A Structural Measure of Bargaining Fragility in Multi-Domain Agreements

Negotiation outcomes are commonly analyzed through equilibrium concepts, yet many agreements fail during implementation for reasons not captured by incentive structure alone This paper introduces a pre-equilibrium screening criterion for bargaining fragility based on a small set of agreement-level quantities characterizing dependency architecture: strain τ (the number of operative obligations requiring tracking), curvature κ (the density and strength of interdependencies among elements), compressibility σ (the extent to which complexity can be reduced through modularization without altering functional meaning), and the stability quotient Γ = κ/τ (average interdependence burden per element). We use the inequality Γ > σ as a classification rule; agreements with Γ > σ are classified as structurally fragile and, in the data, exhibit higher sensitivity to perturbations. Across 42 documented agreements, the diagnostic correctly classifies nearly all observed outcomes, with only a single false positive and no false negatives. The framework operates as a pre-equilibrium screen that complements (rather than replaces) Nash and bargaining equilibrium analyses by identifying agreement architectures that are structurally brittle under small shocks.