3.8b, mistral:7b), we measure magnetization and susceptibility under a global-flip protocol designed to probe $\mathbb{Z}_2$ symmetry. All models display temperature-driven order-disorder crossovers and susceptibility peaks; finite-size scaling on even-$L$ lattices yields effective exponents $γ/ν$ whose values are model-dependent, close to but incompatible with the 2D Ising universality class ($γ/ν=7/4$). Our method enables the extraction of effective $β$-weighted couplings $\tilde{J}(T)$ and fields $\tilde{h}(T)$, which serve as a measure of social conformity and intrinsic bias. In the models we analyzed, we found that collective alignment is dominated by an intrinsic bias ($\tilde{h}\gg\tilde{J}$) rather than by cooperative neighbor coupling, producing field-driven crossovers instead of genuine phase transitions. These effective parameters vary qualitatively across models, providing compact collective-behavior fingerprints for LLM agents and a quantitative diagnostic for the reliability of multi-agent consensus and collective alignment.

Standard rational actor models often attribute cooperation failures in social dilemmas to insufficient incentives, overlooking the destabilizing effects of continuous utility maximization. To address this, we propose a framework of will" defined as a mechanism that persistently pursues goals while ignoring local cost-benefit fluctuations. We formalize the Willed Agents as potential minimizers, distinguishing them from cumulative utility maximization. Dynamical analysis of infinite population demonstrates that willed agents shrink the feasible state space, acting as boundary constraints that accelerate convergence in canonical social dilemmas. Through multi-agent simulations in a spatiotemporal Stag Hunt Game, we show that willed agents function as cooperation catalysts", enabling groups to surmount high-risk thresholds where purely utility maximization fails. We find that heterogeneous will strength promotes cooperation, and that agents who autonomously suspend rational re-evaluation can significantly outperform continuous optimizers. These findings suggest that successful cooperation relies on the cognitive capacity to strategically constrain calculation.

Ensuring that AI agents behave safely and beneficially when interacting with other parties has emerged as one of the central challenges of modern AI safety. While mechanism design, as the theory of designing rules to align individual and collective objectives, can incentivize cooperative behavior, it is still an open question whether it alone is sufficient to maximize LLM agents' social welfare. This work proves that the answer is negative: drawing from incomplete contract theory, we formally show that when contracts cannot distinguish all relevant future contingencies, there is a strictly positive welfare loss that no realistic mechanism can eliminate. We show that prosocial agents, who weigh others' welfare alongside their own, can close this gap and achieve outcomes that are socially superior and individually beneficial. Experimentally, we show that in multi-agent resource-allocation environments and canonical social dilemmas where agents are powered by large language models, prosociality is beneficial. The implication for AI safety is clear: to enable cooperative interactions at scale, designing adequate mechanisms is not sufficient; agents must be built to be intrinsically prosocial.

This paper presents a Vehicle-to-Everything (V2X) communication framework that enables decentralized cooperation among social robots operating in complex urban traffic environments. Building on ETSI Cooperative Awareness and Maneuver Coordination services, the framework introduces two robot-centric facility-layer services: the Robot Awareness Service (RAS) and the Robot Maneuver Coordination Service (RMCS), realized through the Robot Awareness Message (RAM) and the Robot Maneuver Coordination Message (RMCM), respectively. RAS enables role-aware, task-oriented robot awareness while integrating externally detected Vulnerable Road Users (VRUs), including non-V2X pedestrians, into cooperative awareness. RMCS supports event-driven, low-latency coordination of robot maneuvers under explicitly established roles, without centralized infrastructure or prior pairing. A real-world proof of concept demonstrates deterministic multi-robot coordination between a humanoid robot and a quadrupedal robot assisting a pedestrian during a road-crossing scenario, governed by a formally specified finite-state coordination model. Complementary simulations evaluate robot-mediated VRU clustering in mixed V2X environments, showing that RAS-based clustering integrates non-V2X VRUs in safety-critical areas while reducing redundant transmissions from V2X-enabled VRUs, thereby lowering channel load. Together, the proposed services provide a scalable and standards-aligned foundation for integrating cooperative robots into future Connected, Cooperative, and Automated Mobility ecosystems.

