New product design decisions and free sharing of patents with rivals

Abstract Intrigued by observations in the automobile industry where some firms share their new battery technologies with their competitors, we consider the problem where an innovator firm, that owns a novel technology, licenses it to a rival firm that uses the conventional technology to manufacture an existing product. The rival firm uses the licensed technology to develop a new product to compete with the innovator firm in the downstream market. We address the innovator firm’s pricing issue of the new technology licence and characterize the design features of the new product the rival firm develops using the licensed technology. We show that under specific conditions, it makes sense for the innovator firm to license its technology free of charge to the rival firm. We conduct numerical studies to examine the impact of the model parameters on the optimal outcomes and generate some practical insights.


Introduction
There is an emerging phenomenon, where firms, having developed new technologies for their products, sometimes share their innovations with rival firms through licensing. For example, Tesla invented a new battery technology that incurs a lower operational cost and offers higher safety than the existing technologies. In addition, the time to re-charge the battery produced by the new technology is shorter than the other battery technologies in the market. Despite the competitive advantage of the novel battery technology, Tesla has decided to share it with its rival firms (Musk, 2014). According to Elon Musk, CEO, Tesla, the reason to share the new technology patent is to encourage the development of electric and hybrid vehicle technologies (Quinn & Brachmann, 2014). In another example, Toyota has also decided to make its technologies on fuel cell stack, high-pressure hydrogen tank, fuel cell system and software control available to its rivals (Ayre, 2015). Furthermore, in the past, Toyota has also licensed its new technology to rival firms like General Motors and Ford Motors. The reason for sharing new technology patents with rivals is to encourage the development of hybrid electric vehicles and fuel cell electric vehicles (Toyota, 2019 andRidden, 2019). According to Shigeki Terashi, Chief Officer, Toyota ZEV factory: "Based on the high volume of inquiries we receive about our vehicle electrification systems from companies that recognize a need to popularize hybrid and other electrified vehicle technologies, we believe that now is the time for cooperation." (Ridden, 2019) Volkswagen shared its new electric chassis technology with e.Go, a rival electric car start-up (McGee, 2019). Similarly, Ford shared its patents on electric vehicle technology with rivals to accelerate the development of hybrid and electric cars (Paula, 2015). The rival companies can use these patents by paying a licensing fee to Ford (Brachmann, 2015). Such sharing of new technology has also been observed in the logistics industry. For example, Sealand, a container shipping firm, has decided to share its newly patented design of stackable shipping containers with other container shipping firms. The reason is that this could help increase the demand for such containers and various third-party vendors can build compatible containers (Scott, 2015). Intrigued by the above examples in business, we consider the problem where an innovator firm that owns a novel technology licenses it to a rival firm. 1 Often, the innovator firm shares its new technology innovation with rival firms under the usagebased licensing contract. For example, in the automobile industry, innovator firms typically license their vehicle charging technologies to licensee firms via signing usage-based contracts with the latter (Digit press release, 2016). It is noted that Toyota uses the usage-based contract to license its new technology (NDTV Auto, 2016). In another example, Monsanto, an agriculture technology firm, licenses the use of its new technology-based seeds to companies through the usage-based contract (Bunge & Mukherji, 2016). In addition, in the literature, there is empirical evidence on the application of the usage-based contract for new technology licensing (see, for example, Macho-Stadler et al., 1996;Rostoker, 1983). In this study, we consider the scenario where the rival firm pays the innovator firm a unit price for each unit of the final product produced using the latter's new technology.
In practice, consumer's utility is often characterized by the indirect network effect, i.e. the size of the network of consumers that adopts a particular technology affects the consumer utility of using the technology. In the case of the automobile industry, if the size of the network of consumers that adopts a particular kind of vehicle technology (e.g. electric, gasoline-powered, hybrid, etc.) is small, the consumer has fewer reasons to adopt the technology because without having enough fuel stations in the geographical market, the consumer's search/travel cost (to re-fuel the vehicle) increases, so derived utility decreases. On the other hand, the existence of a large network of users makes long-distance travel practical as the number of charging/refueling stations is large.
The network effect is not only confined to the downstream market but can also exist in the upstream market. The existence of a large network of electric car users will not only benefit the downstream consumers but will also motivate the upstream suppliers to invest in the capacity required to supply the inputs for the manufacturing of electric vehicles. This will lower the variable production cost of the automobile manufacturers due to the larger volumes of orders for electric car components. For example, a large network of electric vehicles and hybrid vehicles benefits Tesla due to the emergence of a network of supporting businesses such as car charging stations and mechanics (Hardy, 2015). Furthermore, various firms on the supply side will make significant investments, which will reduce the cost of the other inputs required for the manufacturing of electric/hybrid vehicles (Inagaki, 2015). Therefore, in this research, we incorporate the network effect and upstream economies of scale into our model setting.
While using the innovator firm's new technology, the rival firm needs to decide the optimal design level of its new product. In determining the design features of its new product, the rival firm needs to consider the present offering by the innovator firm (downstream market competitor) and its own existing product manufactured using traditional technology. Ideally, while deciding the new product features, the rival firm seeks to minimize the cannibalization of its existing product, while at the same time wishing to attract a large number of customers that prefers its new product to the competitor's offering. Also, in the downstream market, there is high customer taste heterogeneity. For example, in the automobile industry, consumer taste is heterogeneous in terms of car features, design, technology (new electric, old gasoline-powered or hybrid technology), and ergonomics. Hence, it is important for the rival (licensee) firm to consider market heterogeneity while deciding the optimal design level of its new product. In our paper, we also study how the rival firm decides the optimal design features of its new product.
In view of the above observations, we set out to address the various issues raised by building a model involving two firms that manufacture electric and gasoline-powered vehicles in the automobile sector. The first firm is an innovator that owns the electric vehicle technology, so it produces electric cars. The innovator firm licenses its electric car technology to another firm that produces cars using the conventional gasoline technology through the usage-based licensing contract. The licensee firm that initially produces gasoline-powered cars now invests in developing a hybrid car using the licensed new technology. Finally, there is price competition between the two firms in the downstream market. In such a competition setting, we attempt to answer the following research questions: What is the optimal usage-based licensing fee that the innovator firm should charge the rival firm for using its new technology to develop a new product? What are the optimal design features of the hybrid car that the rival firm should develop using the licensed technology? What are the impacts of the network effect and economies of scale on the rival firm's optimal design decision?
First, we analyze the scenario when the downstream market is highly competitive, and therefore, we observe the complete market coverage. Then, later we consider another extreme case when firms are local monopolists, and therefore, the market is partially covered. Under the complete market coverage scenario, our analysis reveals that as the downstream network effect of the new product increases, the innovator firm decreases the unit licensing fee. Furthermore, we find that when the downstream network effect is high, the product differentiation between the rival firm and innovator firm increases. We also find that large upstream scale economies also lead to a low licensing fee and high product differentiation.
Next, we analyze the impact of the network effects of the rival's existing product (or the network effects of the conventional technology). We find that higher network effects of the rival's product lead to a lower licensing fee. Interestingly, we find that product differentiation between the rival's new product and the innovator's product may increase or decrease with the rival product's network effects. We also find that a higher new product design cost structure at the rival's end leads to a higher licensing fee. Furthermore, a higher product design cost structure leads to higher product differentiation between the innovator's product and the rival's new product.
Finally, it is important to understand the impact of customers' product preference sensitivity to buying products other than their preference points. Interestingly, if the downstream market customer base is highly sensitive, then the innovator firm tends to charge a high licensing fee. In addition, we find that if the downstream market customer sensitivity increases, then product differentiation between the innovator's product and the rival's new product may increase or decrease under certain conditions.
Later in the paper, we also analyze the case when the firms are local monopolists and there exist some customers who do not purchase any of the available products. We again find that high economies of scale and high network effects of new technology may lead to lower technology licensing fees. Interestingly, we find that the design decision (extent of the product differentiation between the rival's new product and the innovator's product) is not impacted by the downstream market parameters like network effects and the upstream market parameters like scale economies. This is because, since the firms are local monopolists, the newly designed rival's product does not impact the segment of customers that purchases other competing products.
We organize the rest of the paper as follows: In Section 2, we briefly review the closely related literature to identify the research gap and position our paper. In Section 3, we introduce the model, together with the corresponding notation and assumptions. In the next section, we characterize the Nash equilibrium of the competition between the innovator and rival firms when the rival firm introduces a differentiated product (hybrid car) in the downstream market. We present numerical studies and insights in Section 5. In Section 6, we consider the case when firms are local monopolists, and there is partial coverage in the downstream market. Finally, we conclude the paper and suggest topics for future research in the last section. We present all the proofs in the Appendix C of the online supplement.

Literature review
Three streams of research are closely related to our study. The first stream pertains to technology licensing, which examines the design of licensing contracts and reasons for new technology licensing. The second stream studies pricing competition in the presence of the network effect. The third stream of research deals with the innovator firm's new product design decision. We briefly review the related works and position our paper in the research literature. Arora and Fosfuri (2003), Rockett (1990), and Gallini and Winter (1985) studied the reasons for new technology licensing. There are papers that consider the design of the licensing contract (Kamien & Tauman, 2002). There are studies considering an upstream firm licensing its new technology to a downstream firm, which include Kamien and Tauman (1986), and Katz and Shapiro (1985). Gaimon (2008) discussed the literature studying the issues faced by a firm that can either commercialize its new technology or license it to other firms. Erat et al. (2013) studied the case where an upstream technology provider licenses its new technology to the end-product manufacturer. Savva and Scholtes (2014) studied the contractual arrangements for co-development, licensing, and codevelopment with opt-out options for joint new product development between an innovator and a large technology firm. Zhang et al. (2018) studied technology licensing in a supply chain under the R&D investment cost-sharing contract. Song et al. (2015) using agent-based modelling studied the competition between firms offering products through fixed-fee perpetual and subscription licensing strategies. Wu and Kao (2018) investigated cooperative mechanisms between a manufacturing and a re-manufacturing firm where technology is licensed under the usage-based contract and technology is co-developed in the R&D joint venture setting. Sun et al. (2004) studied technology licensing under the network effect. However, unlike us, they did not consider new product development investments by the rival firm.

New technology licensing
Recently, Wu (2018) studied competition between an innovating firm and a non-innovating firm under technology licensing. They are different from our work as they did not consider the downstream market network effect and the design decision of the licensee firm. Hu et al. (2017) analyzed new technology licensing under upstream investment decisions. Unlike them, we analyze the impacts of the downstream network effect on the innovator firm's unit licensing fee and the rival firm's product design decision.

Product pricing under network effects
We refer the reader to Farrell and Klemperer (2007) for a comprehensive review of the literature on the pricing decision under the network effect. Katz and Shapiro (1985) considered the positive network effect where the consumer's willingness to pay for a product goes up when others procure the same product. We also consider such a positive network effect. Katz (2005) studied the impact of the network effect on software piracy. Lee and Mendelson (2007) modelled the competition between two firms selling a proprietary product in a multi-segment market characterized by the network effect. They found that given simultaneous entry, customers are better off with incompatible products, while the competing firms are often better off by making their products compatible to reduce the competition of a networked market.
Li (2021) studies product quality and pricing decision under network externalities in monopoly setting. Like them, we also consider the scenario where market demand is impacted by network size. However, in our study, we consider a downstream market structure with competing differentiated products. Li and Chen (2012), similar to our paper, adopted the Hotelling setting involving two sellers exogenously located at the end points to model customer choices between two products under the linear network effect. However, they did not consider the issue of licensing new technology to a competitor seller, which is the crux of our paper.

New product design
We refer the reader to Krishnan and Zhu (2006), and Yang et al. (2008) for reviews of research on product design decisions. We also refer the reader to Zhang (2014) for a comprehensive review of the literature on product configuration. Zhu and He (2017) studied green product design under price competition and greenness competition. Zhang et al. (2017) studied the impact of the development cost on firms' product design strategy and environmental performance. Liu et al. (2018) studied the impact of supply chain integration capabilities on the adoption of the green product design strategy. Zhu et al. (2016) studied the design of the service modes of re-manufactured products. Gmelin and Seuring (2014) elaborated on the issues concerning the integration of sustainability with new product design and development. Shen et al. (2016) studied design enhancement decision under OEM and ODM supply chain structures. Van den Broeke et al. (2018) studied the platform design strategy by considering the tradeoff between investment and production customization. Lee et al. (2019) using agent simulation and ordinal optimization determined the optimal product design decisions. Unlike these studies, we consider the rival firm's product design decision under new technology licensing. Liu et al. (2010) presented a framework to modularize the product family architecture. Kumar et al. (2009) presented a market segmentation based approach to product family design. Albritton and McMullen (2007) applied ant colony optimization to optimize product design. Sadeghi and Zandieh (2011) studied product portfolio management under competition. In contrast, in our model, we consider competition, as well as both upstream economies of scale and the downstream network effect, and study their implications for the innovator firm's pricing decision, i.e. the decision on the technology licensing fee, and for the rival firm's new product design decision. In a recent work, Chakraborty et al. (2021) study the impact of green tax and subsidiary on the demand of electric and gasoline vehicles. Like them, we also consider differentiated products, namely hybrid, electric and gasoline cars. Unlike them, we consider licensing of new technology (electric technology) which is the crux of our paper.
In summary, the above studies on the network effect do not consider the case where a firm competes with another firm to which it licenses its new technology, whereas we focus on such competition. Unlike the studies on new technology licensing reviewed above, we also examine the optimal design features of the new product that the competitor firm develops using the licensed technology.

Upstream market structure
We consider two profit-maximizing firms competing in the automobile market, which we denote as firm i, i 2 fE, Gg, where E denotes the (innovator) firm that produces electric cars (or Product E) and G denotes the (licensee/rival) firm that produces gasoline-powered cars (or Product G). Firm E owns the electric car technology (through a prior patent) and decides to share the technology with its competitor firm G. Then, firm G uses the licensed technology to develop a new product (hybrid cars or Product H) to compete with both electric and gasoline-powered cars. Firm G will incur a fixed cost in developing the new product. It should be noted that we do not model the case where the innovator firm also sells gasoline-powered cars as this will greatly complicate the analysis. The focus of our study is on characterizing the unit licensing fee of the electric car technology. Therefore, we do not consider the competition of gasoline-powered cars. In the final downstream market, firm G sells its hybrid cars and gasoline-powered cars at prices P H and P G , respectively, while firm E sells its electric cars at price P E : As mentioned above, throughout the paper, we denote the electric, hybrid, and gasoline cars by products E, H, and G, respectively.

New technology licensing contract
As motivated in the Introduction section, in our model, firm G pays firm E a unit usage fee w L on each unit of the new product sold using the new technology licensed from the latter, i.e. if firm G sells n units of the new product it develops using the licensed technology, then firm G needs to pay an amount n:w L to firm E.

Downstream market structure
We assume a market of size M consisting of a continuum of homogeneous consumers. The consumers' preferences differ along one dimension of the design features x such that 0 x 1, i.e. the consumers are uniformly distributed over a unidimensional space of the design features, defined by the Hotelling interval ½0, 1: We refer to dimension x as a specific design feature along which the two firms' products are horizontally differentiated. Specifically, we assume that firm E's electric cars are located at 0 and firm G's gasolinepowered cars are located at 1. If both firms' products are sold at the same price, some customers will choose firm E's product while the others will choose firm G's product because they rank the specific design feature differently. This horizontal differentiation reflects consumers' taste heterogeneity in terms of features, design, and ergonomics; particularly, consumers' preferences for a specific technology used in the car (electric, hybrid, or gasoline-powered) in the context of this study. By a hybrid car, we mean a vehicle that combines the technology of the gasoline engine as well as the electric car.
We assume that the disutility of a customer purchasing a car with a design feature other than his/ her ideal design feature is linear in the distance along the Hotelling interval defined above, with a slope t > 0. If t is large, then the customers' willingness to buy a product other than his/her ideal design feature is low. The assumption of the linear Hotelling cost structure is consistent with the previous literature (Shao et al. 2013;.

New product design decision and design cost structure
When firm G invests in the new technology to develop a new product H (say, a hybrid car), it decides the design feature of the product and locates it at h, along the x dimension in the Hotelling interval ½0, 1: In doing so, the firm incurs a fixed investment cost bð1ÀhÞ 2 : Since firm G is specialized in producing the product at location x ¼ 1, the more it deviates from its inherent design specialization, the higher will be the fixed investment cost. Furthermore, for analytical tractability, we assume that the cost structure is quadratic. This assumption is consistent with the product design investment literature (Krishnan & Zhu, 2006;Zhang et al., 2017). In our model, b can be interpreted as the measure of the efficiency of the firm during the design phase. If b is small, the design cost structure is low, so the firm is more efficient.

Downstream market network effects
As the network of consumers using a product increases, the utility of the consumers adopting the product increases, we consider such an indirect network effect in our model. The benefits due to the indirect network effect reflect the networks of electric charging and gasoline re-fueling stations, which make long-distance travel with electric and gasolinepowered cars practical. A larger volume of a particular type of car used by customers will lead to a greater number of charging/refueling stations (for that type) installed by other external business entities. With a large network of charging/re-fueling stations, the consumers would derive higher utility due to such a network effect. Li et al. (2017) provided empirical evidence of such an indirect network effect. They showed that, due to the indirect network effect, a 10% increase in the network size increases the electric/hybrid vehicle adoption rate by 8.4%. Such a rapid expansion of the network of charging stations is due to the collaboration between the innovator firm and fueling infrastructure firms, and the supportive actions adopted by government agencies. 2 Given that a fraction of the customers s buy firm E's product and firm G's hybrid car, we assume that the derived utility of the consumer from purchasing firm E's product is R þ k E ðsÞ: Next, given a fraction of the customers s buying firm G's gasoline car, we assume that the derived utility of the consumer from purchasing the gasoline car is R þ k G ðsÞ: Finally, given that a fraction of the customers s buys firm E's product and firm G's hybrid car, we assume that the derived utility of the consumer from purchasing the hybrid car is R þ k E ðsÞ: R is the maximum utility of the product with a zero network size. 3 k E ðsÞ is the additional utility of the customer due to the size of the network for the electric and hybrid vehicle products purchased by firm E and firm G. Furthermore, k G ðsÞ is the additional utility of the customer due to the size of the network for the gasoline vehicle product purchased by firm G. In our model, k i indicates the consumer's marginal valuation due to the network size. Initially, in the paper, we assume that R is sufficiently large so that no customer derives negative utility from consuming a product. In other words, all the customers buy the car. This assumption of complete market coverage is consistent with the previous literature (Liu & Tyagi, 2011;Liu & Zhang, 2006;Wang et al., 2021). However, in Section 6, we also consider the case where R is very low such that the market is partially covered.
Also note that we assume that the network effects due to purchasing a hybrid car and an electric car are the same because both use the electric car technology. It should be noted that we consider the global network effect within a class of technology group, i.e. even if a consumer adopts a competing product within the same technological group (e.g. electric and hybrid cars), the utility of the other consumers also increases. However, if the consumer adopts a gasoline-powered car (a product in a different technology segment), the utility of the other consumers adopting the hybrid or electric cars will not increase because the technology is different, as distinct fuelling stations are required.

Customer utility function
As discussed above, the customer enjoys the utility given by R when it consumes any product. Furthermore, the customer incurs the disutility of purchasing a product with a design feature other than his/ her ideal design feature. In addition, the customer gains positive utility due to the network effects. Finally, the customer pays the selling price of the product. If a fraction p of all the customers opts for the electric car and a fraction q of all the customers opts for the hybrid cars, then under full market coverage, a fraction 1ÀpÀq of the customers will choose the gasoline car. Therefore, the net utility of the customer located at point x (the reference is point 0, where product E is located) on the Hotelling line under different product purchase scenarios is as follows: As mentioned in Section 3.5, k E and k G denote the marginal valuations due to the network sizes of the electric car technology (used in both product E and product H) and the gasoline car technology (used in product G), respectively.

