Abstract
In this paper we analyze the strategic interaction between a new good producer and a remanufacturer who use negative advertising on television (TV) to compete for a greater share of the market for a particular good. Government regulations limit the total amount of negative advertising time either firm can buy. The two rival firms choose how much negative advertising time to buy simultaneously. Our analysis of this duopolistic interaction leads to four results. First, we provide the normal form representation of the game between the new good producer and the remanufacturer. Second, we specify the best response functions of the two firms. Third, we determine the pure strategy Nash equilibrium of the game under study and point out that this equilibrium is unique. Finally, we ascertain the amount of negative advertising time the two firms would buy if they could come to a binding agreement to curtail this kind of advertising.
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Notes
Go to https://vsc.gsa.gov/green/files/CPG.pdf for additional details. Accessed on 15 March 2017.
In the remainder of this paper, the expressions “original equipment manufacturer” and “new good producer” have the same meaning and hence we shall use them interchangeably.
See Tadelis (2013, pp. 79–100) for a lucid textbook account of static games.
Governments frequently regulate negative or misleading advertising by firms. For instance, in the United States, the Federal Trade Commission has regulations in place that govern advertising on the internet. Go to https://www.ftc.gov/tips-advice/business-center/guidance/advertising-marketing-internet-rules-road for more on this point. As a second example, the United States Food and Drug Administration regulates the kind of advertising that is permitted for prescription drugs. Go to https://www.fda.gov/Drugs/ResourcesForYou/consumers/PrescriptionDrugAdvertising/ucm072077.htm for additional details. Accessed on 15 March 2017. For more general discussions of the regulation of deceptive or negative advertising, the reader should consult Blasco et al. (2016) and Rubin (2008).
In this regard, note that in Australia, there are explicit time limits on the amount of advertising that can be shown on TV. Go to the website of the Australian Communications and Media Authority (ACMA) http://www.acma.gov.au for additional details on this point.
The second-order sufficiency condition is clearly satisfied.
In the model of this paper, the \(i{\text{th}}\) firm’s payoff function is given by Eq. (1). Suppose the coefficient of \(a_{j}\) in Eq. (1) were \(m\) and not 2. Then the payoff function can also be written as \(\prod_{i} (a_{i} , a_{j} ) = a_{i} - (m - a_{i} )a_{j} - a_{i}^{2} .\) To account for the reasonable point that an increase in the negative advertising time purchased by firm \(j\) adversely affects firm \(i,\) we want the coefficient of \(a_{j}\) in the re-written payoff function above to be negative. But this coefficient will only be negative if \(m > a_{i} .\) Now, as shown in Eq. (6), the Nash equilibrium choices require each of the two firms to purchase 1 h of negative advertising time. Given this result, if \(m = 1/2\), then the condition \(m > a_{i}\) would be violated in the Nash equilibrium and increases in the negative advertising time purchased by firm \(j\) would implausibly raise the payoff obtained by firm \(i.\) In sum, for the game-theoretic framework of this paper to make sense, we must have \(m > 1.\).
See Tadelis (2013, pp. 51–52) for a textbook description of the Prisoner’s Dilemma game.
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For their helpful comments on a previous version of this paper, we thank the Editor-in-Chief Yoshiro Higano and two anonymous reviewers. In addition, Batabyal acknowledges financial support from the Gosnell endowment at RIT. The usual disclaimer applies.
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Batabyal, A.A., Beladi, H. A game model of competition between a new good producer and a remanufacturer using negative advertising. Asia-Pac J Reg Sci 1, 329–336 (2017). https://doi.org/10.1007/s41685-017-0031-7
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DOI: https://doi.org/10.1007/s41685-017-0031-7