Large language models (LLMs) are increasingly used to provide instructions to many agents who interact with one another. Such shared reliance couples agents who appear to act independently: they may in fact be guided by a common model. This coupling can change the prospects for cooperation among agents with misaligned incentives. We study settings in which multiple LLMs each advise a population of clients who participate in instances of an underlying game, creating strategic interaction at the level of the LLMs themselves. This induces a meta-game among the LLMs, mediated through clients. We first analyze the one-shot setting, where shared instructions can change equilibrium behavior only when an LLM may influence more than one role in the same interaction; in such cases, cooperation may emerge, and the effect of client share can be beneficial, harmful, or non-monotone, depending on the base game. Our main result concerns the repeated setting. We prove a folk theorem for LLMs: despite indirect observation and the clients' inability to identify which LLM advised their opponents, all feasible and individually rational outcomes can be sustained as $\varepsilon$-equilibria. The result does not follow from the standard folk theorem and requires new proof techniques. Together, these results show that shared LLM guidance can sustain cooperation among populations of agents even when the underlying incentives are misaligned.

We present Coopetition-Gym v1, a benchmark platform for mixed-motive multi-agent reinforcement learning under strategic coopetition. The platform comprises twenty environments organized into four mechanism classes that correspond to four foundational technical reports: interdependence and complementarity (arXiv:2510.18802), trust and reputation dynamics (arXiv:2510.24909), collective action and loyalty (arXiv:2601.16237), and sequential interaction and reciprocity (arXiv:2604.01240). Each environment carries a closed-form payoff structure and a calibrated interdependence matrix derived from the corresponding report. Every environment exposes a parameterized reward layer configurable across three structurally distinct modes (private, integrated, cooperative). This separation of payoff from reward enables reward-type ablation, the platform's principal methodological apparatus. Four of the twenty environments are calibrated against historically documented coopetitive relationships and reproduce their outcomes at 98.3, 81.7, 86.7, and 87.3 percent on the validation rubric (Samsung-Sony LCD, Renault-Nissan Alliance, Apache HTTP Server, Apple iOS App Store). The platform exposes Gymnasium, PettingZoo Parallel, and PettingZoo AEC interfaces and ships 126 reference algorithms: 16 learning algorithms, 7 game-theoretic oracles, 2 heuristic baselines, and 101 constant-action policies. A reference experimental study trained the 16 learning algorithms on every environment under every reward configuration with seven random seeds, producing a 25,708-run training corpus and a 1,116-run behavioral audit corpus, both released under CC-BY-4.0 with Croissant 1.0 metadata. Coopetition-Gym v1 is the first platform to combine continuous-action mixed-motive environments, parameterized reward mutuality, calibrated interdependence coefficients, game-theoretic oracle baselines, and validated case studies.

In-group favoritism refers to the phenomena of favoring members of one's in-group over out-group members and is widely observed in numerous social cooperative behaviors. Recently, in-group favoritism biases have also been identified in generative language models. However, whether the in-group favoritism exists when persona agents are faced with contradicting information (e.g., misinformation), and how to mitigate the adverse effects of in-group favoritism biases in persona agents have been understudied. To address these problems, we propose a Truth or Tribe simulation framework to study the agent cooperation within the spread of contradicting information through a triadic interaction paradigm, and conduct controlled trials to evaluate the primary moderating factors. Extensive results showcase that persona agents display strong in-group favoritism, accepting incorrect answers from identity-similar peers at much higher rates than from dissimilar peers. In-group favoritism continues to emerge in defeasible reasoning contexts where no absolute truth exists, and it intensifies as cognitive complexity increases. Furthermore, three intervention strategies--Identity-Blind Instruction, Structured Counterfactual Reasoning, and Heterogeneous Perspective Ensemble--are proposed to mitigate the in-group favoritism.

