We study information design in multi-agent systems (MAS) with binary actions and strategic complementarities, where an external designer influences behavior only through signals. Agents play the smallest-equilibrium of the induced Bayesian game, reflecting conservative, coordination-averse behavior typical in distributed systems. We show that when utilities admit a convex potential and welfare is convex, the robustly implementable optimum has a remarkably simple form: perfect coordination at each state: either everyone acts or no one does. We provide a constructive threshold rule: compute a one-dimensional score for each state, sort states, and pick a single threshold (with a knife-edge lottery for at most one state). This rule is an explicit optimal vertex of a linear program (LP) characterized by feasibility and sequential obedience constraints. Empirically, in both vaccination and technology-adoption domains, our constructive policy matches LP optima, scales as O(∣Θ∣log∣Θ∣), and avoids the inflated welfare predicted by obedience-only designs that assume the designer can dictate the (best) equilibrium. The result is a general, scalable recipe for robust coordination in MAS with complementarities.
Table 1. Domain adapter: mapping model primitives to MAS applications.
∑θ:θ≻θ⋆μ(θ)Fθ(N)≤0<∑θ:θ⪰θ⋆μ(θ)Fθ(N).
Algorithm 1 Constructing the perfectly coordinated optimal sequential policy πseq⋆
Figure 1. Robust information design under smallest-equilibrium play. Sequential obedience restricts implementability relative to classical persuasion. Under convex potential and welfare, the optimum is an extreme point, yielding a threshold policy computable in O(∣Θ∣log∣Θ∣) time.
Figure 2. Technology adoption with nearly continuous states. Scores S(θ) induce a near-continuous threshold. The robust policy πseq⋆ adopts only where coordination is sustainable, while BCE policy (orange) recommends broader adoption but collapses to no adoption under smallest-equilibrium play.
Figure 3. Welfare under Robust, BCE-Optimistic (classical obedience only), and BCE-Realized (same BCE policy evaluated under smallest-equilibrium). For medium costs, the BCE-Optimistic curve sits above Robust, but BCE-Realized drops to zero , revealing that the optimistic gains are not achievable under conservative play.
We study the consequences of information asymmetries and misaligned incentives in settings with multiple independent agents. We model an interaction between a Sender, who holds vital private information but cannot act, and a Receiver, who must make decisions but is dependent on the Sender's information. We find that the Sender learns an optimal communication strategy that the Receiver reliably acts on. Importantly, this strategy is highly sensitive to the degree of conflict in the agents' rewards and the amount of environmental information the Receiver can already observe. We introduce a mechanism allowing the agents to form linear contracts, where a price is established for the information. We demonstrate that the Sender learns to use these payment structures to improve its rewards, though this comes at a cost of "fairness" between agents as the Sender is able to extract much of the Receiver's surplus. This raises questions about fairness, contract design, and learning in the context of multi-agent systems.
Multi-agent systems (MAS) were expected to overcome the limitation of single-agent systems (SAS) through collaboration. However, under typicality conditions on the task's constraint graph and bounded inter-agent communication, we prove that the success probability of a MAS is closely tied to the connectivity of task constraints, where each agent has limited information-processing capacity. Specifically, the success probability decays exponentially with an information bottleneck that emerges from partitioning the task's constraint graph among agents. We define this quantity as the minimum cut costCmin of the potential constraint graph of each task. This information-theoretic bound applies to both open systems with external feedback and closed systems without. We validate our theory on both synthetic experiments and real-world empirical data from SWE-bench submissions. From our framework, effective MAS design should incorporate task-inherent constraints alongside engineering optimization, and when \Cmin is high, practitioners should restructure tasks rather than simply scaling agents or communication.
Shi Pan, Ming Luo
University College London London, UK · University of Bristol Bristol, UK
We study information design in games where players choose from a continuum of actions and have continuously differentiable payoffs. We show that an information structure is optimal when the equilibrium it induces can also be implemented in a principal-agent contracting problem. Building on this result, we characterize optimal information structures in symmetric linear-quadratic games. With common values, targeted disclosure is robustly optimal across all priors. With interdependent and normally distributed values, linear disclosure is uniquely optimal. We illustrate our findings with applications in venture capital, Bayesian polarization, and price competition.
Alex Smolin, Takuro Yamashita
Toulouse School of Economics, University of Toulouse Capitole and CEPR · Osaka University