Variable cost structure and economies of scale
Both firms incur variable costs for the production of their final products. The unit variable cost of electric/hybrid cars production is a decreasing function of the cumulative demand for thr hybrid cars and electric cars in the automobile market, i.e. we assume volume scale economies in the production of new technology products. As mentioned earlier, this is due to the fact that when the suppliers to these firms have larger volumes of orders for the electric car components, their production costs will reduce. Hence, they would charge lower prices to the buyers that produce the electric/hybrid cars, i.e. product E and product H in our model. We model this by assuming that the variable cost is v E ÀdðD E þ D H Þ, where D H and D E are the demands for the hybrid and electric cars, respectively, and d is the scale economies factor. We assume that the unit variable cost of gasoline-powered cars production is v G : Furthermore, we do not model such volume-cost reduction for the gasolinepowered cars because the market is mature and the (additional) economies of scale are insignificant.

Sequence of events
In summary, the time-line of the sequence of events of the competition game between the two firms is as follows: Event 1 : Firm E licenses the technology to firm G and decides the unit usage fee w L for licensing the new technology. Event 2 : Firm G invests in the new technology and decides the optimal design feature h, to position its product in the market and incurs an investment cost. Event 3 : Both firms E and G simultaneously decide the downstream market prices of their products. Firm G decides the prices of the hybrid car and gasoline-powered car P H and P G , respectively, while firm E decides the price of the electric car P E : Event 4 : Finally, the consumers decide to purchase the products, so the market shares are realized.
We present the game pictorially, along with all the relevant events, in Figure 1. Table 1 summarizes all the notations used this paper. In the following sections, we solve the above game-theoretic model of competition between the two firms by backward induction and characterize the Nash equilibrium outcome of the game.

Model analysis
In this section, we analyze the competition game between the two firms. We solve the game by backward induction. We first solve the customer's product selection problem. Then, we solve the downstream price competition problem, followed by determination of the optimal product positioning of hybrid car by firm G. Finally, we solve firm E's problem of determining the optimal unit licensing fee. We use the terms "increase," "decrease," "larger," and "smaller" in a weak sense throughout the paper.

Downstream market share equilibrium
We first solve the consumer's product selection problem and determine the competing firms' equilibrium market shares. Next, we present the analyses under three scenarios: (i) 0<h<1, (ii) h ¼ 1, and (iii) h ¼ 0. For the case where 0<h<1, firm G launches a hybrid car (product H) along with the existing gasoline-powered car (product G), and competes with the electric car (product E) of firm E. Let y be the fraction of customers that chooses product E and z be the cumulative fraction of customers that chooses either product E or product H (so 0<y<z). This means the fraction of customers that selects product G is 1Àz (see Figure 2). Then, the utility of the consumer (deciding between hybrid and electric car) located at point yð0<y<hÞ is The customer that is indifferent to buying product E and product H is located at y such that Similarly, the utility of a consumer (deciding between hybrid and gasoline car) located at point z (such that h<z<1) is The customer that is indifferent to buying product H and product G is located at z such that Solving (1) and (2), we obtain the equilibrium market shares as follows: Therefore, when 0<h<1, the equilibrium market demands for electric cars, hybrid cars, and gasolinepowered cars are yM, ðzÀyÞM, and ð1ÀzÞM, respectively. From the above expressions, it is evident that as P E increases, the market share of electric cars decreases, while the market share of hybrid cars increases. Similarly, as P G increases, the cumulative  Design factor of the hybrid car b Fixed investment cost parameter (while investing in hybrid cars) t Unit customer cost over the Hotelling line v G Unit production cost of gasoline-powered cars v E Unit production cost of hybrid or electrical cars with zero network size d Scale economies cost-reduction factor for the unit production cost of hybrid or electrical cars w L Unit fee of each product produced under the licensing contract market share of both electric and hybrid cars increases, while the market share of gasoline-powered cars decreases. As mentioned in Section 3.5, we assume that R is sufficiently large so that the customer will buy at least one of the product offerings. 4 This assumption of complete market coverage implies that purchasing a product is highly desirable for all the customers considered in the model; therefore, R is very high. Further, this also implies that the market is highly competitive, and therefore, customers could switch from one product to another in this scenario, that is, the presence of the competing products impacts the purchase decision of the customer. It should be noted that when h ¼ 1, firm G will not use the rival's new technology, so it will not introduce a hybrid car in the downstream market. In this case, firm G will not incur the fixed cost of new vehicle development and will compete in the downstream market only with gasoline-powered cars. This gives rise to the scenario of two-product competition between the electric and gasoline-powered cars (see Figure 3). Similar to the previous analysis of the case with three products, again we determine the market shares in the case with two products along the Hotelling interval ½0, 1: Let u be the fraction of customers that chooses product E. The utility of the consumer located at point u is The customer that is indifferent to buying product E and product G is located at u such that Solving (3), we obtain the threshold for the equilibrium market shares as follows: Hence, for this case, the equilibrium market demands for electric and gasoline-powered cars are uM and ð1ÀuÞM, respectively.
Next, we consider the case where the rival firm introduces a product that is identical to firm E's product, i.e. a pure electric vehicle. In this case, h ¼ 0 in our model setup. The customers are uniformly distributed over the Hotelling line 0, 1 ½ : We assume that firm E's and firm G's electric vehicles are located at 0. Furthermore, firm G's gasoline vehicle is located at 1. Since there is no differentiation between firm E's electric car and firm G's electric car, the prices of both cars in the downstream market should be the same (due to Bertrand competition with no differentiation). We denote the price of the electric vehicle by P E : Moreover, since the electric vehicles of both E and G are identical, the total market share of the electric vehicle will be equally split between firm E and firm G (see Figure 4). Let x be the fraction of customers that chooses the electric car, so the remaining fraction of customers 1Àx will choose the gasoline car. The utility of the customer located at x is RÀtx þ xk E ÀP E if he=she prefers product E, RÀtð1ÀxÞ þ ð1ÀxÞk G ÀP G if he=she prefers product G: The customer that is indifferent to buying product E and product G is located at x such that RÀtx þ xk E ÀP E ¼ RÀtð1ÀxÞ þ ð1ÀxÞk G ÀP G :  Therefore, we have The equilibrium market demand for firm E's electric car is Mx 2 : Furthermore, the demand for firm G's electric car is Mx 2 : Finally, the demand for firm G 0 s gasoline car is Mð1 À xÞ: Overall, we derive the demand for the electric car of firm E ðD EE Þ, and the demands for the gasoline car of firm G ðD G Þ, the electric car of firm G ðD EG Þ, and the hybrid car of firm G ðD H Þ as follows: when 0<h<1, 0 when h ¼ 1: Next, we state the firms' payoff functions and determine the optimal pricing strategy, product design decision, and contract parameters. The payoff functions of both firms are as follows: For the case where h ¼ 0, in the payoff function of firm G, D EG P E þ D G P G is the revenue from selling electric and gasoline cars.
ÞÞ is the total production cost for both kinds of cars. For firm E, D EE P E is the revenue from selling electric cars and D EE ðv E À dðD EE þ D EG ÞÞ is the total production cost for electric cars. Finally, D EG w L is the total licensing fee paid by firm G to firm E for using the electric car technology for producing D EG units of the electric car. Furthermore, when 0<h<1, D G P G þ D H P H is firm G's revenue from selling hybrid and gasoline cars, and D G v G þ D H ðv E À dðD EE þ D H ÞÞ is the total production cost for both kinds of cars.
For firm E, D EE P E is the revenue from selling electric cars and D EE ðv E À dðD H þ D EE ÞÞ is the total production cost for electric cars. Finally, D H w L is the total licensing fee paid by firm G to firm E for using the electric car technology for producing D H units of the electric car. Finally, when h ¼ 1, firm G will not introduce the electric car technology based product in the market. Hence, for this two-product competition case, firm G's payoff is D G P G ÀD G v G and firm E's payoff is D EE P E ÀD EE ðv E À dD EE Þ:

