A game model of competition between a new good producer and a remanufacturer using negative advertising

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1 Asia-Pac J Reg Sci (017) 1: DOI /s ARTICLE A game model of competition between a new good producer and a remanufacturer using negative advertising Amitrajeet A. Batabyal 1 Hamid Beladi Received: 13 October 016 / Accepted: 18 April 017 / Published online: 4 April 017 Ó The Japan Section of the Regional Science Association International 017 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. Keywords Duopoly Nash equilibrium Negative advertising New good producer Remanufacturer JEL Classification L1 M37 D1 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. & Amitrajeet A. Batabyal aabgsh@rit.edu Hamid Beladi Hamid.Beladi@utsa.edu 1 Department of Economics, Rochester Institute of Technology, 9 Lomb Memorial Drive, Rochester, NY , USA Department of Economics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX , USA

2 330 Asia-Pac J Reg Sci (017) 1: Introduction 1.1 Overview According to Lund (1984), the term remanufacturing refers to an industrial process in which worn-out products are restored to like-new condition. This researcher goes on to point out that in remanufacturing, a series of industrial processes, often taking place in a factory environment, leads to the full disassembly of a discarded product. Next, usable parts are cleaned, refurbished, and put into inventory. The product is then reassembled from the old parts and sometimes new parts as well to produce a unit that is fully equivalent and sometimes superior in performance and average lifetime to the original new product. In the United States, in contemporary times, two reasons account for the salience of remanufacturing. First, on the regulatory side, in an attempt to curtail injurious environmental outcomes, the Environmental Protection Agency (EPA) has taken some practical steps. In this regard, it is worth accentuating the agency s implementation in 1995 of the Comprehensive Procurement Guideline. Inter alia, this guideline sought to cut waste and promote resource conservation by making sure that materials collected in recycling programs would be used again to manufacture new products. 1 Second, there are the actual cost savings experienced by firms. To see this, consider the following two examples from Mitra and Webster (008). These researchers have noted that in 1997, Ford was able to avoid the disposal of more than 67,700 lb of toner cartridges and thus saved $180,000 in disposal costs. Similarly, in 1995, Union Carbide saved $75,000 by avoiding disposal costs. Given the growing salience of remanufacturing from both an environmental and a practical perspective, a growing literature has now begun to examine the nature and the desirability of this industrial process from different vantage points. We now briefly survey this literature. 1. Review of the literature Simplifying matters just a little, we can look at remanufacturing either from the perspective of firms or from that of consumers. Let us concentrate on firms first. Lebreton and Tuma (006) study remanufacturing in the context of the disposal of 600,000 tons of used tires in Germany. On the basis of their analysis, these researchers point to specific factors that are likely to elevate remanufacturing rates in this country. Ferrer and Swaminathan (006) analyze the competition between an original equipment manufacturer (OEM) and an independent operator (IO). In a multi-period setting, the IO may intercept cores of products made by the OEM to sell remanufactured products in subsequent time periods. These researchers show that when the threat of competition rises, the OEM is more likely to fully utilize all available cores and offer the remanufactured product itself, at a lower price. 1 Go to for additional details. Accessed on 15 March 017. 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.

3 Asia-Pac J Reg Sci (017) 1: Do remanufactured products cannibalize new product sales? This question has been analyzed by Atasu et al. (010) who show that a product portfolio that includes both new and remanufactured products can make it likely for a firm to get to additional market segments and thereby block competition from new low-end products or third-party remanufacturers. New and remanufactured goods are often sold in the same market and, therefore, it makes sense to consider them together in the design of a product line. Aydin et al. (015) adopt this last point of view and set forth a new methodology that permits them to compute the maximum profit and the market share associated with a product line. Shi et al. (015) study the stability of the Nash equilibrium arising in the game between an OEM and a remanufacturer. They show that a higher willingness-topay (WTP) on the part of consumers can either fortify or weaken the stability of the relevant Nash equilibrium. Even so, a higher WTP always hurts the OEM and benefits the remanufacturer. Finally, Batabyal and Beladi (016a) is the only paper we are aware of that has analyzed the competitive interaction between an OEM and a remanufacturer when the goal of both firms is to use expenditures on product development to capture a dominant share of the market in which they are operating. We now discuss remanufacturing from the perspective of consumers. In this regard, note that just as firms can take actions to increase their market share, for any good such as a cell phone, consumers can also influence the market shares obtained by an OEM and a remanufacturer through their purchases of one or the other kind of good. Having said this, to the best of our knowledge, Batabyal and Beladi (016b) is the only paper to have conducted a game-theoretic analysis of the strategic interaction between two types of consumers who, with their individual purchase decisions, attempt to raise the market share of either new or remanufactured toner cartridges. In the course of their analysis, these two researchers note that one way to extend the analysis in their paper would be to analyze a game in which the firms that produce the new and the remanufactured goods are able to influence consumer preferences by advertising the relative strengths of their goods. Several researchers such as Giuntini and Gaudette (003) and Hong et al. (015) have recognized the importance of advertising in making consumers aware of the properties of both new and remanufactured goods. Even so, as these and other researchers have pointed out, there is very little theoretical research on advertising and its effects in the context of remanufacturing. Given this lacuna in the literature, in this paper, we analyze the hitherto unstudied 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. Section.1 describes the simple static game model 3 in which an OEM and a remanufacturer choose how much negative advertising time to buy simultaneously. Government regulations limit the total amount of negative advertising time either 3 See Tadelis (013, pp ) for a lucid textbook account of static games.

