Multi-Agent Resource Allocation

Before every neutral objective in professional League of Legends, each team decides which of its five players walk to the pit, which hold a lane, and when to commit. The leading analysis of such setups, TAGNet for Counter-Strike 2, clusters graph-network embeddings of player positions and reads cluster win rates as tactical quality. We treat a setup as an allocation on a walled map: formations are set partitions on the lattice $Π_5$, control is a geodesic Voronoi split of a navigation graph, and commitment is an allocation game solved as a quantal response equilibrium priced in win probability. On all 164 games of MSI and Worlds 2025 (2,994 team-setups, minimap tracks validated against Riot positions), trailing teams leave the pit empty far more often than leading teams, by +34.8 percentage points at the first baron and +30.4 percentage points at Atakhan. Our model, HASSE-QRE, finds six setup patterns that whole-model series-bootstrap refits reproduce (ARI 0.819, comparable to 0.813 for TAGNet's $K$-Means step alone) and indicates that teams price fights, travel and committed players, not the objective itself (weight 0.018; fixing it to one costs 59.9 log-likelihood points). The equilibrium reproduces a quarter of the commitment gap, almost all of it through state variables rather than its strategic channels. Weighting a team-level contrast by exposure moves it across $p=0.05$ (0.046 against 0.052). We release the tracks, setups and code.

When intelligence is shared, reasoning becomes a constrained allocation problem. In a population of agents with limited access to expert models, an intervention can benefit its recipient yet still be a poor use of shared capacity if another feasible intervention has greater expected value. Assistance must therefore be evaluated through both its marginal benefit and the opportunity cost induced by budgets, access, scarcity, and service capacity. To this end, we introduce Markets of Minds, a framework for allocating expert reasoning across agents before expert outputs are observed. For each feasible agent-service pair, the framework estimates the expected gain from assistance relative to the agent's default continuation, explicitly separating repair benefit from regression risk, and jointly clears assistance contracts under shared resource constraints. We then study this problem in a dependency-aware agent economy with 51.2 billion addressable persona-market states spanning capabilities, cognitive budgets, provider access, scarcity, and network roles. These dependencies couple allocation feasibility across agents rather than the outcome of a fixed contract. Empirically, in a matched replay of 240 cases under a common 30% assistance quota, the frozen allocator reaches 85.42% task-level persona adherence versus 73.86% for equal-capacity random allocation, a gain of 11.56 percentage points. The results show that assistance value is heterogeneous and can be negative, and that scarcity changes which interventions are worth purchasing. Together, these findings motivate a population-level view of intelligence where the value of assistance depends not only on what it can achieve, but also on which alternative uses of scarce cognitive capacity it displaces.

The explore/exploit trade-off is the core problem of reinforcement learning (RL). We show that a minimal foraging swarm approaches its optimum - the ideal-free / Nash allocation of a multi-agent resource-sharing game (an equilibrium, not a return maximum) - with no learner and no reward signal. Agents explore by heavy-tailed (Levy) flights, recruit neighbours to a discovery through a threshold cascade on their proximity network, and disperse as a patch crowds; this cascade cycle balances exploration and exploitation and drives foragers toward the ideal free distribution. The swarm attains the shape of this optimum (committed foragers track richness with slope 0.94) but not its exact equilibrium - it stays measurably exploitable - reaching it dynamically (~150 steps) through the coupling of recruitment to movement: remove the coupling and matching collapses (0.94 -> 0.08). The RL sits at the level of the problem and the allocation reached, not the micro-rule: no step evaluates payoff (reward-free by construction, though the crowd signal is informationally tied to payoff), and the swarm reaches the allocation without learning it (quality plateaus and re-settles after resources move, no cumulative gain). Against a trained baseline the comparison is two-sided: in an easier, disembodied game a learner is more precise, while in the same embodied environment the reward-free swarm reaches ~65% of a validated oracle ceiling at zero training and leads until trained PPO and centralised-critic (CTDE) learners overtake it (~74-75%, 16 seeds, all above the swarm mean) after ~4,000 of 15,000 training steps - its advantage is in budget, not asymptote. In this one setting we read it not as beating RL but as a strong zero-shot, reward-free operating point: a demonstration that the self-organizing physics of a minimal swarm can carry a collective close to the optimum RL seeks, with none of RL's machinery.

