(3) — asymmetric positioning equilibrium

For $t>0$, suppose only A uses personalized pricing. A is the targeting follower and B is the uniform-price leader. The positioning subgame has an equilibrium at

The positioning comparison includes moves to every real point, including a move across the rival's location. It provides the positions used in the asymmetric implementation-payoff cells.

Formalization Note This is a weak equilibrium: A can move to the reflected position $3/2$ and tie its equilibrium gross profit. At coincident positions the leader may have multiple optimal prices, so the predicate chooses an optimal continuation after a deviation. The source optimizes over ordered locations; the statement checks the full real-location game.