4 33 Asia-Pac J Reg Sci (017) 1: firm can buy. 4 Section. provides the normal form representation of the game between the two rival firms. Section.3 specifies the best response functions of the two firms. Section.4 first determines the pure strategy Nash equilibrium of the game under study and then points out that this equilibrium is unique. Section.5 ascertains 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. Finally, Sect. 3 concludes and then discusses two ways in which the research described in this paper might be extended. Analysis.1 The theoretical framework Consider a particular market in which a new good producer and a remanufacturer produce cell phones for sale to consumers. Note that the subsequent analysis does not depend in any way on the specific good we have chosen to concentrate on. The focus on cell phones is purely for concreteness. Each of the two firms under consideration can choose to buy time on television (TV) shows to broadcast negative advertisements against its rival. Let a i 0 denote the advertising time purchased by firm i where i ¼ 1; : We suppose that these decisions to buy time are made simultaneously. In the relevant time period, existing government regulations prevent either of the two firms from purchasing more than h of negative advertising time. Obviously, this means that neither firm can buy more than h of negative advertising time. Once again, the reader should note that our choice of this upper limit of is without loss of generality. Indeed, our analysis applies to any strictly positive upper limit although our focus on the positive integer makes the subsequent analysis transparent. 5 Given a pair of advertising time purchases ða i ; a j Þ; the payoff to firm i in this negative advertising game is given by the function Y ða i ; a j Þ¼a i a j þ a i a j a i ; ði; j ¼ 1; ; i 6¼ jþ: ð1þ i 4 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 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 Drugs/ResourcesForYou/consumers/PrescriptionDrugAdvertising/ucm07077.htm for additional details. Accessed on 15 March 017. For more general discussions of the regulation of deceptive or negative advertising, the reader should consult Blasco et al. (016) and Rubin (008). 5 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) for additional details on this point.

5 Asia-Pac J Reg Sci (017) 1: Three aspects of the payoff function Q i ða i; a j Þ, in Eq. (1), are worth emphasizing. First, because the ith firm s payoff depends on the advertising time purchased by the jth firm, clearly, the dealings between these two firms are strategic in nature. Let us comprehend this point in greater detail. The term a i denotes the direct and positive effect on the payoff to firm i. The term a j denotes the negative effect of firm j s choice on the payoff to firm i. The term a i a j denotes the effect on the payoff to firm i from the interaction between the two firms. The term a i term is the quadratic term which ensures that the ith firm s payoff function is concave in its own decision variable a i : The reader should understand that in what follows, we shall be analyzing the entire payoff function in Eq. (1) and not just selected terms. This can be seen clearly, for instance, in the first-order necessary condition given in Eq. (3) below. In addition, because we are interested in studying the phenomenon of negative advertising in this paper, the payoff function in Eq. (1) is structured as it is with positive, negative, interaction, and concavity terms. Second, the ith firm s payoff is increasing in its own advertising time purchase as long as 1 þ a j [ a i : Put differently, the ith firm s payoff is increasing in its own advertising time purchase as long as this purchase is not too high. Finally, the ith firm s payoff function is concave in its advertising time purchase. This means that increases in the amount of negative advertising time purchased by the ith firm raises this firm s payoff but at a decreasing rate. With this background in place, our next task is to provide the normal form representation of the above static game between the two rival firms.. The game in normal form We need to stipulate the number of players, their strategy spaces, and their payoff functions. Clearly, there are two firms or players and hence the set of players N ¼ f1; g: For the ith firm, the strategy space is given by the set S i ¼ ½0; Š: Finally, the payoff to firm i is given by the function Q i ða i; a j Þ in Eq. (1). Let us now specify the best response functions of the two firms..3 The best response functions In the negative advertising game under consideration, the ith firm solves max fai g½a i a j þ a i a j a i Š: ðþ The first-order necessary condition for an optimum is 6 1 þ a j a i ¼ 0: ð3þ Simplifying Eq. (3), the best response function of firm i is given by a i ða j Þ¼ 1 þ a j : ð4þ 6 The second-order sufficiency condition is clearly satisfied.