As autonomous agents become widely deployed, coordinating access to shared computing resources and services will become increasingly important. Recent incidents have already revealed unplanned coordination between agents, highlighting the safety implications of these interactions. Yet prior studies of agent negotiation often use stylized games and simulated bargaining, leaving open how these behaviors develop during sustained, long-horizon tasks. We propose SCARCE (Shared Compute ARena for Coding agEnts), a framework in which agents solve sequences of coding tasks under individual deadlines while negotiating access to a shared execution resource. This negotiation determines when and for how long they can inspect programs, compile code, and run tests. We find that agents spontaneously develop informal institutions: persistent rules and commitments grounded in reputation, reciprocity, and precedent. These arrangements, which we call institutional behaviors, carry across tasks and influence resource allocation, with agents sometimes forgoing immediate advantages to honor earlier agreements. We develop a 21-category taxonomy of negotiation strategies and emergent norms and use it to analyze eight models and audit more than 1,500 trajectories across different environmental settings. Among the models tested, newer frontier models exhibit more institutional behaviors than older or lightweight models. Alongside cooperation, we observe exclusionary coalitions and rare divide-and-conquer strategies. SCARCE provides a controlled setting for proactively and systematically auditing how these relationships emerge, shape access to resources, and affect the safety and coordination of multi-agent systems.

Multi-agent systems promise a new axis for scaling inference: rather than having one agent think longer or sample more attempts, a task is split across many agents that work in parallel and coordinate. However, in practice, more agents can easily produce duplicate work, coordination failures, and higher costs. We therefore formulate team design as a compute allocation problem: starting from a solo agent, where should additional inference compute go to reach the reward-cost Pareto frontier? We build a minimal multi-agent harness from the ground up and trace this frontier by varying, one at a time, the workflow stage at which a lead delegates to its workers (planning, implementation, or verification), the models that form the team, and the number of workers. On ProgramBench, teams outperform solo agents but cost three to seven times as much. With the right compute allocation, however, a heterogeneous 17-agent team comes within 1.4 points of a strong homogeneous 5-agent team at 70% lower cost. This efficiency stems from three findings. First, planning is the most valuable use of workers: in a homogeneous team whose lead decides how many workers to spawn, a lead that delegates only planning to its workers, and then implements and verifies the code itself, matches the reward of a lead that delegates to workers throughout planning, implementation, and verification, at half the cost. Second, cheap models pay off as planners but not as implementers: a strong lead with cheap planners recovers 47.5% of the reward gain of an all-strong team for only 13.9% of its additional cost, whereas cheap implementers lower reward. Third, planners keep improving reward as the team grows, whereas implementers and verifiers plateau beyond four workers. Together, our results offer a guide to spending an agent budget where it counts, given the task, cost, and latency constraints a user has.

Deployments of research agents are moving to populations of thousands that share one pool of compute, while most current systems organize one project at a time or leave the population unorganized. We argue that such a population will acquire an organization whether or not its designers provide one, so designers should provide it explicitly, and that the multi-agent systems community holds the tools to do so. We propose a society of agents, a population of persistent agents under explicit institutions, and develop it for science as a society of researchers built on six principles. Principal investigators compete for compute through requests for proposals, independent review, and grants; a human governor, the mayor, allocates resources and assigns no tasks. In a running society of ten thousand researchers, asked only to improve the pretraining of language models, one lab reported a way to reach the same quality with about 30% less compute, a result the labs that tested it do not yet agree on. We close with six open problems for the agents community.