Downstream pricing game
Next, in Proposition 1, we state the Nash equilibrium of the pricing game between firm G and firm E.
Proposition 1: The equilibrium downstream market prices are as follows: When h ¼ 0, we have Furthermore, when 0<h<1, we have . Consumer preference line: Product G competes with product E offered by both firms E and firm G.
From the above expressions, we note that @P G @k E <0, @P H @k G >0, and @P E @k G >0, i.e. as the network effect of electric/hybrid cars increases, the price of the gasoline-powered car decreases. However, as the network effect of the gasoline-powered car increases, the prices of both hybrid and electric cars increase. This result is not so intuitive as one would expect the prices of products H and E to be lower to attract customers to buy hybrid/electric cars. The reason is that since firm G is selling both hybrid and gasoline cars, it would like to increase the price of the hybrid car and sell it like an expensive car with a low demand (hence earning a higher margin). Similarly, firm E also increases the price and earns a higher margin from selling the electric car. Performing further analysis of the price equilibrium, we obtain the following result.
Proposition 2: As the unit licensing fee w L increases, the prices of all the three products increase.
The above result implies that as the unit licensing fee increases, the price of the hybrid car increases. Since the hybrid car is expensive, firm E increases the price of the electric car. Furthermore, we find that firm G also increases the price of the gasolinepowered car because the market price of the product developed based on the competing technology is high. The increased price of the gasoline car may not lead to customers switching to buy the hybrid car because the price of the hybrid car has also increased. This insight is interesting because the above insight suggests that if the licensing fee of the new technology is high, then it leads to an increase in the market prices of the products developed based on both the new and conventional technologies. This is especially true when the customers derive a very high utility value from all the competing products in the market, i.e. R is very high such that everyone buys the product. Next, we provide insights on the impact of product differentiation and the customer cost of choosing a non-preferred product design. For analytical tractability, we normalize the scale economies cost parameter to zero.
Proposition 3: Given that firm G decides to design its hybrid cars at Hotelling line location h and w L is firm E's unit licensing fee, the following hold: a. As h increases, P G and P H decrease, whereas P E increases. b. As t increases, the prices of all the three products increase.
From Proposition 3(a), as h increases, the differentiation between the hybrid and electric cars increases, so it makes sense for firm E to increase the electric car's price. However, as h increases, the differentiation between the hybrid and gasoline cars decreases. Due to the lower level of differentiation, firm G lowers the prices of both hybrid and gasoline cars. The intuition behind this is that in a high range of h, firm G tries to grasp a larger market share of the electric/hybrid car segment by reducing P H : Furthermore, since the price of the hybrid car is low, firm G also decreases the price of the gasolinepowered car to increase the sales volume of this market segment. Next in Proposition 3(b), we find that as customers' cost t increases, the prices of all the products in the market increase, i.e. if t increases, the customer's disutility from purchasing the product far away from his/her preferred design increases. Therefore, the firms strategically increase the prices of all the products in the market. One would expect that with an increase in t, since customers' disutility increases, the firm should decrease its product price to encourage customers to purchase its product. However, in our setting, the customers derive a high utility value from the product (R is very high and the market is fully covered). Therefore, an increase in the price of the product does not encourage the customer to buy the competing product. This is because the prices of all the competing products increase with t.

Firm G's optimal product design strategy
Next, having established the downstream Nash equilibrium, we study the optimal product positioning problem of firm G when it decides to invest in the hybrid car technology ðh < 1Þ: For this case, the firms will attain the price equilibrium as derived in Proposition 1. The payoff of firm G is as follows: Þ À DHwLÀbð1ÀhÞ 2 when 0<h<1 ( In the above expression, when 0<h<1, bð1ÀhÞ 2 is the investment cost incurred for the development of the hybrid car. Furthermore, when h ¼ 0, the investment cost incurred by firm G to develop electric cars is bð1Þ 2 : Given the licensing fee w L , the optimal design level for firm G is h Ã ðw L Þ 2 argmax p G f g : Solving the above optimization problem, we obtain the optimal product positioning of firm G as follows: As w L increases, the optimal product design decision decreases. Proposition 4(a) states the equilibrium design decision of firm G. It is noted that the above expression is increasing in b, i.e. as b increases, firm G invests in a less differentiated product as compared with firm E. Furthermore, if b is very large, h tends towards 1. Proposition 4(b) implies that as the unit licensing fee charged by firm E increases, firm G invests in a less differentiated hybrid product. The reason is if the licensing fee decreases, the unit margin of offering the hybrid car increases. Therefore, overall, the profit of firm G's hybrid product line increases. Therefore, to further increase the electric and hybrid product network sizes, firm G offers a highly differentiated product in a lower range of the licensing fee.

