Bertrand oligopoly revisited. (Q5943371)

Summary: This paper reconsiders Bertrand duopoly and oligopoly in the spatial formulation due to \textit{H. Hotelling} [``Stability in Competition'', Econ. J. 41, 41--57 (1929); Bulletin A. M. S. 34, 423 (1928; JFM 54.0575.04)]. The equilibrium configurations of price and location structure are considered, given elastic demand, and a full dynamics is formulated in order to cheek for stability of equilibrium and the possibilities of complex dynamics, such as occurs easily with Cournot oligopoly. The main discussion concerns Hotelling's original case of two sellers on a given interval, though results for different cases, such as three firms on a circle, and lattices in 2D are indicated.