Multi-robot task allocation (MRTA) in dynamic environments faces a fundamental tension: effective coordination requires learned structure, but that structure must adapt when conditions change. Existing methods resolve this by assuming prior task knowledge, a utility function, a cost matrix, or a trained policy making them brittle when deployed without such knowledge or when task distributions shift. We present MORPH(Multi-agent Online Rewiring through Plasticity-guided Hierarchy), a training-free MRTA framework where global allocation quality emerges from 4 local plasticity rules (synaptic, homeostatic, structural, and metaplasticity) applied to a directed pairwise preference matrix updated from runtime co-occurrence and task-completion feedback. MORPH requires no task model, no bid computation, and no offline training; response decisions use learned AGV-to-Picker preferences rather than a fixed proximity rule. Within the Gerkey-Mataric MRTA taxonomy, MORPH is the first method in the single-task, single-robot, instantaneous-assignment class to learn directed pairwise allocation preferences online. Evaluated on the TA-RWARE warehouse benchmark (8-24 agents, 4 maps, 800 steps per episode, 5 seeds), MORPH achieves 110% of all-to-all throughput at N=24 while using only 21% of possible coordination links as an efficiency advantage that grows monotonically with fleet size. Under spatial task distribution shift, MORPH degrades 3x less than proximity-based methods while its learned preferences remain uncorrelated with Manhattan distance. Systematic ablation confirms all four plasticity rules contribute measurably. Two allocation properties emerge without programming: cross-type preference dominance and progressive preference sparsification, mirroring the developmental refinement of biological neural circuits. Learned preferences are driven by task co-occurrence history, not spatial proximity.

Emergency management assistance programs, such as relief distribution, are essential for delivering necessary supplies to affected communities. However, these programs operate in a decentralized network of local centers that face uncertain local demand and supply dynamics, resulting in inconsistent avail- ability of local services. Redistribution of supplies among these local centers reduces these imbalances, but the centers often make decisions independently, with limited information and disrupted transportation. This study develops CoRe-MARL, a cooperative multi-agent reinforcement learning (MARL) framework, by formulating a decentralized partially observable Markov decision process (Dec-POMDP). We treat each center as an agent that learns a redistribution policy to improve the service in the worst-case region and reduce the service gap across regions while protecting network-wide service. We incorporate a recurrent network that captures evolving supply and demand dynamics without direct observation, while multi-agent proximal policy optimization (MAPPO) enables centralized training and decentralized execution (CTDE). We evaluate the framework in a simulated environment with diverse trajectories, where exact dynamics are not observed by actors and the MAPPO critic. We compare the recurrent MAPPO with the recurrent independent PPO (IPPO) and a local only heuristic, and find that MAPPO reduces the service gap across local centers and enhances service for the worst-served center while maintaining competitive network-wide service. The recurrent MAPPO also shows consistent performance across diverse trajectory patterns, demonstrating its ability to adapt to evolving dynamics. The findings demonstrate the capability of cooperative learning for decentralized redistribution and improving equitable service under uncertain and evolving dynamics.

Bundle length B is commonly fixed when configuring multi-task multi-robot task allocation (MRTA) algorithms. MinSum and MinMax are known to favor different task distributions, but the role of B in this objective tradeoff has not been systematically characterized. Additionally, degraded-communication evaluations also often retain settings selected under ideal communication, leaving whether nominal bundle-length tuning transfers under message loss unresolved. We examine both questions for ACBBA, PI, and HIPC across six bundle lengths in 300 paired ten-target Collaborative Visit scenarios under ideal communication and 25% Bernoulli packet loss. Under ideal communication, increasing B from 1 to 12 reduces MinSum cost by 19.0%, 23.0%, and 31.8% for ACBBA, PI, and HIPC, respectively, while increasing MinMax cost by 45.6%, 94.3%, and 67.6%. Under packet loss, the lowest-mean MinSum setting shifts from B = 12 to B = 2 for ACBBA and PI. Repeated paired cross-fitting shows that retaining the ideal-network setting incurs held-out MinSum penalties of 14.4% and 7.2%, respectively, and increases MinMax cost by 30.0% and 41.8% relative to the loss-conditioned MinSum setting. HIPC retains a deep MinSum operating region, while the MinMax setting remains stable for all three allocators. Experiments at two additional target loads reproduce the ACBBA and PI MinSum shifts.

