The location model with two periods of price competition

Game Theory;Location Theory;Nash Equilibrium;Price Competition

The Location Model with Reservation Prices

In this paper, we analyze a variant of the standard Hotelling model of spatial competition where firms first choose locations along the line and then, given these locations, compete in prices.Consumers have a finite reservation price and incur a quadratic transportation cost.We show that there exists a unique subgame perfect Nash equilibrium with identical prices for the location-then-price game if the reservation price is sufficiently high.In that case the degree of differentiation is nondecreasing in the reservation price, for differentiation relaxes price competition.If the reservation price is lower, there is a continuum of subgame perfect Nash equilibria due to the fact that firms may act as local monopolists and the other firm's location choice becomes of less importance.All equilibria yield the same profit, however

Spatial competition with intermediated matching

This paper analyzes the spatial competition in commission fees between two match makers. These match makers serve as middlemen between buyers and sellers who are located uniformly on a circle. The profits of the match makers are determined by their respective market sizes. A limited willingness to pay is incorporated by means of reservation prices. If the fraction of buyers and sellers is unequal, the match makers are willing to subsidize the short side of the market, while the long side is exploited completely, provided reservation prices are sufficiently high. Competition is then concentrated entirely on the short side. When reservation prices are low, two local monopolies will emerge.Matching;Price Competition;Intermediation;Microeconometrics;microeconomics

On the Existence of Unique Equilibria in Location Models

In this paper, we study a two-stage location-then-price game where consumers are distributed piecewise uniformly, each piece being referred to as an interval.Although the firms face a coordination problem, it is obvious that, for any given locations and prices, there is a unique indifferent consumer.So only the exact interval in which the indifferent consumer is located may be uncertain for the firms.Therefore, we encompass the firms with beliefs about the interval in which the indifferent consumer is located.Given their beliefs, the firms' expected profit functions are quasi-concave.We consider the situation where firms first choose beliefs and then maximize the corresponding expected profit in two stages as a psychological game.We show that there exists a unique psychological equilibrium for this game, which consists of a subgame perfect Nash equilibrium for the two-stage game given certain beliefs, and of beliefs such that the equilibrium outcome is consistent with these beliefs.This equilibrium outcome is found easily by applying a coordination argument.

Spatial competition with intermediated matching

Matching;Price Competition;Intermediation;Microeconometrics

Non-uniformities in spatial location models

Location Theory;Demand;General Equilibrium;Location Models;management science

The generalized circular model

In this paper we present a generalization of the circular model. In this model there are two concentric circular markets, which enables us to study two types of markets simultaneously. There are switching costs involved for moving from one circle to the other circle, which can also be thought of as transformation costs. Consumers have valuations for the product of the firms, depending on the circle they live on. Equilibrium prices then of course are affected by both switching costs and consumers' valuations. An interesting insight that comes from this approach is that an extension of the circular model may invalidate the familiar principle that free entry is characterized by too many firms. Furthermore we discuss the effect of introducing reservation prices on the equilibrium outcome using a constructive approach