Model of spatial competition on discrete markets

The paper’s supplemental material derives the OS (One-Step) stationarity band for each seller from the full-information indifference distance and flux formulas, and—using discreteness—collapses each band to the equalities 2pα − pβ = dαβ + 2nα − 1 and 2pβ − pα = dαβ + 2(N − nβ) + 1 (their Eqs. S27, S29), then solves to obtain p*α = N + (a − b)/3 and p*β = N − (a − b)/3 (Eqs. S30, S31) . It also identifies when the Hotelling pair lies outside the allowed domain |pβ − pα| ≤ dαβ via |pHα − pHβ| ≥ dαβ, yielding 5nβ − 2(N + 1) ≤ nα < N + 1 − nβ (Eq. S10) . The candidate solution independently reconstructs the same OS equalities (via a half-integer one-step improvement argument), solves the same 2×2 system to Hotelling prices, and derives exactly the same feasibility condition. The only nuance is that the paper formally proves sufficiency (outside-domain ⇒ no convergence to Hotelling), and reports necessity for OS from simulations, whereas the candidate adds a brief argument for necessity; this aligns with the paper’s numerical finding for OS (SM text) .