Geoscience Reference
In-Depth Information
potential entrant who must decide whether or not to enter and, if yes, where to locate
his store (the choices of the follower are limited to zero or one store as to ensure
tractability), followed by price competition. Given high setup costs, the leader is a
monopolist and further entry is blocked. For moderate setup costs, the incumbent
locates two stores at the social optimum, and entry is deterred. For even lower setup
costs, entry can no longer be deterred by the incumbent.
Meza and Tombak's (
2009
) model uses uniform distribution, “sufficiently
high” reservation prices, quadratic transportation costs, and potentially different
production costs. The paper suggests a three-stage model, in which timing (of
entry), location, and price are determined. The low-cost firm is the leader. It is
possible for a higher-priced firm that is driven from the market, to re-enter at a later
stage. With a small difference in costs, firms enter the market immediately with
maximal differentiation. For a somewhat larger cost difference, the low-cost leader
enters immediately, soon followed by the higher-cost firm, still maintaining maximal
differentiation. For an even larger cost difference, the low-cost leader locates at an
interior point, followed by its competitor that locates as far away as possible from
the leader. With a very high cost difference, the low-cost leader locates at the center
of the market and effective blocks all further entry.
14.4.12
UD1, Plane, Nash Equilibria
The paper by Irmen and Thisse (
1998
) considers a duopoly in
d
-dimensional real
space with weighted squared Euclidean distances. Customers have a utility function
that includes a reservation price, the product's price, and the sum of weighted
distances between customer and the firm (the customer's ideal point and the product
features, as this model is discussed in feature space). The key result is that if there
is a main characteristic of the product, then there is a unique equilibrium in the
location game, in which the two products exhibit maximum differentiation in that
feature, while otherwise being identical. The authors cite an interesting application
of their result in the news magazines
Time
and
Newsweek
, whose main difference
is in the cover story. The similarity of this result and that by Tabuchi (
1994
) should
also be noted.
14.4.13
UD2a, Linear Market, Nash Equilibria
The contribution by Eiselt (
1991
) appears to have been the first to use attraction
function of the type “facility attractiveness divided by an increasing function of
distance” for the purpose of locating competitive facilities. It is shown that as long
as the weights are unequal, no equilibrium exists. The author then allows repeated
sequential relocation. It turn out that facilities shuttle but converge towards fixed
points whose location depends exclusively on the weights: if weights are similar,
