Spatial Cournot Competition
This chapter reviews the literature on spatial Cournot competition with endogenous firms’ locations in the past 30 years, which started from Hamilton et al. (Spatial Discrimination: Bertrand vs. Cournot in a Model of Location Choice. Regional Science and
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2.1
Introduction
Competitive location theory started with Hotelling (1929),1 who assumed that there are two identical firms selling homogenous goods to consumers living along a linear market with unit length (the “main street”). These consumers are uniformly distributed along this main street, and each buys exactly one unit of the product from the firm with the lowest full price (mill price plus linear transport cost). Firms pursue maximization of their own profits. They decide their locations simultaneously in the first stage
1 Early spatial models such as Ricardo (1817), Von Thünen (1826), Weber (1909), and Christaller (1933) are focused on land use and simple location theory.
F.-C. Lai () Research Center for Humanities and Social Sciences, Academia Sinica, Nankang, Taipei, Taiwan Department of Public Finance, National Chengchi University, Taipei, Taiwan e-mail: [email protected] © The Author(s) 2020 S. Colombo (ed.), Spatial Economics Volume I, https://doi.org/10.1007/978-3-030-40098-9_2
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of the game. In the second stage, they simultaneously determine the prices of their products. Hotelling (1929) “showed” that in equilibrium, these two firms will locate at the center of the linear market and share the market equally. At first glance, Hotelling’s model seems correct, so his model was later heavily cited, and there were many extended studies, such as Lerner and Singer (1937), Smithies (1941), and Downs (1957). However, 50 years later, D’Aspremont et al. (1979) proved that Hotelling’s equilibrium result is invalid. The reason is that when the two firms locate close to one another, the price equilibrium provided by Hotelling (1929) cannot be sustained, because one of them will undercut the other and monopolize the entire market. In this situation, the profit of the undercutting firm is higher than what it would earn under co-existence, so the equilibrium of the Hotelling (1929) model is invalid; in fact, it is wrong.2 D’Aspremont et al. (1979) proposed to use quadratic transport cost functions instead of linear transport cost functions, in order to make the game structure be correct, such that a price equilibrium exists for any location pair. However, their modification needs to pay a price, that is, the equilibrium locations will be at the two ends of the linear market, which is very different from Hotelling’s observation about the reality.3 Since the Hotelling (1929) model had already been misused for 50 years at the time of d’Aspremont et al.’s work in 1979, once the model was proved to be wrong, its impact on the academic world was foreseeable. Many scholars have tried to save the Hotelling (1929) model with slight modifications or directly switch to using quadratic transport cost functions to avoid the game structure problem. Several attempts will be briefly introduced in the following, where spatial Cournot competition will be highlighted.
2 Modern
game theory had not yet appeared in 1929. For example, John Nash was born in 1928, and thus Harold Hotelling did not yet know o
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