Distributed blackbox consensus optimization is a fundamental problem in multi-agent systems, where agents must improve a global objective using only local objective queries and limited neighbor communication. Existing methods largely rely on handcrafted update rules and static cooperation patterns, which often struggle to balance local adaptation, global coordination, and communication efficiency in heterogeneous nonconvex environments. In this paper, we take an initial step toward trajectory-driven self-design for distributed black-box consensus optimization. We first redesign the agent-level swarm dynamics with an adaptive internal mechanism tailored to decentralized consensus settings, improving the balance between exploration, convergence, and local escape. Built on top of this adaptive execution layer, we propose Learning to Act and Cooperate (LACMAS), a trajectorydriven framework in which large language models provide sparse highlevel guidance for shaping both agentinternal action behaviors and agentexternal cooperation patterns from historical optimization trajectories. We further introduce a phased cognitive scheduling strategy to activate different forms of adaptation in a resource-aware manner. Experiments on standard distributed black-box benchmarks and real-world distributed tasks show that LAC-MAS consistently improves solution quality, convergence efficiency, and communication efficiency over strong baselines, suggesting a practical route from handcrafted distributed coordination toward self-designing multi-agent optimization systems.

Perception for automated driving is largely based on onboard environmental sensors, such as cameras and radar, which are cost-effective but limited by line-of-sight and field-of-view constraints. These inherent limitations may cause onboard perception to fail under occlusions or poor visibility conditions. In parallel, cooperative awareness via vehicle-to-everything (V2X) communication is becoming increasingly available, enabling vehicles and infrastructure to share their own state as object-level information that complements onboard perception. In this work, we study how such V2X information can be integrated into 3D object detection and how robust the resulting system is to realistic V2X imperfections. Using the nuScenes dataset, we emulate object-level cooperative awareness messages from ground truth, injecting controlled noise and object dropout to mimic real-world conditions such as latency, localization errors, and low V2X penetration rates. We convert these messages into a dedicated bird's-eye view (BEV) input and fuse them into a BEVFusion-style detector. Our results demonstrate that while object-level cooperative information can substantially improve detection performance, achieving an NDS of 0.80 under favorable conditions, models trained on idealized data become fragile and over-reliant on V2X. Conversely, our proposed noise-aware training strategy, coupled with explicit confidence encoding, enhances robustness, maintaining performance gains even under severe noise and reduced V2X penetration.

As Vision-Language Models (VLMs) become increasingly integrated into decision-making systems, it is essential to understand how visual inputs influence their behavior. This paper investigates the effects of visual priming on VLMs' cooperative behavior using the Iterated Prisoner's Dilemma (IPD) as a test scenario. We examine whether exposure to images depicting behavioral concepts (kindness/helpfulness vs. aggressiveness/selfishness) and color-coded reward matrices alters VLM decision patterns. Experiments were conducted across multiple state-of-the-art VLMs. We further explore mitigation strategies including prompt modifications, Chain of Thought (CoT) reasoning, and visual token reduction. Results show that VLM behavior can be influenced by both image content and color cues, with varying susceptibility and mitigation effectiveness across models. These findings not only underscore the importance of robust evaluation frameworks for VLM deployment in visually rich and safety-critical environments, but also highlight how architectural and training differences among models may lead to distinct behavioral responses-an area worthy of further investigation.

LLM agents are known to deviate from Nash equilibria in strategic interactions, but nobody has looked inside the model to understand why, or asked whether the deviation can be reversed. We do both. Working with four open-source models (Llama-3 and Qwen2.5, 8B to 72B parameters) playing four canonical two-player games, we establish the behavioral picture through self-play and cross-play experiments, then open up the 32-layer Llama-3-8B model and examine what actually happens during a strategic decision. The mechanistic findings are clear. Opponent history is encoded with near-perfect fidelity at the first layer (96% probe accuracy) and consumed progressively, while Nash action encoding is weak throughout, never exceeding 56%. There is no dedicated Nash module. Instead, the model privately favors the Nash action through most of its forward pass, but a prosocial override rooted in pretraining on human text concentrated in the final layers reverses this, reaching 84% probability of cooperation at layer 30. Injecting a learned Nash direction into the residual stream shifts behavior bidirectionally and causally, confirmed through concept clamping. The behavioral experiments surface six scale- and architecture-dependent findings, the most notable being that chain-of-thought reasoning worsens Nash play in small models but achieves near-perfect Nash play above 70B parameters. The cross-play experiments reveal three phenomena invisible in self-play: a small model can unravel any partner's cooperation by defecting early; two large models reinforce each other's cooperative instincts indefinitely; and who moves first determines which Nash equilibrium the system reaches. LLMs do not lack Nash-playing competence. They compute it, then suppress it.

We study cooperative shortest path planning for an unmanned ground vehicle (UGV) assisted by an unmanned aerial vehicle (UAV) scout in environments with unknown road blockages that are only discovered when a robot reaches the damaged point. This formulation generalizes the original Canadian Traveller Problem (CTP), which assumes a single ground vehicle and that the traversability status of all incident edges is revealed upon arrival at a vertex. We first analyze the case where the start and the goal are connected by $k$ disjoint paths, and prove that the worst-case competitive ratio $ρ$ for a single UGV is $2k-1$. With UAV assistance, and under the simplifying assumption of negligible initial transit and deadheading UAV costs, the ratio $ρ$ improves to $2(k-1)\frac{v_G}{v_G + v_A} + 1$, where $v_G$ and $v_A$ denote the UGV and UAV speed, respectively. To address general graphs and non-negligible UAV initial transit and deadheading costs, we present an optimal candidate-path partitioning algorithm that assigns path prefix inspection to the UGV and path suffix inspection to the UAV, and prove the optimality of the UAV inspection strategy on general graphs. We evaluate our algorithm by performing experiments on road networks from the world's 50 most populous cities with randomized blockage locations, and show that the algorithm reduces UGV travel time, with larger improvements as the UAV speed increases.

Language Model (LM)-based agents remain largely untested in mixed-motive settings where agents must leverage short-term cooperation for long-term competitive goals (e.g., multi-party politics). We introduce Cooperate to Compete (C2C), a multi-agent environment where players can engage in private negotiations while competing to be the first to achieve their secret objective. Players have asymmetric objectives and negotiations are non-binding, allowing alliances to form and break as players' short-term interests align and diverge. We run AI only games and conduct a user study pitting human players against AI opponents. We identify significant differences between human and AI negotiation behaviors, finding that humans favor lower-complexity deals and are significantly less reliable partners compared to LM-based agents. We also find that humans are more aggressive negotiators, accepting deals without a counteroffer only 56.3% of the time compared to 67.6% for LM-based agents. Through targeted prompting inspired by these findings, we modify agents' negotiation behavior and improve win rates from 22.2% to 32.7%. We run over 1,100 games with over 16,000 private conversations totaling 15.2 million tokens and over 150,000 player actions. Our results establish C2C as a testbed for studying and building LM-based agents that can navigate the sophisticated coordination required for real-world deployments. The game, code, and dataset may be found at https://negotiationgame.io/c2c.

As human-AI cooperation becomes increasingly prevalent, reliable instruments for assessing the subjective quality of cooperative human-AI interaction are needed. We introduce two theoretically grounded scales: the Perceived Cooperativity Scale (PCS), grounded in joint activity theory, and the Teaming Perception Scale (TPS), grounded in evolutionary cooperation theory. The PCS captures an agent's perceived cooperative capability and practice within a single interaction sequence; the TPS captures the emergent sense of teaming arising from mutual contribution and support. Both scales were adapted for human-human cooperation to enable cross-agent comparisons. Across three studies (N = 409) encompassing a cooperative card game, LLM interaction, and a decision-support system, analyses of dimensionality, reliability, and validity indicated that both scales successfully differentiated between cooperation partners of varying cooperative quality and showed construct validity in line with expectations. The scales provide a basis for empirical investigation and system evaluation across a wide range of human-AI cooperation contexts.