6 334 Asia-Pac J Reg Sci (017) 1: Inspecting Eq. (4), we see that firm i s optimal purchase of negative advertising time a i is increasing in firm j s optimal purchase of negative advertising time a j : Therefore, consistent with the definition given in Tadelis (013, p. 93), the optimal purchases of the two firms are strategic complements and the negative advertising game that we are studying in this paper is a game with strategic complements. We now proceed to find the pure strategy Nash equilibrium of this game..4 The Nash equilibrium From Eq. (4), we know that the best response functions of the two rival firms are given by a 1 ¼ 1 þ a and a ¼ 1 þ a 1 : ð5þ Solving these two best response functions simultaneously, we obtain the pure strategy Nash equilibrium that we seek. Specifically, we get ða 1 ; a Þ¼ð1; 1Þ: ð6þ Note that Eq. (6) gives us the only solution to the two best response functions given in Eq. (5). From this it follows that the Nash equilibrium to the negative advertising game specified in Eq. (6) is unique. Our last task in this paper is to ascertain the amount of negative advertising time the OEM and the remanufacturer would buy if they could come to a binding agreement among themselves to curtail their negative advertising..5 A binding agreement Substituting ða 1 ; a Þ¼ð1; 1Þ in Eq. (1) we see that when the new good producer and the remanufacturer play their Nash equilibrium strategies, their payoff is negative and equal to Q ið1; 1Þ ¼ 1: This unsavory state of affairs clearly suggests that both firms would be better off if they could come to a binding agreement among themselves to not buy any time for negative advertising on TV shows. 7 Some thought ought to convince the reader that when the OEM and the remanufacturer choose to buy no TV time for negative advertising, that is, when ða 1 ; a Þ¼ð0; 0Þ; relative to the -1 payoff, their payoff is higher and specifically equal to Q ið0; 0Þ ¼0: Therefore, if a binding agreement were possible then both the 7 In the model of this paper, the ith firm s payoff function is given by Eq. (1). Suppose the coefficient of a j in Eq. (1) were m and not. Then the payoff function can also be written as Q i ða i; a j Þ¼ a i ðm a i Þa j a i : 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 ¼ 1=, 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:.

7 Asia-Pac J Reg Sci (017) 1: OEM and the remanufacturer would choose to not engage in negative advertising at all. This particular outcome arises because the negative advertising game that we have been analyzing thus far is a variant of the well-known Prisoner s Dilemma game for two players. 8 This completes our analysis of negative advertising and competition between an OEM and a remanufacturer. 3 Conclusions In this paper, we examined the strategic interaction between a new good producer and a remanufacturer who used negative advertising on TV shows to compete for a greater share of the market for a specific good. Government regulations limited the total amount of negative advertising time either firm could buy. The two rival firms chose how much negative advertising time to buy simultaneously. Our analysis of this interaction led to four results. First, we provided the normal form representation of the game between the new good producer and the remanufacturer. Second, we specified the best response functions of the two firms. Third, we determined the pure strategy Nash equilibrium of the game under study and pointed out that this equilibrium was unique. Finally, we ascertained 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. The analysis in this paper can be extended in a number of different directions. In what follows, we suggest two possible extensions of this paper s research. First, it would be useful to compare and contrast our results with an analysis in which an OEM and a remanufacturer attempt to increase their share of the market for a particular good using positive advertising. Second, it would also be instructive to study the efficacy of advertising as a market share enhancing device when an OEM and a remanufacturer have access to other such devices including, but not limited to, price reductions and loyalty discounts. Studies that analyze these aspects of the underlying problem will provide additional insights into the functioning of markets with remanufacturing and the ways in which such markets can effectively enhance the preservation of scarce resources. References Atasu A, Guide VDR, Van Wassenhove LN (010) So what if remanufacturing cannibalizes my new product sales? Calif Manag Rev 5:56 76 Aydin R, Kwong CK, Ji P (015) A novel methodology for simultaneous consideration of remanufactured and new products in product line design. Int J Prod Econ 169: Batabyal AA, Beladi H (016a) A game model of competition for market share between a new good producer and a remanufacturer. Econ Bull 36: Batabyal AA, Beladi H (016b) A game model of new and remanufactured goods, brown and green consumers, and market share dominance. J Quant Econ 14: See Tadelis (013, pp. 51 5) for a textbook description of the Prisoner s Dilemma game.

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