On the existence and social optimality of equilibria in a Hotelling game with uncertain demand and linear-quadratic costs
The B.E. Journal of Theoretical Economics, Vol. 11 (2011) / Issue 1 / Topics
This paper examines a variant of the Hotelling two-stage mill-pricing duopoly game with `linear-quadratic' transport costs and the uniform customer distribution subject to a random shock. The demand is equally likely to be found anywhere in a fixed interval of feasible product characteristics, with the ex-post differentiation of tastes parametrized to reflect the degree of uncertainty. It turns out that, for uncertainty big enough, the presence of a linear component in the cost function no longer rules out an analytical solution to the game, which is a common problem in spatial competition models. In particular, a subgame-perfect equilibrium is shown to exist in which the firms' locations approach the socially efficient ones as uncertainty further increases, regardless of the curvature of the cost function. When the demand uncertainty reaches maximum, mill-pricing is equivalent to spatial price discrimination under the most general conditions.
Product differentiation decisions under ambiguous consumer demand and pessimistic expectations
International Journal of Industrial Organization, forthcoming (Nov. 2012)
This paper studies product differentiation decisions in a spatial duopoly with limited information on consumer demand. In particular, a situation is discussed in which the firms do not know the exact distribution of the random location of consumer demand and its responsiveness to price changes (measured by the scale of transport costs), but resolve the resulting ambiguity using the α-maxmin or minimax regret criteria. When the firms are sufficiently pessimistic (α is high enough), results are in contrast with the existing literature. In particular, an increase of demand location uncertainty decreases the equilibrium product differentiation, intensifying the second-stage competition in prices, although the effect is dampened by uncertainty about transport costs. Endogenizing the choice of objective function leads to the dominance of an extreme form of pessimism, which turns out to be socially-optimal.