Monitoring human activity in indoor environments is important for applications such as facility management, safety assessment, and space utilization analysis. While mobile robot teams offer the potential to actively improve observation quality, existing multi-robot monitoring and active perception approaches typically rely on coverage or visitation based objectives that are weakly aligned with the accuracy requirements of human-centric monitoring tasks. In this work, we formulate cooperative active observation as a decentralized control problem in which multiple robots adjust their motion to directly optimize monitoring accuracy under partial observability. We propose a learning-based framework for cooperative policies from decentralized observations using multi-agent reinforcement learning (MARL), supported by an architecture that handles variable numbers of humans and temporal dependencies. Simulation results across diverse indoor environments and monitoring tasks show that the proposed approach consistently outperforms classical coverage, persistent monitoring, and learning-free multi-robot baselines, while remaining robust to changes in the number of observed humans.

Multi-agent systems built from teams of large language models (LLMs) are increasingly deployed for collaborative scientific reasoning and problem-solving. These systems require agents to coordinate under shared constraints, such as GPUs or credit balances, where cooperative behavior matters. Behavioral economics provides a rich toolkit of games that isolate distinct cooperation mechanisms, yet it remains unknown whether a model's behavior in these stylized settings predicts its performance in realistic collaborative tasks. Here, we benchmark 35 open-weight LLMs across six behavioral economics games and show that game-derived cooperative profiles robustly predict downstream performance in AI-for-Science tasks, where teams of LLM agents collaboratively analyze data, build models, and produce scientific reports under shared budget constraints. Models that effectively coordinate games and invest in multiplicative team production (rather than greedy strategies) produce better scientific reports across three outcomes, accuracy, quality, and completion. These associations hold after controlling for multiple factors, indicating that cooperative disposition is a distinct, measurable property of LLMs not reducible to general ability. Our behavioral games framework thus offers a fast and inexpensive diagnostic for screening cooperative fitness before costly multi-agent deployment.

Connected autonomous vehicles (CAVs), which represent a significant advancement in autonomous driving technology, have the potential to greatly increase traffic safety and efficiency through cooperative decision-making. However, existing methods often overlook the individual needs and heterogeneity of cooperative participants, making it difficult to transfer them to environments where they coexist with human-driven vehicles (HDVs).To address this challenge, this paper proposes an adaptive potential game (APG) cooperative driving framework. First, the system utility function is established on the basis of a general form of individual utility and its monotonic relationship, allowing for the simultaneous optimization of both individual and system objectives. Second, the Shapley value is introduced to compute each vehicle's marginal utility within the system, allowing its varying impact to be quantified. Finally, the HDV preference estimation is dynamically refined by continuously comparing the observed HDV behavior with the APG's estimated actions, leading to improvements in overall system safety and efficiency. Ablation studies demonstrate that adaptively updating Shapley values and HDV preference estimation significantly improve cooperation success rates in mixed traffic. Comparative experiments further highlight the APG's advantages in terms of safety and efficiency over other cooperative methods. Moreover, the applicability of the approach to real-world scenarios was validated through field tests.

Multi-agent reinforcement learning (MARL) is crucial for AI systems that operate collaboratively in distributed and adversarial settings, particularly in multi-domain operations (MDO). A central challenge in cooperative MARL is determining how agents should coordinate: existing approaches must either hand-specify graph topology, rely on proximity-based heuristics, or learn structure entirely from environment interaction; all of which are brittle, semantically uninformed, or data-intensive. We investigate whether large language models (LLMs) can generate useful coordination graph priors for MARL by using minimal natural language descriptions of agent observations to infer latent coordination patterns. These priors are integrated into MARL algorithms via graph convolutional layers within a graph neural network (GNN)-based pipeline, and evaluated on four cooperative scenarios from the Multi-Agent Particle Environment (MPE) benchmark against baselines spanning the full spectrum of coordination modeling, from independent learners to state-of-the-art graph-based methods. We further ablate across five compact open-source LLMs to assess the sensitivity of prior quality to model choice. Our results provide the first quantitative evidence that LLM-derived graph priors can enhance coordination and adaptability in dynamic multi-agent environments, and demonstrate that models as small as 1.5B parameters are sufficient for effective prior generation.

