Complete Solution of the Hotelling Problem: Equilibrium in Secure Strategies for the Price Subgame

We study the classical problem of spatial competition between two players with linear transport costs proposed by (Hotelling, 1929). We employ the concept of the equilibrium in secure strategies (ESS). The reviewed definitions of the ESS and of the best secure response are presented. The set of the secure responses in the Hotelling game is obtained both in the case of elastic and inelastic demand. The complete solution of the two-stage location-price Hotelling game is given for the inelastic demand.