§4 Stage 1 — benchmark positions, prices and profits

For $t>0$, when both firms use uniform pricing, the positioning subgame has an equilibrium at $x_A=-1/4$ and $x_B=5/4$. Each then charges $3t/2$ and earns gross profit

The position equilibrium compares each firm's profit with deviations to every real position and with price equilibria following those deviations. It supplies the no-PP cell of the implementation game.

Formalization Note The predicate quantifies over price equilibria after deviations, without asserting that one exists after every possible deviation. Reservation value is omitted because the covered-market assumption makes it cancel.