Toward Formalizing Nash’s Ideal Money: A Robust Framework for Preserving Price Stability, and Incentive Compatibility Through Index Anchoring and Resilience Objectives in Monetary Policy

We develop a formal theory of “ideal money” that extends Nash’s proposal for a nonpolitical value standard and his critique of discretionary monetary authorities as implicit “pardoners” of overindebtedness. The core contribution is a precise, equilibrium-compatible notion of minimal distortion to productive incentives: a sound regime should preserve the unit of account for long-horizon contracting while limiting the incentive wedges created by nominal risk, expected rescues, and targeted price suppression. We cast monetary design as a robust feedback-control problem around an objective index anchor, defining a tracking error and establishing bounded-gain stability under bounded (potentially adversarial) disturbances. We then broaden “soundness” from scalar anchor tracking to system-level resilience by requiring safe-set invariance of a macro-financial state that includes inflation uncertainty, leverage/maturity mismatch, and credit stress. To formalize modern interventions, we introduce explicit policy wedges: a relative-price wedge and a pardon/transfer wedge, and we show how these wedges propagate through collateral and balance-sheet dynamics into credit spreads and sectoral tilts in capital allocation and labor deployment. Finally, we adopt a two-stage treatment of interventions: exogenous “distortion accounting” to quantify the induced misallocation for any bounded wedge path, and an endogenous political-economy layer in which constitutional constraints reduce the equilibrium frequency and magnitude of such wedges. Together, these elements provide a mathematically explicit criterion for sound money: a regime that robustly preserves the value standard, remains resilient under shocks, and minimizes measurable incentive distortions induced by discretion.