Entry of Innovator and License in Oligopoly
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Entry of Innovator and License in Oligopoly Masahiko Hattori1 · Yasuhito Tanaka1 Received: 6 June 2019 / Revised: 30 January 2020 / Accepted: 13 February 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract When an outside innovating firm has a cost-reducing technology, it can sell licenses of its technology to incumbent firms using a combination of royalty and fixed fee. Alternatively, the innovating firm can enter the market and at the same time sell licenses, or enter the market without license. We examine the credibility of the threat of entry by the innovating firm using a two-step auction under oligopoly with three firms, one outside innovating firm and two incumbent firms. With general demand function, we show that the credibility of the two-step auction depends on the form of the cost function of the new technology, whether it is concave or convex. Also we analyze the optimal strategy for the innovator in a case of linear demand and quadratic cost functions in which the two-step auction is credible. Keywords License · Entry · Oligopoly · Innovating firm · Two-step auction JEL Classification D43 · L13
1 Introduction In Proposition 4 of Kamien and Tauman (1986), it was argued that in an oligopoly when the number of firms is small (or very large), strategy to enter the market and at the same time license the cost-reducing technology to the incumbent firm (license with entry strategy) is more profitable than strategy to license its technology to the incumbent firm without entering the market (license without entry strategy) for the innovating firm. However, their result depends on their definition of license fee. They defined the license fee in the case of licenses without entry by the difference between the profit of an incumbent firm in that case and its profit before it buys a license without entry of the innovating firm. However, it is inappropriate from the game theoretic view point. If an incumbent firm does not buy Masahiko Hattori
[email protected] Yasuhito Tanaka [email protected] 1
Faculty of Economics, Doshisha University, Kamigyo-ku, Kyoto, 602-8580, Japan
Journal of Industry, Competition & Trade
a license, the innovating firm may punish the incumbent firm by entering the market. The innovating firm can use such a threat if and only if it is a credible threat. In a duopoly case with one incumbent firm, when the innovating firm does not enter nor sell a license, its profit is zero; on the other hand, when it enters the market without license, its profit is positive. Therefore, threat of entry without license is credible under duopoly, and then even if the innovating firm does not enter the market, the incumbent firm must pay the difference between its profit when it uses the new technology and its profit when the innovating firm enters without license as a license fee. For example, Hattori and Tanaka (2018) presented analyses of license and entry choice by an innovating firm in a duopoly. However, in an oligopoly with more than one incumbe
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