Value of Communication

• Value of communication is a measure quantifying the marginal contribution of information exchange in reducing prediction cost and enhancing control performance.
• It employs methodologies such as VoI, topology optimization, and information-theoretic metrics to balance system performance with resource constraints.
• Empirical studies in CPS, MARL, vehicular networks, and quantum channels reveal significant gains in efficiency and strategic resource allocation.

The value of communication is a principled, quantifiable measure of the marginal contribution that exchanged information makes to a collective or individual objective, subject to explicit resource constraints. Precise definitions depend on context, encompassing networked control systems, multi-agent coordination, economic protocols, semantic communications, and quantum channels. Core methodologies center on optimization over communication topologies, marginal utility analysis, information-theoretic metrics, and trade-off frontiers.

1. Conceptual Foundations and Formal Definitions

In cyber-physical systems (CPS), the value of communication is the marginal reduction in prediction or control cost attributable to activating a specific communication link between agents. Consider an LTI CPS of $M$ agents, each with local dynamics and outputs. The cyber-layer topology, encoded as a binary matrix $\delta_{ij}$ indicating whether agent $j$ shares information with agent $i$, is traditionally fixed but can instead be treated as a design variable. Formally, the value of link $j \rightarrow i$ is quantified via the decrease in least-squares prediction cost $J_{\mathrm{pred}}$ when $\delta_{ij}$ changes from $0$ to $1$, normalized by the per-link cost $c_{ij}$ (Nestor et al., 12 Sep 2024):

$$\text{Value}_{j \rightarrow i} = \frac{\Delta J_{\mathrm{pred}}}{c_{ij}}.$$

In multi-agent and semantic communication, the value of communication is often grounded in a value-of-information (VoI) metric, measuring the task-relevant gain from a message or observation. In VIL2C (Zhang et al., 24 Nov 2025), VoI is expressed as the ratio of semantic influence (KL divergence in the action probability space) to communication latency:

$$\mathrm{VoI}_{i,j} = \frac{D_{\mathrm{KL}}(P(a_j|o_j, m_i) \parallel P(a_j|o_j))}{\tau_{i,j}}.$$

In goal-oriented semantic architectures, communication value is embedded within context/task-aware tensor metrics (GoT), permitting the quantification and unification of AoI, VoI, UoI, AoII as cost measures directly tied to downstream action utility (Li et al., 2023).

In quantum information, the communication value (cv) of a channel $\Phi$ is the supremum of the optimal success probability for transmitting classical messages and is expressible in terms of conditional min-entropy over the cone of separable operators (Chitambar et al., 2021):

$$\mathrm{cv}(\Phi) = \max_{\{\rho_x\}, \{M_x\}} \sum_x \mathrm{Tr}[M_x \, \Phi(\rho_x)].$$

It controls one-shot simulation cost and channel capacity.

2. Optimization Frameworks and Trade-off Analysis

Topology optimization is essential to realizing the value of communication in distributed CPS. When the full model is unavailable, data-driven methods identify optimal communication graphs by solving mixed-integer second-order conic programs (MISOCPs) that jointly minimize prediction error and communication cost (Nestor et al., 12 Sep 2024):

$$\min_{K, \delta} \sum_{i,j} c_{ij} \, \delta_{ij} + \| Y^F - K [U^P; Y^P; U^F] \|_F^2 \ \text{subject to} \ \delta_{ij} \in \{0,1\}, \ \text{link constraints}.$$

Pareto frontiers describe the optimal trade-offs between estimation or control quality and communication budget. The slope of the Pareto curve, $\eta(F)$, gives the absolute value of communication, revealing the marginal utility per unit cost (Luo et al., 1 Dec 2025).

In MARL systems, resource allocation is optimized to maximize VoI under budget constraints (bandwidth, power), as in:

$$\max_{\{B_{i,j},P_{i,j}\}} \sum_j \mathrm{VoI}_{i,j}(B_{i,j},P_{i,j}), \quad \sum_j B_{i,j} \leq B_{\mathrm{budget}}, \ \sum_j P_{i,j} \leq P_{\mathrm{budget}}.$$

The KKT conditions guarantee proportional allocation to high-importance links (Zhang et al., 24 Nov 2025).

Auction-based mechanisms such as DALA for LLM agents formalize communication as a knapsack problem:

$$\max_{W \subseteq \mathcal{A}} \sum_{i \in W} b_i, \quad \text{s.t.} \sum_{i \in W} L(m_i) \leq B_{\max}$$

where $b_i$ is a bid representing value-per-token, directly enforcing resource rationality (Fan et al., 17 Nov 2025).

3. Information-Theoretic Quantification and Algorithms

Communication value metrics are rooted in information theory. In nearly decomposable value functions (Wang et al., 2019), the utility of agent-to-agent message is formalized as the mutual information between actions and communication bits, while entropy regularization drives message succinctness:

$$J_c(\theta_c) = \sum_{j \neq i} \left\{ I(A_j; M_{ij} | T_j, M_{(i)j}) - \beta H(M_{ij}) \right\}.$$

Agents transmit only when their message offers significant reduction in uncertainty, achieving efficient coordination with minimal communication.

