A marginal-value activation rule and greedy router are proposed, a Shapley-submodularity sandwich bound linking the error of marginal-value routing to a per-agent diminishing-returns quantity is proved, and performance is robust to activation cost and redundancy weight but falls to under strong violations of submodularity or noisy value estimates.
Abstract
Modern agentic AI systems combine multiple large language model agents with heterogeneous skills, yet most architectures either fix communication in advance or allow full broadcast. Both can be inefficient because token cost, latency, redundancy, and error propagation increase with the number of active agents and communication links. We model agent selection and communication as a cooperative game with task-conditioned net utility $U(C\mid x)=V(C\mid x)-\sum_{i\in C}c_i$, separating coalition-level costs from agent activation costs. We propose a marginal-value activation rule and greedy router, extend the model to optimize communication edges with per-edge costs, and use estimated Shapley values to predict which agents are worth contacting before and during execution. We connect the problem to submodular maximization and prove two limited guarantees: a curvature-refined bound for a monotone, cardinality-constrained special case, and a tight $1/2$-approximation, with a correction for signed objectives, for an unconstrained non-monotone case via double greedy. Neither guarantee applies directly to the main router, which remains a heuristic. We also prove a Shapley-submodularity sandwich bound linking the error of marginal-value routing to a per-agent diminishing-returns quantity. In synthetic experiments, greedy routing achieves $99.5%$ of brute-force-optimal utility while activating $1.96$ of $8$ agents on average, compared with $38.8%$ for full broadcast. Performance is robust to activation cost and redundancy weight but falls to $66%$ under strong violations of submodularity or noisy value estimates. We distinguish the framework from Shapley pricing, hedonic coalition formation, and communication-graph pruning, and propose evaluation on real multi-agent LLM benchmarks.
Large language model multi-agent systems (LLM-MAS) rely on inter-agent communication to solve complex reasoning tasks, yet rigorous guarantees relating consensus performance to computational resources remain limited. Here, we present a novel way to characterize collective belief dynamics as a discrete-time switched system in which communication topologies have distinct consensus-contraction rates and token costs. By augmenting the belief dynamics with the remaining computational budget, we define a consensus safe set that jointly captures agreement and resource feasibility. We derive explicit bounds on consensus time and token expenditure and construct a consensus-budget certificate region guaranteeing finite-time convergence without resource exhaustion. We further establish conditions under which adaptive topology switching achieves a trade-off between convergence speed and communication cost relative to fixed-topology strategies. Numerical experiments and live LLM-MAS deployments show the predicted consensus-cost trade-offs, demonstrating how control-theoretic certificates can enable resource-aware coordination in AI systems.
James A. Flagg, Esteban A. Hernández-Vargas· 0 citations
We introduce and study an online variant of the multi-agent contract model. In our model, agents arrive one-by-one and are active with a certain probability. Upon arrival of agent $i$, the principal offers a linear contract $\alpha_i$, specifying the fraction of the principal's reward transferred to agent $i$. Agents can either exert effort or not, incurring a cost if they do. The set of agents that exert effort determines the principal's expected reward through a reward function $f$. After all agents have arrived, the agents form a (pure) Nash equilibrium. As our main result we design an $O(1)$-competitive policy for submodular rewards, compared to the offline optimum. We also show that this result is tight in two ways. First, if we require that agents make decisions on the spot, then for submodular rewards any policy is $\Omega((\log n)/(\log \log n)^2)$-competitive. Second, for the broader class of XOS (a.k.a., fractionally subadditive) rewards, any online policy is $\Omega((\log \log n)/(\log \log \log n))$-competitive. The latter result reveals a surprising separation between submodular and XOS rewards: unlike related settings such as offline contract design and prophet inequalities, where constant-factor guarantees for submodular rewards extend to XOS rewards, the online contract setting separates the two classes.
Paul Dütting, Michal Feldman, Yoav Gal-Tzur et al.· 0 citations
A neural scheduling framework for distributed multi-robot task allocation, consisting of a multi-decoder graph attention model (MDGAM) policy model and a critic-free group relative multi-agent policy gradient (GRMAPG) training algorithm, which improves task-completion performance over existing heuristic and learning-based methods.
The El Farol Bar game is a classical model of coordination under uncertainty that traditionally treats the venue as a passive constraint. In this work, we reconceptualize the problem by modeling the bar as a strategic player endowed with AI-driven learning capabilities. We extend the original framework in two principal directions: first, by introducing partial observability, whereby agents observe only subsets of past attendees; and second, by transforming the bar from a passive capacity threshold into an active mechanism designer that adjusts pricing policies to balance revenue, utilization, and sustainability constraints. Agents employ AI-based learning to form beliefs and adapt attendance strategies under incomplete information, while the bar applies policy learning to optimize dynamic pricing. The resulting two-sided learning system frames coordination as a co-evolutionary process between boundedly rational agents and an adaptive institution, offering insights into congestion management, resource allocation, and mechanism design in complex adaptive systems.
Iosif Polenakis, Kalliopi Kastampolidou, T. Andronikos· 0 citations
The collaboration tax is formulated as the team-decentralisation loss of a two-player cooperative game with private information, with two propositions characterising its sign and its equivalence to a max-superadditivity violation.
Wei-Xiang Sun, Zehong Wang, Hong Huang et al.· 0 citations
Multi-agent systems powered by large language models (LLMs) have demonstrated potential for collaborative problem-solving, yet increasing the number of agents often introduces redundant reasoning and communication overhead, sometimes degrading performance. We propose AgentDropout, a dynamic strategy inspired by dropout regularization in neural networks, which selectively deactivates low-contribution agents during multi-agent collaboration. At each round of discussion, AgentDropout computes a semantic novelty score for every agent by measuring the divergence of its output relative to the current group consensus. Agents whose novelty score falls below an adaptive threshold are temporarily deactivated, reducing token consumption without sacrificing viewpoint diversity. We evaluate AgentDropout on mathematical reasoning (GSM8K), commonsense reasoning (StrategyQA), and collaborative code generation (HumanEval) tasks. Across three independent runs, AgentDropout achieves accuracy comparable to or modestly above fixed 5-agent debate while reducing total token consumption by 38.0–43.5% and debate rounds by 20.5% on average. Pareto analysis reveals a promising efficiency–quality trade-off, suggesting that dynamic agent deactivation may be useful for deploying multi-agent LLM systems under computational budget constraints.
Zhengxi Xiao, Qi Guo, Yuyue Wang et al.· 2026 8th International Confe...· 1 citation
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