P1 contrasts remarkably with the case in which Firm 3
has the (weakly) lowest SLR, or φ3 ≤ φ1 (recall that φ2 >
φ1). In this situation, Firm 3 lacks sufficient discount motivation
to capture its switcher segment and thus becomes a
high-priced niche retailer focusing on its loyal segment.
Because Firm 1’s SLR is not the lowest, it finds that it is
worthwhile to play for s123. Segments s12 and s123 implicitly
combine into a single switcher segment that only Firms 1
and 2 serve. The resultant equilibrium is defined as follows: