Testing the Consent-Friction Functional: Preference-Design Artifacts and the Contention-Bounded Limits of Coordination Friction in Multi-Agent Reinforcement Learning

Technical Summary: Testing the Consent-Friction Functional

Problem Statement
The paper addresses the empirical adequacy of the "consent-friction functional," a theoretical proposal derived from a single axiom regarding authorization and stakes. The functional posits that coordination friction ($F$) in multi-agent systems is a composite of three kernel variables: preference alignment ($\alpha$), stakes ($\sigma$), and entropy ($\varepsilon$). The proposed form is $F = \sigma(1 + \varepsilon)/(1 + \alpha)$. While the theory predicts that friction increases with stakes and entropy and decreases with alignment (diverging as $\alpha \to -1$), the specific monotone functional form and the claim that a single index predicts coordination loss remain untested. The paper aims to empirically validate this functional and, crucially, to identify whether apparent coordination findings are genuine structural effects or artifacts of experimental design.

Methodology
The study employs a rigorous, multi-stage experimental design in a four-agent, shared-resource Multi-Agent Reinforcement Learning (MARL) environment.

1. Initial Factorial Sweep (Sign-Blind): A $5 \times 5 \times 5$ full factorial design ($N=125$ conditions, 30 replications each, totaling 3,750 runs) manipulated alignment ($\alpha$), stakes ($\sigma$), and entropy ($\varepsilon$). Agents utilized Independent Q-Learning (IQL). The initial design realized alignment by interpolating agent targets between a shared base vector and an idiosyncratic component, a method that inadvertently created a "sign-blind" data-generating process (DGP) where cross-agent correlation depended only on $|\alpha|$, never producing genuine opposition.
2. Control Battery (The Correction): To diagnose and correct artifacts, the authors executed a series of targeted re-runs:
   • Signed DGP Repair: Re-ran the experiment using a genuinely signed equicorrelation sampler (spanning $\rho \in [-1/3, +0.8]$) and a two-team block design (reaching $\rho = -1$) to test signed alignment rather than magnitude.
   • Learner Robustness: Re-ran the signed sweep using Value-Decomposition Networks (VDN), a centralized training/decentralized execution (CTDE) additive learner, to test if findings were artifacts of independent learning non-stationarity.
   • Separable-Resource Control: Removed the shared resource pool, giving each agent an independent resource stream, to isolate whether effects were due to preference correlation or shared-state contention.
   • Partial-Sharing Dose-Response: Varied the fraction of resources shared ($w \in \{0, 1/3, 2/3, 1\}$) to test if the effect scales with the degree of contention.
   • Clean Opposition ($n=2$): Reduced the agent count to two to achieve a verified $\rho = -1$ without positive-semidefinite matrix constraints or within-team cooperation confounds.
   • Feasibility-Learning Decomposition: Decomposed the reward gap into an irreducible "feasibility floor" (the gap between the per-agent ideal and the achievable joint optimum) and a "learning shortfall" (the gap between the joint optimum and realized performance).

Key Results

1. Rejection of the Single-Index Functional Form: The canonical composite $F = \sigma(1 + \varepsilon)/(1 + \alpha)$ is rejected as a single-index predictor. While the independent-effects model (separating $\sigma$ and $\alpha$) decisively outperforms the composite in both the initial and signed designs, the specific monotone form $1/(1+\alpha)$ is directionally supported only over the cooperative range ($\rho > 0$). The predicted divergence as $\alpha \to -1$ is not observed; opposition does not increase friction beyond indifference.
2. Three Artifacts Identified and Pealed Back:
   • The "Stakes Dominate" Artifact: In raw data, stakes appeared dominant ($\eta^2 \approx 0.74$). However, because the reward is homogeneous of degree 1 in $\sigma$, this is a mechanical scaling effect. Upon stake-normalization, the ranking inverts, revealing preference structure as the dominant axis.
   • The Symmetric U-Shape Artifact: The initial "U-shape" (where neutral alignment was worst) was a sign-blind artifact. Because the initial DGP never produced negative correlation, the "adversarial" arm was actually a strong cooperative arm. Once the DGP was fixed to span genuine negative correlation, the U-shape vanished, replaced by a monotone decline only in the cooperative range.
   • The "Opposition Helps" Artifact: No design showed opposition ($\rho < 0$) outperforming indifference ($\rho = 0$). In clean tests ($\rho = -1$), opposition showed no detectable advantage and was directionally worse for IQL.
3. The Contention-Bounded Survivor: The only surviving structural effect is that cooperative alignment lowers the coordination gap, but this effect is strictly contention-bounded.
   • In a shared-pool environment, cooperative alignment reduces the gap.
   • In a separable-resource environment (no shared state), the effect vanishes entirely (slope $\approx 0$).
   • A partial-sharing sweep confirms a monotone dose-response: the effect steepens only once a majority of resources are shared.
4. Feasibility vs. Learning: A decomposition of the reward gap reveals that the reduction in friction under cooperation is almost entirely driven by the feasibility floor collapsing (the achievable joint optimum rises as targets align). The learning shortfall (the actual coordination performance relative to the achievable optimum) does not decrease; in fact, it slightly increases. Thus, cooperative alignment makes the problem more feasible, not necessarily easier to learn.
5. Robustness: The cooperative effect is robust to the shift from Independent Q-Learning to additive Value Decomposition (VDN), with curve correlations of 0.976. However, the effect is not robust to the removal of shared-state contention.

Significance and Claims
The paper claims a dual contribution: an empirical characterization of the consent-friction functional and a methodological demonstration of how design choices can manufacture spurious coordination findings.

• Empirical Verdict: The paper does not vindicate the functional as a universal law. Instead, it refines the theory: the denominator's sign ($1+\alpha$) is supported for cooperative alignment, but the adversarial divergence prediction is false, and the single-ratio multiplicative form is insufficient. The surviving effect is narrow: cooperative alignment reduces coordination gaps only in common-pool environments where agents physically contest shared resources, and this reduction is primarily a matter of feasibility (the optimum is easier to reach) rather than reduced learning friction.
• Methodological Contribution: The paper offers a "control battery" as a standard for mixed-motive MARL experiments. It argues that researchers must verify that preference-sampling designs genuinely span signed correlations (avoiding magnitude-only traps), normalize for reward homogeneity before declaring factors dominant, and distinguish between preference effects and shared-state contention.
• Modesty: The authors explicitly state that these findings are bounded to the specific environment family tested (continuous shared resources, quadratic loss, $n=4$ agents). They do not claim these results generalize to all MARL benchmarks or non-value-based learners (e.g., policy-gradient methods), leaving those for future work. The paper frames its findings as a "worked example" of catching and correcting one's own artifacts, rather than a definitive diagnosis of the entire field.