Determination of firm E's optimal unit licensing fee
We now solve firm E's problem of determining its optimal licensing fee to charge firm G. Firm E's optimization problem is as follows: We have derived the analytical expressions for the solution to the above optimization problem. However, due to the large number of parameters, we only analyze the equilibrium for the case where the production cost is normalized to zero and the market size is normalized to 1. Later, we conduct numerical studies without these parameter restrictions. We formally state the equilibrium of this case as follows: Proposition 5: The optimal licensing fee decided by firm E is as follows: Under the condition p E ðh 6 ¼ 0, 2 þ4k 2 G ðtÀ18bÞ 2 þ6kE t À648b 2 À11t 2 þ189bt where Q ¼ t 2 ð5184b 2 þ259t 2 À2304btÞÀ2tk G ð2592b 2 þ35t 2 À720btÞ: Otherwise, under the condition In Proposition 5, we characterize the optimal licensing fee. Due to the complexity of the obtained expressions, we provide in the next section further details on the behaviour of the characterized equilibrium through numerical studies.

Numerical studies and practical insights
Next, through numerical studies, we further elaborate on the impacts of the various model parameters on the firms' decisions. First, we study the impacts of the network effect of electric and hybrid vehicles. Our analysis reveals that as the consumer's marginal valuation due to the size of the electric/hybrid cars network k E increases, firm E's licensing fee decreases. In a very high range of k E , it makes sense for firm E to license its new technology free of charge (see Figure 5(a)). The reason is that by reducing the new technology pricing when the network effects are very high, firm E increases the demand for its own electric vehicle (more customers buy the electric vehicle when k E is high).
Furthermore, as k E increases, it is optimal for firm G to develop a highly differentiated hybrid car from firm E's electric cars (see Figure 5(b)). The intuition behind this is that by designing a highly differentiated product, the firm increases the network sizes of the hybrid and electric cars (which further increases the consumer's utility). Overall, firm G benefits as it earns high profit due to the hybrid car's high-volume sales. Since firm E's electric car is highly differentiated as compared with firm G's hybrid car, higher network effects also increase the demand for the electric cars. Due to the high volume sales of the electric and hybrid cars, we find that the gasoline cars' demand is low when the network effects are high.
In our numerical studies, we observe that the price of the electric car is lower than that of the hybrid and gasoline cars (see Figure 5(c)). The reason is that firm G strategically charges a higher gasoline car price because it maximizes its profit by earning a high margin from the gasoline car's lower market volume. Interestingly, we find that the price of the hybrid car is higher when k E is very high. However, the gasoline car's price is higher when k E is low. The reason is that when k E is very high, firm E increases the price of the electric car, so firm G does not drastically reduce the price of the hybrid car. In our setting, R is very high (the market is completely covered); therefore, setting high price does not lead to a drastic decrease in the demand for product H. However, it reduces the price of the gasoline car at a higher rate to increase the demand. As k E increases, the prices of hybrid and gasolinepowered cars decrease, whereas the price of the electric car decreases, and beyond a certain threshold of k E , the price of the electric car increases. The reason is that at very high k E , the network sizes of both the hybrid and electric cars are large, so it makes sense for firm E to charge high prices.
Interestingly, in our analysis, we find that as k E increases, the profit of firm G decreases (see Figure  5(d)). However, the profit of firm E decreases until a threshold, beyond which it increases. The intuition is that, due to the high network effect of the electric car, the demand for the gasoline car reduces, which reduces the overall profit of firm G. However, when k E is in a lower range, and when it increases, the profit of the electric car firm reduces because it does not get much network effect demand benefit and, at the same time, it starts charging a lower licencing fee to the rival firm. However, when k E is very high, even if firm E shares the patent with the rival for free, firm E makes a high profit due to a high volume of the electric car sold because of the high network effect and high margin on the sale of the electric car (due to the high scale economies effect).
The above insights have interesting implications for innovator firms like Tesla. Our study reveals that in the short-run (when the network effect of a new technology may not be very large), due to sharing of the new technology, the innovator firm may experience some decline in profit even if the network effect increases. This is due to the increased market competition and a lower price of the new technology license. However, in the long term (when the network effect is very large), the profit of the innovator firm will increase due to a high market share and a lower cost structure even if it shares the new technology with the rival for free.
Next, we study the impact of the design cost structure on the technology pricing and the rival's design decisions (see Figure 6). Our analysis reveals that as b increases, the new technology licence fee increases (see Figure 6(a)). Furthermore, we find that the innovator licenses the new technology to the rival firm free of cost in a very low range of the design cost parameter. The reason is, if the design cost is very high, then the rival tends to offer a highly differentiated product from the electric vehicle (see Figure 6(b)). Overall, the market size of both electric car and hybrid car is high. Therefore, when b is high, firm E strategically charges high technology licensing price to earn high profit from the downstream rival's market.
Furthermore, we find that as b increases, the price of the electric car increases (see Figure 6(c)). The reason is that in a high range of b, firm G's hybrid car is highly differentiated, so it makes sense for firm E to increase the price of the electric car.
Next, we find that the price of the gasoline car decreases with b. This is because of the lower differentiation between the hybrid and gasoline cars; by reducing its gasoline car price, it tries to increase the demand. Interestingly, we find that, as b increases, the price of the hybrid car decreases until a threshold value, beyond which it increases. One would expect that as b increases, the firm should decrease the price of the hybrid car due to the lower cost of technology. However, we find that this is not always the case. The reason is that when b is very high, the price of the electric car is high, due to high differentiation between the electric and hybrid cars, firm G strategically increases the price of the hybrid car (this is also driven by the fact that the market is highly competitive and all the customers will buy a product). On the other extreme, when b is very low, firm G strategically increases the prices of both the gasoline and hybrid cars to earn high margins from a large market of gasoline and hybrid Figure 6. Impact of design cost structure ðbÞ on firms' decisions and payoffs.
car buyers. Due to the above pricing strategy, we observe that in a low range of b, the price of the gasoline car is higher than that of the hybrid car. However, in a high range of b, the price of the hybrid car is higher than that of the gasoline car.
Moreover, the profit of firm E increases with increase in b (see Figure 6(d)). The reason is due to the higher differentiation between the electric and hybrid cars, the market price and the demand for the electric car are high in a high range of b. Interestingly, as b increases, the profit of firm G decreases until a threshold, beyond which it increases. This is because when b is high, the profits are high due to the higher price of the hybrid car. On the other extreme, when b is in a very low range, then the profit is high due to the higher price of the gasoline car.
