The Privacy Subsidy in Glosten-Milgrom: Bid-Ask Spread and Welfare under Flip-Noise Direction Observation

Battle Count: 83

Highly relevant to quantitative trading in the context of market making, privacy-preserving exchange design, and adverse selection modeling. The closed-form spread formula mu(1-2eta)*Delta directly informs how privacy mechanisms affect execution costs. The privacy subsidy mu*eta*Delta quantifies the protocol cost of privacy, critical for fee calibration in MPC-based exchanges. The counter-intuitive result that noise traders also benefit from privacy (Corollary 1) has implications for market design. However, the paper is purely theoretical with no empirical validation or trading strategy implementation.

The results are closed-form analytical expressions (spread = mu(1-2eta)*Delta, subsidy = mu*eta*Delta) that are trivially implementable. The model requires only three parameters: informed-trader fraction mu, flip probability eta, and value range Delta. No numerical optimization, simulation, or complex algorithms are needed. The main complexity lies in the theoretical derivation rather than implementation.

The paper provides complete closed-form proofs (Theorems 1 and 2, Lemma 1, Proposition 1, Corollary 1) with all algebraic steps shown. The model setup is fully specified with explicit parameters. No empirical data or code is required for verification. The results are purely analytical and can be independently verified from the stated assumptions.