In ad hoc teamwork, the expected divergence point (EDP) quantifies how long agents can rely solely on observation before communication becomes optimal (Macke et al., 2021):

$$\mathrm{edp}(s, \pi_1 | \pi_2) = \mathbb{E}_{Tr_2 \sim \pi_2} [\, \mathrm{dp}(\pi_1 | Tr_2) \,|\, Tr_2 \text{ starts in } s \,]$$

Direct computation enables planning algorithms to trigger queries only when their expected benefit exceeds cost.

Semantic communications and 6G systems use tensorized representations—GoT—to capture the dynamic and task-sensitive value of communication, facilitating cross-layer optimization. For V2X safety, KL-based VoI measures dictate whether and when to forward safety-critical data, ensuring only high-value communications are prioritized (Abedi et al., 28 Sep 2025).

4. Empirical Validation and Systemic Impacts

Empirical studies across distributed control (Nestor et al., 12 Sep 2024), MARL (Zhang et al., 24 Nov 2025), vehicular networks (Giordani et al., 2019), and LLM agents (Fan et al., 17 Nov 2025) demonstrate several common findings:

• Selecting communication links by marginal utility yields up to 25% reductions in closed-loop MPC cost versus random topology.
• Prioritizing communication by VoI (in latency, semantics, or token cost) sharply increases application performance and efficiency: e.g., VIL2C approaches latency-free performance across MARL tasks, with graceful degradation under resource constraints.
• In vehicular networks, VoI-aware scheduling maintains 99.9% reliability for safety-critical packets even under high congestion, with 30% mean AoI reduction for prioritized updates.
• Auction-based communication among LLM agents (DALA) achieves state-of-the-art reasoning accuracy with 90+% reduction in token usage, and emergent resource-rational silence.
• In mixed-autonomy traffic, VoI-driven ISAC frameworks achieve 33%+ reduction in collision risk and 66% improvement in time-to-collision metrics by transmitting only predictive data (Abedi et al., 28 Sep 2025).

These results confirm that quantifying, ranking, and enforcing the value of communication transforms bottlenecks into strategic optimizations.

5. Structural and Strategic Implications

The structural value of communication extends to economic, social, and networked environments. In organizations, the unique value accrues when communication protocols eliminate costly misreporting through adversarial public advocacy, ensuring perfect information aggregation at zero persuasion cost—achieving robust and efficient equilibria immune to collusion (Vaccari, 2022).

In sender-receiver games with mediation, optimal protocols are geometrically characterized by the feasible distribution over posteriors that maximizes the sender’s expected utility under zero-covariance constraints. Mediation strictly improves value only when local improvability over the cheap-talk frontier exists, precisely delimited by quasiconcave envelope analysis (Corrao et al., 2023).

Social network theory reveals that communication nearly always enhances individual accuracy—even under group-level accuracy loss—by reducing opinion variance through mixing. Optimal design requires balancing centralization, herding, and calibration, configuring network influence to maximize individual learning and aggregate wisdom (Pilgrim et al., 28 Jun 2024).

Position value in hypergraph games quantifies each player's marginal contribution via Shapley value over hyperlinks, allocating surplus according to both channel connectivity and agent's position (Shan et al., 2016).

6. Limitations, Lower Bounds, and Design Principles

Fundamental limits on communication value emerge in both theoretical analysis and practical systems. In multi-agent reasoning, proven bounds demonstrate when communication is necessary, beneficial, or wasteful (Rizvi-Martel et al., 14 Oct 2025):

• For associative recall, constant-depth and marginal communication suffice.
• For state tracking, parallelism enables logarithmic depth with communication growing linearly in agent count.
• For $k$-hop reasoning, communication and depth inherently scale with the problem.

Communication-optimal algorithms in linear algebra (eigen/SVD) attain lower bounds on required data movement, yielding up to three orders of magnitude efficiency gains in realistic settings (Ballard et al., 2010). In quantum channels, only specific classes exhibit multiplicative communication value; truly quantum effects enable super-additivity, breaking single-letter capacity (Chitambar et al., 2021).

Strategic silence and protocol rationality are crucial: when communication cost outweighs expected gain (e.g., in interstellar threat scenarios (Gruber, 4 Oct 2025)), sophisticated indices govern the transition from silence to engagement, balancing urgency, risk, and feasible success.

7. Future Directions and Open Challenges

Key challenges include:

• Unified frameworks for goal-oriented semantic communications across heterogeneous multi-tenant networks (Li et al., 2023).
• Developing cross-layer co-design integrating perception, inference, communication, and actuation, guided by mission-specific value metrics.
• Robust online learning of value functions under nonstationarity and adversarial settings.
• Deepening understanding of value under mediation, regulation, and dynamic game-theoretic feedback.
• Extending the value-of-communication paradigm to multi-modal, cross-organizational, or human-in-the-loop systems with complex, evolving objectives.

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