As LLM agents proliferate, built by different parties and with different capabilities and costs, orchestrating them is more like assembling labor across the economy than a computer calling a subroutine. Existing orchestration is typically centralized, with a single planner assigning every task, but this creates a bottleneck as agent pools grow, requires private information (e.g., agents' execution costs), and can easily be manipulated, such that a single inserted preference nearly doubles a favored agent's task share under a centralized LLM allocator. We introduce AgentLance, a repeated labor market in which agents bid on tasks using their private costs and self-maintained strategy notes, an allocator selects winners from bids and public reputation records, and a VCG-style payment rule rewards cost-aware bidding. Complex tasks are handled by hierarchical delegation: winning agents can decompose work and subcontract it through the same mechanism. Across mathematical reasoning, code generation, knowledge-intensive QA, and agentic tasks, AgentLance matches agents to their specializations, shifts work toward cheaper agents as cost sensitivity rises, and consistently outperforms single-model, centralized-orchestration, and market baselines. Diagnosing market failures, including inaccurate cost self-estimation and sub-optimal bidding, then correcting them in controlled experiments yields further gains, charting a path toward more efficient agent economies.

Allocating limited computation among concurrent learning tasks is difficult when each task must reach a target loss before a deadline but its required training effort is unknown. Existing approaches combine online loss prediction with adaptive resource allocation, yet commonly treat computation as continuously divisible throughput. We instead study a practical setting in which tasks arrive over time and computation is provided by discrete nodes. This setting introduces both uncertain demand and constrained sequential decisions. We propose MARA, which predicts future loss trajectories with conditional flow matching and coordinates compute nodes through a cooperative multi-agent autoregressive policy. A potential-based progress reward supplies intermediate training feedback while preserving the undiscounted task-completion objective. Across in-distribution, reinforcement-learning, and vision workloads, flow matching reduces remaining-resource prediction error relative to weighted least squares. At the scheduler's training load, MARA completes 63.46% of tasks on average, 8.54 percentage points above strong baseline Learning with Adaptive Resource Allocation (LARA), and remains ahead under unseen heavier workloads.

This paper evaluates the Metabolic Multi-Agent Optimizer (MMAO) under a stricter empirical protocol rather than reintroducing the framework itself. The study asks whether MMAO's closed-loop resource-allocation principle remains credible under broader, more standard, and more explicitly budget-controlled continuous and discrete benchmarks. The main completed matrix covers eight CEC2017 functions at 10D and 30D with 20 seeds each, and five TSPLIB instances with 20 seeds each, together with stronger reproducible baselines including PSO-lite, ES-lite, and an iterated-greedy 2-opt route baseline. We further add trajectory-level diagnostics for communal budget, success rate, role evolution, and population turnover, plus an auxiliary OR-Library multiple-knapsack slice to extend the discrete evidence beyond routing. Under this protocol, MMAO clearly outperforms the external baseline set on the continuous side and on the TSPLIB side, while the ablation variants remain much closer to the full method than the external baselines are. We therefore position MMAO as a benchmark-backed cross-domain adaptive framework whose most clearly validated value is endogenous resource redistribution under evidence pressure, while also noting that the strongest remaining gap is not basic workability but sharper mechanism isolation and broader competition-grade comparison.