The above insights have interesting implications. Based on our analysis, one might expect that if the design cost structure of the rival firm is high, then the rival firm tends to offer a less differentiated product in its existing offerings and a more differentiated product to compete with the innovator's product. Therefore, the innovator may charge a high price for the new technology licence when the design cost structure is high. In fact, if the design cost structure is low, then it is possible that the innovator may share its technology for free of cost. Finally, we find that the innovator firm makes a greater profit by sharing the new technology, for which the rival's design cost structure is higher.
We also study the impact of the upstream economies of scale parameter d (see Figure 7). We find that, as the scale economies parameter increases, firm E's licensing fee decreases (see Figure 7(a)). This makes sense as due to the large upstream scale economies, firm E would like to expand the network of hybrid and electric cars, by lowering its licensing fee to the extent that the fee is zero in a high range of d.
Furthermore, we find that, as d increases, it is optimal for firm G to increase the differentiation of its hybrid car from firm E's electric car (see Figure  7(b)). This is because with an increase in d, the prices of the hybrid and electric cars fall, and the market price increases, which further increases the demands for the electric and hybrid segments (see Figure 7(c)). Now, by designing a highly differentiated product, the firm increases the network sizes of the hybrid and electric cars. Overall, by doing so, firm E generates high revenues from high-volume sales of the electric car and also obtains high margins because of lower production costs. We also find that, as the scale economies parameter increases, the profit of firm E increases, and firm G's profit decreases (see Figure 7(d)).
Next, we study the impact of the customer's travel cost (from its ideal product design choice) (see Figure 8). In our model, cost t may be interpreted as customers' sensitivity to buying products located at points other than their preference points (Katewa & Jain, 2020). Thus, if t is high, then the customers are highly sensitive, whereas if t is low, then the customers are less sensitive. Our analysis reveals that as the customer cost parameter t increases, the licensing cost of the new technology increases. Furthermore, if the customer is less sensitive, i.e. t is very low, then it is possible for the innovator firm to share the new technology for free with the rival firm (see Figure 8(a)).
Our analysis further reveals that as the customer's travel cost increases, the degree of product differentiation between the electric and hybrid cars decreases (h decreases) if and only if product differentiation is above a threshold value (see Figure  8(b)). The reason is that if the customers are highly sensitive (i.e. t is very high and is above the threshold value), then by positioning a less differentiated hybrid car from the electric car, firm G tries to increase the demand of its hybrid car and lower the demand for the electric car. However, when t is below a threshold value, by decreasing product differentiation (with a decrease in t), firm G strategically tries to increase the market demand for the gasoline car.
Through our analysis, we observe that as t increases, the prices of all the products in the market increase (see Figure 8(c)) (also discussed earlier in Proposition 3(b)). The reason is that when t is high, differentiation between the hybrid and gasoline cars is low. Therefore, firm G increases the prices of both product offerings to increase its profit. Moreover, since the price of the hybrid car is high, firm E also increases the price of the electric car (due to complete market coverage). Finally, we find that, as t increases, the profits of both firms E and G increase (see Figure 8(d)). This is due to the high product prices in a high range of t.
Based on our insights, it is important for the innovator firm to understand the downstream market customers' profile. If the customers are highly sensitive to the type of product offering, then the innovator firm should charge a high price for the new technology. However, if the customers are less sensitive, then the innovator firm may consider sharing the new technology with the rival for free. Interestingly, our analysis reveals that the innovator firm earns a higher profit if the customer base consuming the product based on the new technology is highly sensitive (or the travel cost is high).
Finally, we study the impact of the network effect of the competing technology (see Figure 9). In our analysis, we find that, as k G increases, the equilibrium licensing fee decreases. In a high range of k G , we find that it makes sense for firm E to license the new technology free (see Figure 9(a)). Due to the high network effect of the gasoline car, the tendency of the customers is to buy the gasoline car, so by strategically lowering the licensing fee, firm E motivates firm G to increase the demand for the hybrid car. Furthermore, firm E also decreases the price of the electric car to increase the demand for the electric car. Overall, firm E would benefit from a larger market size, which increases demand and reduces the cost structure.
Interestingly, we find that, as k G increases, the design differentiation (h) between the electric and hybrid cars increases until a threshold, beyond which it decreases (see Figure 9(b)). The reason is that in a low range of k G (below a threshold), by introducing a differentiated product, firm G tries to increase the market sizes of the electric and hybrid cars so as to make a higher profit from selling the hybrid car. However, when k G is very high (above a threshold), by reducing differentiation, firm G tries to increase the market size of the gasoline car. By doing so, it tends to make a higher profit from selling the gasoline car.
Overall, we find that as the network effect of the gasoline car increases, the prices of the electric and hybrid cars decrease (in a low range of k G ) (see Figure 9(c)). Since, the prices of the electric and hybrid cars are lower, firm G reduces the price of the gasoline car in a low range of k G : However, in a high range of k G , due to a strong network effect of the gasoline car, firm E again increases the price of the gasoline car. Next, we find that in a very high range of k G , the price of the gasoline car is higher than that of the hybrid car.
In our analysis, we find that, as k G increases, the profit of firm E decreases (see Figure 9(d)). This is because the market price of the electric car decreases with k G : Interestingly, we find that, as k G increases, the profit of firm G decreases until a threshold, beyond which it increases. The reason is that in a low range of k G , increasing the network effect of the gasoline car decreases the price of the hybrid car, which reduces the profit from selling the hybrid car. However, when k G is very high, increasing the network effect of the gasoline car increases its profit due to a high demand for the gasoline car as well as due to a high price of the gasoline car in the downstream market.
Please note that in all our numerical studies, we have also checked firms' payoffs when firm G does not introduce the new product in the market. We find that both firms are better off when firm G introduces the new product in the market.
Next, we briefly discuss the details of various robustness checks we perform in this study. Recall that we assume in our model that all three types of products have the same maximum utility with a zero network size R for the consumers. In the numerical studies, we check when all three products have different maximum utility with the zero network size. We find that all the above insights are robust. In our paper, we also assume that the electric and hybrid cars have the same variable cost structure. In another set of numerical studies, relaxing this assumption, we again find that our insights are robust. We also consider scale economies in gasoline cars production and we find that our insights are robust. In some of the results, we also consider the special case where d ¼ 0. It is noted that for those results, we also perform numerical studies for Figure 8. Impact of customer design sensitivity parameter (t) on firms' decisions and payoffs.
the case where d>0: Intuitively, our insights remain the same when d is non-zero.

