Solution of the Hotelling’s game in secure strategies

Abstract

We show that the price-setting subgame in the classic Hotelling’s model (1929) with the linear transport costs has the unique equilibrium solution for all location pairs under the assumption that duopolists secure themselves against being driven out of the market by undercutting. In contrast to the modified zero conjectural variation approach of Eaton and Lipsey (1978) we assume that the players consider the threat of ‘pressing out’ of the market as a real possibility. We employ the concept of equilibrium in secure strategies (EinSS) as the generalization of the Nash equilibrium. The EinSS coincides with the Nash Equilibrium when Nash Equilibrium exists and postulates the incentive of players to maximize their profit under the condition of security against the actions of other players.