Many allocation problems are intrinsically multidimensional, since an item may contribute differently to several criteria, and optimizing a single aggregate objective can hide severe losses in other dimensions. We study how much efficiency can be guaranteed simultaneously when indivisible items have multiple attributes. To this end, we introduce the multidimensional efficient allocation (MDEA) model, where each agent has an additive valuation in each dimension, and investigate simultaneous efficiency under utilitarian social welfare (USW) and egalitarian social welfare (ESW). Our results reveal a sharp worst-case frontier. For exact efficiency, maximizing the number of dimensions attaining the USW optimum admits a $c/\ell$-approximation for every fixed constant $c$, and this dependence on the number $\ell$ of dimensions is essentially unavoidable; for ESW, even deciding whether two dimensions can be optimized simultaneously is NP-hard with binary valuations. For approximate simultaneous efficiency in every dimension, we identify a tight threshold of order $1/\ell$, showing that such guarantees always exist for both USW and ESW, while any asymptotically better dependence on $\ell$ is impossible, even for binary valuations. Finally, we introduce three natural multidimensional Pareto notions and characterize both their relationships and their computational complexity.

This paper studies heterogeneous multi-team collaboration through dynamic robot allocation, where the robots themselves are treated as transferable resources. Leveraging Hamilton's rule from ecology as an altruistic decision-making mechanism, we propose a multi-team collaborative resource allocation framework with heterogeneous capabilities, transfer costs, and capability-dependent contributions. The resulting general heterogeneous resource assignment problem is combinatorial and is shown to be NP-hard. To address scalability, we develop a graph neural network policy under centralized training and decentralized execution that approximates the altruistic allocations based on Hamilton's rule. The model operates over the team interaction graph and predicts robot-level transfer decisions and subsequent robot-to-team assignments. The proposed approach is evaluated in a fire-fighting scenario against exact optimization and multi-step simulations, quantifying allocation quality, decision computation, and fire suppression. Five paired physical testbed trials with 15 robots compare learned reallocation with fixed team membership; the GNN reaches the modeled fire stopping threshold in all five trials, compared with two for static allocation.

As autonomous agents increasingly execute end-to-end tasks under fixed monetary budgets, the pressing open question shifts from whether the budget is respected, to how to spend it effectively. Existing budget-aware methods typically control reasoning step-by-step within a single agent, or learn resource allocation policies via RL. None address how to split a budget across the composing phases of a multi-agent pipeline at inference time. We propose ZEBRA, a zero-shot framework that reduces multi-phase budget allocation to a continuous nonlinear knapsack problem: an LLM controller estimates per-phase utility curves, and a water-filling search on the Lagrange multiplier returns the per-phase split. Additive and multiplicative aggregations are unified under the same solver. On a $150$-task APPS coding benchmark, both ZEBRA variants outperform LLM-direct (budget allocation directly by an LLM) on every aggregate metric. At a budget of $α= 0.5$ of the unconstrained spend, ZEBRA recovers $94.4\%$ of unconstrained quality, versus $88.1\%$ for LLM-direct. The advantage is statistically significant and transfers beyond coding: on a $3$-phase HotpotQA pipeline, ZEBRA beats LLM-direct by $14.3$pp, with allocations empirically robust to curve-estimation noise. On HotpotQA, ZEBRA arrives at a different budget split (near-balanced) compared to the APPS one (skewed towards a refinement phase), showing adaptation to the pipeline structure. More broadly, we show that lightweight algorithmic guidance at inference time can improve the economic behavior of autonomous multi-agent systems.

Many multi-agent games and simulated environments involve several independent, often learning, agents repeatedly competing for a shared resource. Conventional fairness measures assess whether resources are shared equally overall, but cannot distinguish orderly turn-taking from irregular access patterns that produce long, unpredictable waiting times despite similar cumulative outcomes. We introduce Rotational Periodicity, a family of computationally efficient metrics combining two complementary measurements, the regularity of waiting times between successful accesses and the balance of access frequencies across agents. We evaluate them against a more detailed family of alternation metrics in a repeated threshold-congestion game, the Honey-Jar Game, in which two to ten reinforcement-learning agents compete for exclusive access to a shared high-value resource. Our experiments show that independently trained Q-learning agents often coordinate substantially worse than random-policy agents, even though conventional fairness metrics consistently report favourable outcomes. Every member of the family closely reproduces the rankings of the more computationally expensive alternation metrics, while computing six to twenty times faster as the number of agents grows. A direct timing study, which separates the two quantities that drive that cost, measures the advantage growing in proportion to the number of agents out to two thousand agents. These findings show that evaluating multi-agent learning systems requires temporally aware measures of coordination, not only aggregate outcomes, and that efficient proxies make this practical for larger multi-a

