Timing of entry and location/product differentiation

• Published date: 01 June 2018
• Date: 01 June 2018
• DOI: http://doi.org/10.1111/ijet.12151
• Author: Chia‐Hung Sun

Timing of entry and location/product differentiation

Chia-Hung Sun

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This research considers two alternative timing games, the precommitment game and the

preemption game, where duopoly firms choose their respective timing of market entry and post-

entry profits are generated by price competition in a spatial modelalaHotelling (1929). We find

that the time of first entry is increasing and the time of second entry is decreasing in location

differentiation. The results are robust and valid both from an equilibrium analysis and from a

welfare analysis. We also note that the difference in equilibrium entry times is too close from the

viewpoint of social welfare.

Key words Hotelling model, precommitment game, preemption game, timing game

JEL classification L13, D21, R10, O30

Accepted 13 January 2017

1 Introduction

Without a doubt, time and space, combined into space-time, are very important in everyday life. The

spatial economics literature presents findings on the impact of space on an agent’s economic

decisions, compared to the analysis from non-spatial economics. Conversely, the timing games

literature investigates the issue of a firm’s timing decision on market entry, with the model of a

timing game mostly based on a non-spatial context. The present study contributes further to the

analysis of spatial issues in the related literature by examining a timing game of entry under a spatial

market.

The purpose of this study is to examine how location differentiation affects firms’ timing of entry

into a market. We assume that duopoly firms are exogenously symmetrically located in a Hotelling

(1929) linear city. The two first decide whether and when to enter the market and then compete on

price in the product market. We explore the equilibrium outcomes both when the firms can

precommit to their timing of entry the so-called precommitment game proposed by Reinganum

(1981a, b) and when they are flexible in altering their timing of entry the so-called preemption

game offered by Fudenberg and Tirole (1985). We also illustrate welfare analysis by investigating the

optimal timing of entry and compare the private and social incentives for market entry.

In reality there are some commonly observed ‘‘stylized facts’’ for market entry timing. First, there

is an initial delay of entry into a new market (new technology entry). Second, there are differences in

the adoption and diffusion rates of the timing of new technology entry among firms in the same

industry as well as across industry sectors. In some industries, once the initial adoption of new

technology occurs, the remaining firms utilize the new technology at an accelerating pace. In



Department of Economics, Soochow University, Taipei, Taiwan. Email: jerry52.sun@msa.hinet.net

Financial support from the Ministry of Science and Technology (103-2410-H-031-010) is deeply appreciated.

doi: 10.1111/ijet.12151

International Journal of Economic Theory 14 (2018) 179–200 ©IAET 179

International Journal of Economic Theory

contrast, in some industries the initial adoption of new technology undergoes a decelerating

adoption process.

1

It is well known that if geographical space is seen as a product space, then a spatial model is also

able to explain product locations, and our analysis can be extended to the context of a product

differentiation model. In this case, location differentiation denotes the degree of product

substitutability, and smaller location differentiation corresponds to more competitive pressure. Our

analysis can thus be applied to investigate how the timing of entry differs across industries with

different degrees of competitive pressure. As will be shown, greater location differentiation (i.e. less

fierce competition) helps explain the stylized facts of delaying first entry as well as the accelerating

process in technology adoption.

This study is related to the timing games literature with strategic interaction in the product

market. A pioneering work in this literature is Reinganum (1981a, b), who uses a game-theoretic

approach with unobservable actions between players to investigate firms’ incentives to adopt a new

technology.

2

Reinganum (1981a, b) assumes that firms can precommit to their timing of technology

adoption at the beginning of the game and shows that the model has a unique Nash equilibrium, in

which the equilibrium involves sequential adoption with higher payoffs for the first mover (i.e. a new

technology is diffused over time and there is a first-mover advantage). The precommitment game

captures the idea that the costs of altering the adoption plans are prohibitively high or there are

infinitely long information lags.

Based on a precommitment game, Lippman and Mamer (1993) investigate the case where only

one firm can adopt the new technology (i.e. winner takes all). Some approaches deal with uncertainty

and rivalry in the product market. For instance, Stenbacka and Tombak (1994) and Gotz (2000)

extend the model of Reinganum (1981a, b) by assuming that the length of time required for

successful implementation is uncertain.

The preemption game, based on Fudenberg and Tirole (1985), captures the idea that firms can

observe their rivals’ adoptions and are flexible in altering their timing of entry, but they cannot

credibly commit to maintaining their timing of entry. This could occur because the costs of altering

adoption plans are not significant or the information lags are negligible. Fudenberg and Tirole

(1985) show that a potential advantage from being first is the introduction of an incentive for

preempting rival firms, thus speeding up the time at being the first to adopt a new technology, until

payoffs are the same for both firms (i.e. rent equalization).

3

For subsequent applications, Hendricks (1992) finds that uncertainty about the innovative

capabilities of the rival firm tends to slow down the first adoption of a new technology in the

preemption game. Riordan (1992) notes that regulation schemes may slow adoption by making

preemptivestrategies less attractive. Riordan and Salant(1994) consider strategic technology adoption

1

Hoppe (2002) and Milliou and Petrakis (2011) introduce some examples of the initial delay in new technology adoption:

the adoptions of computer-aided design (CAD), the basic oxygen furnace (BOF), and computer numerically controlled

(CNC) machine tools. On the other hand, the adoption and diffusion rates of information and communication

technology (ICT) differ across industry sectors. See Griliches (1957), Mansfield (1985), and Asterbo (2002) for detailed

discussions.

2

On the other hand, some literature contributions deal with uncertainty regarding the value of a new technology, but no

strategic interaction in the product market is considered. See, among others, Jensen (1988), Kapur (1995), and Vettas

(1998).

3

The mechanism at work is as follows. As a result of the potentially higher payoffs for the leader than for the follower, the

follower can profitably deviate to adopt the new technology just before the leader does. The leader anticipates this and

adopts the new technology at an earlier time so that the follower is indifferent between adopting just before or much after

that time. Consequently, the potential early-mover advantage stimulates preemption, until payoffs are equalized for both

firms.

Timing of entry Chia-Hung Sun

180 International Journal of Economic Theory 14 (2018) 179–200 ©IAET