Uniqueness of counterfactual equilibria without signaling and with full information

Establish uniqueness of the counterfactual market equilibria considered in Section 8 for the no-signaling (NS) and full-information (FI) scenarios, in which workers choose only one-dimensional bids and employers’ beliefs either rely solely on observables (NS) or on true abilities (FI). Proving uniqueness would ensure that the simulated hiring patterns and welfare comparisons are not dependent on equilibrium selection.

Background

To quantify the isolated effect of LLMs eliminating signaling, the paper simulates counterfactual equilibria where workers submit only bids and employers either infer ability from observables or observe it directly. The authors note that multiplicity is less likely in these simplified environments but do not provide a formal uniqueness proof.

A uniqueness result would validate that the reported changes in hiring by ability/cost quantiles and welfare (workers, employers, total) are not artifacts of equilibrium selection and would strengthen the robustness of the policy conclusions.