Robust Information Design for Multi-Agent Systems with Complementarities: Smallest-Equilibrium Threshold Policies

Farzaneh Farhadi; Maria Chli

cs.GTFeb 26, 2026

Robust Information Design for Multi-Agent Systems with Complementarities: Smallest-Equilibrium Threshold Policies

Authors: Farzaneh Farhadi, Maria Chli

Organizations: Aston University, Birmingham, United Kingdom

Abstract

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.

Figures & tables

Domain	States $\theta$	Cost $c$	Complementarity $\lambda_{\theta}$	Objective $V$
Vaccination	Disease prevalence; vaccine effectiveness	Health risks; monetary/time costs	Herd immunity (coverage $\uparrow$ )	Social welfare from reduced infection
Tax / Fare Compliance	Enforcement level (audit rate, penalties)	Payment of taxes or fares	Compliance spillovers (norms/deterrence)	Revenue net of enforcement
Public Good Provision	Project productivity/value	Individual contribution cost (effort, money)	Thresholds / increasing returns	Surplus from funded project
Technology Adoption	Market demand; regulatory push; ecosystem readiness	Migration, retraining, integration costs	Interoperability / network effects	Industry efficiency / consumer surplus

Table 1. Domain adapter: mapping model primitives to MAS applications.

\sum_{\theta:\,\theta\succ\theta^{\star}}\mu(\theta)F_{\theta}(N)\;\leq\;0\;<\;\sum_{\theta:\,\theta\succeq\theta^{\star}}\mu(\theta)F_{\theta}(N).

Algorithm 1 Constructing the perfectly coordinated optimal sequential policy

\pi^{\mathrm{seq}\,\star}

Panel of Figure 1 — 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 $\mathcal{O}(|\Theta|\log|\Theta|)$ time.

Figure 2. Technology adoption with nearly continuous states. Scores $S(\theta)$ induce a near-continuous threshold. The robust policy $\pi^{\mathrm{seq}\,\star}$ 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.

Information Design

Information design studies how to choose what signals people or algorithms receive to shape decisions, incentives, and outcomes.

See all 15 papers

Information and Contract Design for Repeated Interactions between Agents with Misaligned Incentives
May 11, 2026Nanda Kishore Sreenivas, Kate LarsonImperfect-Information Games Multi-Agent Communication
University of Waterloo
How Task Structure Limits Multi-Agent Success: An Information-Theoretic Analysis
Jun 11, 2026Shi Pan, Ming LuoMulti-Agent Collaboration Multi-Agent Systems
University College London London, UK · University of Bristol Bristol, UK
Information Design in Smooth Games
Sep 14, 2026Alex Smolin, Takuro YamashitaGame Theory Information Design
Toulouse School of Economics, University of Toulouse Capitole and CEPR · Osaka University

May 11, 2026J/K move · Enter open · S save

Information and Contract Design for Repeated Interactions between Agents with Misaligned Incentives

Nanda Kishore Sreenivas, Kate Larson

University of Waterloo

Imperfect-Information Games Multi-Agent Communication Multi-Agent Reinforcement Learning

Open paper AskPDF arXiv

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.

Abstract

Information Design

Explore similar work

Information and Contract Design for Repeated Interactions between Agents with Misaligned Incentives

How Task Structure Limits Multi-Agent Success: An Information-Theoretic Analysis

Information Design in Smooth Games