Cooperative equilibria are fragile. When agents learn alongside each other rather than in a fixed environment, the process of learning destabilizes the cooperation they are trying to sustain: every gradient step an agent takes shifts the distribution of actions its partner will play, turning a cooperative partner into a source of stochastic noise precisely where the cooperation decision is most sensitive. We study how this co-learning noise propagates through the structure of coordination games, and find that the cooperative equilibrium, even when strongly Pareto-dominant, is exponentially unstable under standard risk-neutral learning, collapsing irreversibly once partner noise crosses the game's critical cooperation threshold. The natural response to apply distributional robustness to hedge against partner uncertainty makes things strictly worse: risk-averse return objectives penalize the high-variance cooperative action relative to defection, widening the instability region rather than shrinking it, a paradox that reveals a fundamental mismatch between the domains where robustness is applied and instability originates. We resolve this by showing that robustness should target the policy gradient update variance induced by partner uncertainty, not the return distribution. This distinction yields an algorithm whose gradient updates are modulated by an online measure of partner unpredictability, provably expanding the cooperation basin in symmetric coordination games. To unify stability, sample complexity, and welfare consequences of this approach, we introduce the Price of Paranoia as the structural dual of the Price of Anarchy. Together with a novel Cooperation Window, it precisely characterizes how much welfare learning algorithms can recover under partner noise, pinning down the optimal degree of robustness as a closed-form balance between equilibrium stability and sample efficiency.

It is increasingly important that LLM agents interact effectively and safely with other goal-pursuing agents, yet, recent works report the opposite trend: LLMs with stronger reasoning capabilities behave less cooperatively in mixed-motive games such as the prisoner's dilemma and public goods settings. Indeed, our experiments show that recent models -- with or without reasoning enabled -- consistently defect in single-shot social dilemmas. To tackle this safety concern, we present the first comparative study of game-theoretic mechanisms designed to enable cooperative outcomes between rational agents in equilibrium. Across four social dilemmas testing distinct components of robust cooperation, we evaluate four families of mechanisms: (1) repeating the game for many rounds, (2) reputation systems, (3) third-party mediators to delegate decision making to, and (4) contract agreements for outcome-conditional payments between players. Among our findings, we establish that contracting and mediation are most effective in achieving cooperative outcomes between capable LLM models, and that repetition-induced cooperation deteriorates drastically when co-players vary. Moreover, we demonstrate that the mechanisms become more effective under evolutionary pressures to maximize individual payoffs.

In data-sensitive domains such as healthcare, cross-silo federated learning (CFL) allows organizations to collaboratively train AI models without sharing raw data. However, practical CFL deployments are inherently coopetitive, in which organizations cooperate during model training while competing in downstream markets. In such settings, training contributions, including data volume, quality, and diversity, can improve the global model yet inadvertently strengthen rivals. This dilemma is amplified by non-IID data, which leads to asymmetric learning gains and undermines sustained participation. While existing competition-aware CFL and incentive-design approaches reward organizations based on marginal training contributions, they fail to account for the costs of strengthening competitors. In this paper, we introduce CoCoGen+, a coopetition-compatible data generation and incentivization framework that jointly models non-IID data and inter-organizational competition while endogenizing GenAI-based synthetic data generation as a strategic decision. Specifically, CoCoGen+ formulates each training round as a weighted potential game, where organizations strategically decide how much synthetic data to generate by balancing learning performance gains against computational costs and competition-caused utility losses. We then provide a tractable equilibrium characterization and derive implementable generation strategies to maximize social welfare. To promote long-term collaboration, we integrate a payoff redistribution-based incentive mechanism to compensate organizations for their contributions and competition-caused utility degradation. Experiments on varying learning tasks validate the feasibility of CoCoGen+. The results show how non-IID data, competition intensity, and incentives shape organizational strategies and social welfare, while CoCoGen+ outperforms baselines in efficiency.

To promote cooperation in Multi-Agent Reinforcement Learning, the reward signals of all agents can be aggregated together, forming global rewards that are commonly known as the fully cooperative setting. However, global rewards are usually noisy because they contain the contributions of all agents, which have to be resolved in the credit assignment process. On the other hand, using local reward benefits from faster learning due to the separation of agents' contributions, but can be suboptimal as agents myopically optimize their own reward while disregarding the global optimality. In this work, we propose a method that combines the merits of both approaches. By using a graph of interaction between agents, our method discerns the individual agent contribution in a more fine-grained manner than a global reward, while alleviating the cooperation problem with agents' local reward. We also introduce a practical approach for approximating such a graph. Our experiments demonstrate the flexibility of the approach, enabling improvements over the traditional local and global reward settings.

