Secure strategy equilibrium in Hotelling's model of spatial competition

The problem of spatial competition was formulated in 1929 by Harold Hotelling. He considered two firms playing a two-stage game. They choose locations in stage 1 and prices in stage 2. If locations are chosen by competitors Nash equilibrium do not always exist. For studying these cases we employ the concept of secure strategy equilibrium (SSE) which allows to solve the game of choosing prices for any locations. We examine a nontrivial particular case when prices grow if market moves from a monopoly to a duopoly.