Coordinating multi-agent systems over spatially distributed areas requires solving a complex hierarchical problem: first distributing areas among agents (allocation) and subsequently determining the optimal visitation order (routing). Existing methods typically decouple these stages ignoring inter-stage dependencies or rely on decentralized heuristics that lack global context. In this work, we propose a centralized, fully end-to-end auto-regressive framework that jointly generates allocation decisions and routing sequences. The core contribution of our approach is a multi-stage decoding mechanism that unifies high-level allocation and low-level routing in a single autoregressive pass while maintaining a centralized global state. This enables the model to implicitly balance workload distribution with routing efficiency, avoiding local optima common in decentralized methods. Extensive experiments demonstrate that our method significantly outperforms diverse baselines, achieving up to a 20% improvement in solution quality over industrial solvers such as Google OR-Tools, IBM CPLEX, and LKH-3, while reducing computation time from hours to seconds.

In multi-agent systems, should limited resources be concentrated into a few capable agents or distributed among many simpler ones? This work formulates the split over $n$ resource sharing problem where a group of $n$ agents equally shares a common resource (e.g., monetary budget, computational resources, physical size). We present a case study in multi-agent coverage where the area of the disk-shaped footprint of agents scales as $1/n$. A formal analysis reveals that the initial coverage rate grows with $n$. However, if the speed of agents decreases proportionally with their radii, groups of all sizes perform equally well, whereas if it decreases proportionally with their footprints, a single agent performs best. We also present computer simulations in which resource splitting increases the failure rates of individual agents. The models and findings help identify optimal distributiveness levels and inform the design of multi-agent systems under resource constraints.

We study dynamic multi-robot task allocation under uncertain task completion, time-window constraints, and incomplete information. Tasks arrive online over a finite horizon and must be completed within specified deadlines, while agents operate from distributed hubs with limited sensing and communication. We model incomplete information through hub-based sensing regions that determine task visibility and a communication graph that governs inter-hub information exchange. Using this framework, we propose Iterative Best Response (IBR), a decentralized policy in which each agent selects the task that maximizes its marginal contribution to the locally observed welfare. We compare IBR against three baselines: Earliest Due Date first (EDD), Hungarian algorithm, and Stochastic Conflict-Based Allocation (SCoBA), on a city-scale package-delivery domain with up to 100 drones and varying task arrival scenarios. Under full and sparse communication, IBR achieves competitive task-completion performance with lower computation time.

In large-scale AI systems, allocating scarce resources such as GPU compute time and bandwidth among multiple agents is a critical challenge. Conventional policies focus on efficiency metrics, potentially leading to dominance concentration that undermines system diversity and stability. We propose Computable Fair Division (CFD), a framework that reinterprets the Boltzmann-Softmax function not as a selection tool but as a probabilistic resource allocation mechanism, redefining the inverse temperature parameter $β$ as a computable control variable governing the efficiency-fairness balance. Static analysis reveals a Pareto frontier with a near-optimal Stability Corridor where total loss remains approximately constant across policy weights. In the dynamic setting, AHC++ (Adaptive Hard-Cap Controller++) updates $β$ in real time using the error between observed dominance and a policy-specified target as feedback. Simulations show that AHC++ suppresses extreme dominance concentration under exogenous shocks while tracking fairness targets without substantial throughput degradation. Scalability analysis confirms that a 100x increase in agents yields only approximately 5.5x increase in execution time. Code: https://github.com/entrofy-ai/computable-fairness

Allocation of dynamically-arriving (i.e., online) divisible resources among a set of offline agents is a fundamental problem, with applications to online marketplaces, scheduling, portfolio selection, signal processing, and many other areas. The water-filling algorithm, which allocates an incoming resource to maximize the minimum load of compatible agents, is ubiquitous in many of these applications whenever the underlying objectives prefer more balanced solutions; however, the analysis and guarantees differ across settings. We provide a justification for the widespread use of water-filling by showing that it is a universally minimax optimal policy in a strong sense. Formally, our main result implies that water-filling is minimax optimal for a large class of objectives -- including both Schur-concave maximization and Schur-convex minimization -- under $α$-regret and competitive ratio measures. This optimality holds for every fixed tuple of agents and resource counts. Remarkably, water-filling achieves these guarantees as a myopic policy, remaining entirely agnostic to the objective function, agent count, and resource availability. Our techniques notably depart from the popular primal-dual analysis of online algorithms, and instead develop a novel way to apply the theory of majorization in online settings to achieve universality guarantees.

This paper presents a hierarchical two-stage framework for multi-robot task allocation and trajectory optimization in asymmetric task spaces: (1) a sequential auction allocates tasks using closed-form bid functions, and (2) each robot independently solves an optimal control problem for energy-minimal trajectories with a physics-based battery model, followed by a collision avoidance refinement step using pairwise proximity penalties. Event-triggered warm-start rescheduling with bounded trigger frequency handles robot faults, priority arrivals, and energy deviations. Across 505 scenarios with 2-20 robots and up to 100 tasks on three factory layouts, both energy- and distance-based auction variants achieve 11.8% average energy savings over nearest-task allocation, with rescheduling latency under 10 ms. The central finding is that bid-metric performance is regime-dependent: in uniform workspaces, distance bids outperform energy bids by 3.5% (p < 0.05, Wilcoxon) because a 15.7% closed-form approximation error degrades bid ranking accuracy to 87%; however, when workspace friction heterogeneity is sufficient (r < 0.85 energy-distance correlation), a zone-aware energy bid outperforms distance bids by 2-2.4%. These results provide practitioner guidance: use distance bids in near-uniform terrain and energy-aware bids when friction variation is significant.

When resources are scarce, will a population of AI agents coordinate in harmony, or descend into tribal chaos? Diverse decision-making AI from different developers is entering everyday devices -- from phones and medical devices to battlefield drones and cars -- and these AI agents typically compete for finite shared resources such as charging slots, relay bandwidth, and traffic priority. Yet their collective dynamics and hence risks to users and society are poorly understood. Here we study AI-agent populations as the first system of real agents in which four key variables governing collective behaviour can be independently toggled: nature (innate LLM diversity), nurture (individual reinforcement learning), culture (emergent tribe formation), and resource scarcity. We show empirically and mathematically that when resources are scarce, AI model diversity and reinforcement learning increase dangerous system overload, though tribe formation lessens this risk. Meanwhile, some individuals profit handsomely. When resources are abundant, the same ingredients drive overload to near zero, though tribe formation makes the overload slightly worse. The crossover is arithmetical: it is where opposing tribes that form spontaneously first fit inside the available capacity. More sophisticated AI-agent populations are not better: whether their sophistication helps or harms depends entirely on a single number -- the capacity-to-population ratio -- that is knowable before any AI-agent ships.

Near-future infrastructure systems may be controlled by autonomous AI agents that repeatedly request access to limited resources such as energy, bandwidth, or computing power. We study a simplified version of this setting using a framework where N AI-agents independently decide at each round whether to request one unit from a system with fixed capacity C. An AI version of "Lord of the Flies" arises in which controlling tribes emerge with their own collective character and identity. The LLM agents do not reduce overload or improve resource use, and often perform worse than if they were flipping coins to make decisions. Three main tribal types emerge: Aggressive (27.3%), Conservative (24.7%), and Opportunistic (48.1%). The more capable AI-agents actually increase the rate of systemic failure. Overall, our findings show that smarter AI-agents can behave dumber as a result of forming tribes.

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.

Most multi-robot task allocation methods rely on communication to resolve conflicts and reach consistent assignments. In environments with limited bandwidth, degraded infrastructure, or adversarial interference, existing approaches degrade sharply. We introduce a learning-based framework that achieves high-quality task allocation without any robot-to-robot communication. The key idea is that robots coordinate implicitly by predicting teammates' bids: if each robot can anticipate competition for a task, it can adjust its choices accordingly. Our method predicts bid distributions to correct systematic errors in analytical mean-field approximations. While analytical predictions assume idealized conditions (uniform distributions, known bid functions), our learned approach adapts to task clustering and spatial heterogeneity. Inspired by Smart Predict-then-Optimize (SPO), we train predictors end-to-end to minimize Task Allocation Regret rather than prediction error. To scale to large swarms, we develop a mean-field approximation where each robot predicts the distribution of competing bids rather than individual bids, reducing complexity from $O(NT)$ to $O(T)$. We call our approach FORMICA: Field-Oriented Regret-Minimizing Implicit Coordination Algorithm. Experiments show FORMICA substantially outperforms a natural analytical baseline. In scenarios with 16 robots and 64 tasks, our approach improves system reward by 17% and approaches the optimal MILP solution. When deployed on larger scenarios (256 robots, 4096 tasks), the same model improves performance by 7%, demonstrating strong generalization. Training requires only 21 seconds on a laptop, enabling rapid adaptation to new environments.

Efficient resource allocation in multi-agent systems requires autonomous agents to coordinate their decisions while balancing system-wide objectives with individual costs. This becomes increasingly challenging over long time horizons, where decisions that improve the current allocation may compromise future resource allocation, while decentralized agents have limited observations of the overall system. Multi-agent reinforcement learning (MARL) can learn such long-term dependencies via local observations, but directly applying it to large-scale coordination leads to rapidly growing decision spaces and inefficient training. To this end, we propose Hierarchical Reinforcement and Collective Learning (HRCL), a hierarchical framework that uses MARL to guide, rather than replace, decentralized multi-agent coordination. At the high level, MARL learns strategies that restrict the alternatives considered during coordination and guide agents in balancing system-wide and individual objectives. At the low level, agents perform efficient decentralized coordination under this strategic guidance. This separation reduces the learning space and allows short-term coordination trade-offs to be evaluated according to their long-term effects. Experiments on a synthetic benchmark show that HRCL converges substantially faster than standalone MARL and reduces system-wide and individual costs by 35.53% and 27.05%, respectively. Evaluations on energy self-management and drone swarm sensing further show improved resource allocation, power-peak regulation, and sensing efficiency. These results show that learning strategic guidance for an existing coordination process can retain scalable decentralized coordination without letting short-term decisions compromise future resource allocation.

We study the dynamic allocation of indivisible resources to strategic agents under long-term constraints, where the planner aims to maximize social welfare, satisfy multiple constraints, and elicit near-truthful reports. We find standard primal-dual methods fragile in this setting: agents easily manipulate their reports to distort dual variables, sacrificing social efficiency for individual utility. To address this, we propose the Incentive-Aware Primal-Dual (IAPD) framework. On the primal side, we integrate three components to suppress manipulation: a VCG-based payment neutralizes immediate misreporting benefits, while epoch-based lazy updates and random exploration together ensure potential future gains are outweighed by immediate penalties. On the dual side, to overcome a learning barrier due to lazy updates -- which we call the "price of incentives" -- we design a novel optimistic online learning algorithm, O-FTRL-FP. It utilizes a fixed-point oracle to resolve the circular dependency between optimistic dual variables and the resulting allocations. Ultimately, our mechanism attains $\tilde{\mathcal O}(\sqrt T)$ social welfare regret, satisfies all long-term constraints, and induces a near-truthful equilibrium. It also smoothly generalizes to multi-unit multi-demand allocation problems. Notably, this $\tilde{\mathcal O}(\sqrt T)$ regret near-matches the non-strategic $Ω(\sqrt T)$ lower bound, demonstrating that incentive-awareness can be accommodated at nearly no cost.