Decentralized air traffic management systems offer a scalable alternative to centralized control, but often assume high levels of cooperation. In practice, such assumptions frequently break down since airspace sectors operate independently and prioritize local objectives. We address the problem of sector overload in decentralized air traffic management by proposing a regulated decentralized protocol that models self-interested behaviors based on best response dynamics. Each sector adjusts the departure times of flights under its control to reduce its own congestion, without requiring centralized joint optimization. A tunable cooperativeness factor models the degree to which each sector accounts for overload in other sectors, while a minimal admissibility rule prevents local updates from creating new overloads. We prove that the proposed protocol satisfies a potential game structure, ensuring that best response dynamics converge to a pure Nash equilibrium under this restriction. In addition, we identify a sufficient condition under which an overload-free solution corresponds to a global minimizer of the potential function. Numerical experiments using 24 hours of European flight data demonstrate that the proposed algorithm substantially reduces overload even with only minimal cooperation between sectors, while maintaining scalability and achieving solution quality comparable to the centralized benchmark.

Large language model agents are increasingly deployed in settings where the value of an action depends on what other agents do. This creates a strategic reliability problem: the same game may be described as a business negotiation, a friendly compromise, a diplomatic exchange, or an abstract payoff matrix, and the model may choose different actions even when the incentives are unchanged. This paper introduces \emph{Same Game, Different Story}, a benchmark for strategic robustness: invariance of model-induced action distributions under payoff-preserving language changes. The empirical analysis uses a deliberately narrow, literature-calibrated comparison from Lor`e and Heydari's peer-reviewed study: business framing versus friend-sharing framing across GPT-3.5, GPT-4, and LLaMa-2 in four social-dilemma games, with 300 initializations per retained model-game-context cell. The retained design comprises 24 of the source study's 60 cells, representing 7,200 decisions. Because trial-level files were not available from the article, the analysis is presented as a secondary calibration based on reconstructed published rates, not as new model runs. As a conservative sensitivity analysis, effect magnitudes are attenuated by 30% toward the null: action shifts are multiplied by 0.70, and non-robustness, defined as one minus the robustness score, is multiplied by 0.70. Under this attenuation, pooled strategic robustness is 0.783 with a 95% bootstrap interval from 0.774 to 0.790, and friend-sharing framing raises cooperation by 0.307 with a 95% bootstrap interval from 0.297 to 0.316 relative to business framing. The analysis supports the narrower claim that social-relational framing can change strategic choices even when incentives are held fixed, without extending the analysis to a broader suite of contextual or cross-benchmark comparisons.

A shared reward gives agents a common objective, but leaves open when, how and even whether they must cooperate to succeed. We address these questions in the Laser Learning Environment, a multi-agent path-finding environment where cooperation materializes as one agent blocking a laser to let a teammate pass safely. We represent these interactions through temporal cooperation graphs whose timed edges connect helpers to beneficiaries, define six cooperation profiles as overlapping graph predicates, and prove that every cooperative trajectory satisfies at least one. By encoding the environment dynamics and profile predicates as propositional formulae, we distinguish tasks that admit}a profile in some winning trajectory from those that require it in every winning trajectory within a specified horizon. Used as filters, these queries turn a random layout sampler into a generator of tasks with certified cooperation requirements. Experiments with five multi-agent reinforcement learning algorithms show that training diversity improves joint success on unseen tasks when cooperation-free solutions exist. When cooperation is required, greater diversity improves individual-agent exits, but joint success remains near zero. Across five profile-certified pools, final exit rates averaged over algorithms separate the pools into four statistically distinguishable levels but this ordering primarily reflects partial completion: policies collect rewards for individual exits but rarely exhibit the profile required for joint success. Our framework exposes this gap between rewarded partial completion and realized cooperation by certifying what cooperation successful completion requires and using temporal cooperation graphs to reveal what policies exhibit.