What happens when the firms are local monopolists?
In the main model, we consider the case where R is very high, so the downstream market is completely covered. In this section, we consider another extreme scenario where R is very low, so there always exist customers that do not buy any product and the firms enjoy local monopoly. Similar to the above analysis, we solve the problem through backward induction. Next, we characterize the equilibrium downstream market shares. Similar to our analysis in Section 4, we were able to show that the demands for both firms' products are as follows: Þ when 0<h<1, and 0 when h ¼ 1: We provide the details on the derivation of the above demand expressions in Appendix B of the online supplement file. From the above expressions, we see that when 0<h<1, the demand for all the Figure 9. Impact of network effects of gasoline car ðk G Þ on firms' decisions and payoffs.
vehicles is not affected by the design parameter h of the hybrid car. In our model setup, firms are local monopolists, so customers which buy electric and gasoline cars are not affected by the hybrid car's design because R is very low and only customers who are very near to the location h would buy product H. Therefore, in this setup, the hybrid car design decision will not influence customers of electric or gasoline cars to purchase the hybrid car. Due to the above rationale, the payoffs of the players are not affected by h. Next, similar to Proposition 1 of the main model, Proposition 6 gives the pricing equilibrium in this setting.
Proposition 6: The equilibrium downstream market prices are as follows: When h ¼ 0, we have Furthermore, when 0<h<1, we have where L ¼ Rtð6d 2 M 2 À 11dMt þ 2t 2 Þ þk E Rð3k E ð5t À 6dMÞ À ðt À 3dMÞð11t À 2dMÞÞ, and Q ¼ Rtð3d 2 M 2 À 5dMt þ t 2 Þ þk E Rðk E ð6t À 9dMÞ Àðt À3dMÞð5t À dMÞÞ. Finally, when h ¼ 1, we have Similar to insights provided by Proposition 2, we find that as w L increases, the price of product H increases, however, the price of product E decreases. Furthermore, we find that w L does not impact the price of product G. This is because the demand for gasoline cars is only impacted by its own price and is independent of the pricing of rival products. Furthermore, if the technology licensing fee charged by firm E increases, the price of product H increases (due to the higher cost structure). Interestingly, the price of product E decreases with w L . The intuition is that by reducing the price of the electric car, the firm tries to increase the overall network size of the products developed based on the new technology. This further increases the demand for products E and H. Unlike the main model, the overall market expansion of the electric car technology is possible in this setting due to partial market coverage. Therefore, we observe such a strategy by firm E. Unlike the complete market coverage scenario, the customer sensitivity parameter t does not impact the price of gasoline cars. However, t affects the price of electric and hybrid cars.
As discussed above, unlike the main model in this setting, the payoff of firm G is not affected by the design parameter of product H. Due to customers preferring products nearest to their preference points, and faraway customers not purchasing the product, the gasoline firm may choose any h (as long as partial market coverage of all the products exists in our setup and firms enjoy local monopoly). Next, we solve firm E's optimal licensing problem when the scale economies parameter is normalized to zero.
Proposition 7: Under the local monopoly scenario, the equilibrium pricing of the new technology licence is as follows: Under the condition p E ðh 6 ¼ 0, From the above expression, we find that if firm G introduces hybrid vehicles in the market, then w L ¼ w Ã L1 : Furthermore, as the network size of the electric car technology increases, the equilibrium licensing fee decreases. The reason is that by charging a low licensing fee, firm E tries to increase the market size of firm E's hybrid cars (the price of the hybrid car will decrease due to the low cost of the technology). Overall, some new customers will be acquired by firm G that did not buy any product. Due to the high network effect, firm E's electric car market also expands (overall market coverage increases). However, when w L ¼ w Ã L2 , we see that network effects do not impact the licensing fee. The reason is that when h ¼ 0, the market of the electric car is split and does not expand as compared with the case where firm G does not introduce hybrid vehicle in the market. Similar to the main model, we find that as the customer sensitivity parameter (t) increases, the optimal licensing fee w Ã L1 increases. Finally, in the numerical studies, we also observe that the optimal licensing fee w Ã L1 decreases with the scale economics parameter.

Conclusions
In this study, we investigate the new technology licensing strategy for an innovator firm towards a rival firm. Based on a game model of competition between the two firms, we consider the problem where the rival firm uses the licensed technology to develop a new product to compete with the innovator firm in the downstream market. We characterize (i) the licensing fee charged by the innovator firm, (ii) the rival firm's optimal product design, and (iii) both firms' optimal downstream prices.
We find that as the downstream market network effect increases or the upstream scale economies (for electric/hybrid vehicle production) increase, the licensing fee decreases. In addition, differentiation between the cars of both firms increases. Furthermore, we find that as the new product's design cost structure increases, the optimal licensing fee increases. Moreover, we find that a higher new product design cost structure also leads to greater product differentiation between the innovator's product and the rival's new product. Interestingly, our analysis reveals that a higher network effect of the conventional technology (or the rival technology) product also motivates the innovator firm to reduce the licensing fee.
Furthermore, we find that as the rival technology's network effect increases, product differentiation increases until a threshold, beyond which it decreases. Our analysis reveals that higher customer disutility of purchasing the non-preferred product leads to a higher licensing fee. However, we find that higher customer utility may increase or decrease product differentiation.
Next, our analysis reveals that it makes sense for the electric car producer to share its innovation free of charge when the network effect is very large or when the upstream economies of scale are very large. We further find that a very low new product design cost structure at the rival's end or very low customer disutility of purchasing a non-preferred product may motivate the innovator to share the new technology license free of cost. We also find that a high network effect of the old technology might lead to free sharing of the new technology by the innovator. This provides the potential reasons for firms like Tesla and Toyota to share their new technologies with their competitors.
Later, in our paper, we also consider the case when the downstream market is partially covered and firms are local monopolists. We find that high network effects, low customer demand sensitivity, or high scale economies effects may lead to lower new technology licensing fees. Further, unlike the complete market coverage scenario, we find that the new product design decision is not impacted by the above upstream supply related and the downstream customer market factors. Table 2 summarizes our research findings and their managerial implications.
Our work is not without limitations. Our model setup incorporates supply-side scale economics and demand-side network effects and studies their impacts on product pricing, license pricing, and new product design. Future research can explore the impacts of other factors such as vertical product differentiation on the above decisions. Therefore, it is possible that if the electric car has higher product quality (due to vertical differentiation), the downstream price of the electric vehicle may be higher than that of the gasoline car. This may further impact the electric car technology license pricing. We believe this will add various new interesting insights into the new technology sharing literature. Furthermore, our analysis considers two extreme scenarios: either market is fully covered, or the firms are local monopolists. Future research can explore the scenario of the market competition with partial market coverage. It would be interesting to see if the insights of our analysis are robust.
Moreover, researchers may consider R&D collaboration between an innovator firm and a rival firm. This problem may be explored again using a threestage model. In the first stage, the innovator decides the licensing fee; then both firms make innovation efforts, either jointly or individually, that enhance (product) quality; and finally, there is downstream competition. Intuitively, we believe that if the rival firm is highly effective (or capable) in the collaboration stage, then there might be some conditions under which the innovator firm will share its technology for free. We suggest future research to address this interesting and challenging problem.