Sooner or Later? The Role of Adoption Timing in New Technology Introduction

Abstract

Motivated by several industry examples, we study the interaction between a technology provider introducing a new technology and downstream manufacturers adopting the new technology into their products. The manufacturers, once decided on their adoption timing, both cooperate in making demand‐boosting investments to promote the technology and compete in price in the product market. Our main objective is to explore the important question of how the technology provider manipulates manufacturers’ adoption timing. We develop a stylized continuous‐time multi‐stage game‐theoretic model with one technology provider and two downstream manufacturers, and derive pure‐strategy equilibria for the manufacturers and the technology provider. We find that in the absence of the technology provider's intervention, in equilibrium there is simultaneous adoption when the market competition is relatively mild, and sequential adoption otherwise. In particular, under the sequential‐adoption equilibrium, the second manufacturer strategically postpones adoption in order to freeride on the first manufacturer's demand‐boosting investment. We show that manufacturers’ equilibrium adoption timing is not always in line with the technology provider's interest. To align these different preferences, we suggest that when the competition is in a relatively mild region, the technology provider can make an initial investment to incentivize both manufacturers to adopt the technology early, whereas when the competition is relatively intense, an exclusive period should instead be offered to one manufacturer to keep the other from adopting the technology early. Interestingly, these self‐interested interventions often improve the efficiency of the system. Finally, we show that our main findings remain robust when we assume that the effect of manufacturers’ demand‐boosting investments decreases over time, or when we allow the technology provider to optimize over the technology's licensing fee.

Keywords

technology introduction technology adoption timing freeriding

Introduction

When a new technology is introduced, downstream manufacturers adopt the technology, develop products that feature the technology, and present them to the product market. Hence, the success of the new technology is heavily dependent on the products that embody the technology, and those products in turn rely on the unique technology to distinguish themselves from other products. In this study, we are interested in the interplay between the technology provider and the downstream manufacturers within the same technology ecosystem; specifically, we investigate manufacturers’ choice of adoption timing, potential interventions by the technology provider, and those interventions’ impact on the technology ecosystem that is comprised of both parties.

The adoption timing of downstream manufacturers can be critical to a successful new technology introduction, and at the same time has strategic significance to the manufacturers. For example, in 2009, China Mobile was granted a license to develop its 3G mobile network in China, using a Chinese‐owned internationally incompatible standard: TD‐SCDMA. The success of the new standard depended not only on its technical specifications, but also on the quality of available handsets that were made compatible with the TD‐SCDMA standard (Virki 2010). Hence, one challenge for China Mobile was to convince and incentivize handset manufacturers to adopt the new standard and invest in promoting TD‐SCDMA handsets. Although manufacturers understood that such investment would boost the prospect of TD‐SCDMA standard, they were also concerned about competition among themselves. As a result, some handset manufacturers such as ZTE and Lenovo chose to adopt the standard early, whereas others like Nokia decided to wait (MobileWorldLive 2009). Another example, that goes beyond the introduction of “intellectual technology” and the adoption of it onto a physical product, offers a similar flavor. During iPhone's first launch into the US market, AT&T (the “manufacturer”) was chosen by Apple (the “technology provider”) to be the exclusive network service provider (e.g., Siegler 2010). Whereas enjoying being a monopolist, AT&T also invested heavily in marketing campaigns for iPhone during that period of time. Later on when iPhones eventually became available in Sprint and T‐Mobile, the two firms only needed to invest very little in marketing iPhone, as consumers are already highly familiar with the product.

These two examples also demonstrate one distinct feature that strongly influences downstream manufacturers’ adoption timing decisions: cooperation coexisting with competition. In particular, besides competing with each other, downstream manufacturers within the same technology ecosystem also have the incentive to cooperate and promote the new technology, so that the overall consumer base for both manufacturers will be larger. This type of promotion corresponds to generic advertising (in contrast to brand advertising) in the marketing literature (e.g., Bass et al. 2005, Krishnamurthy 2000,2001), which is particularly effective in the introductory stage of the technology to increase consumers’ awareness of its uses and benefits. For instance, when P&G introduced Pampers diapers, it tried to enhance product acceptance by highlighting the advantages of using disposable diapers; similarly, De Beer's early advertisement campaign literally invented the concept of a diamond engagement ring by associating diamond with love and long‐term commitment (Bass et al. 2005). Importantly, both marketing campaigns have boosted not only demand for their own respective brands, but also that for other competitors. Likewise, during the introduction of TD‐SCDMA standard, ZTE and Lenovo's promotion of their handsets under the standard will raise consumers’ awareness of the new standard and its benefits, and hence increase the demand for later adopters such as Nokia. This spillover in marketing investment then makes it important for the manufacturers to decide when to adopt the new technology—whether to adopt it earlier to exploit the less competitive product market or to wait and freeride on the early adopter's investment.

We next take a closer look at the decisions of the technology provider in the two motivating examples. When iPhone was first introduced to the US market, Apple reportedly signed an exclusive 5‐year long deal with AT&T that excluded other network operators from carrying the iPhone (e.g., Siegler 2010); by contrast, China Mobile not only allowed multiple handset manufacturers to compete at the same time, but also on its own made a $6.6 billion investment in marketing and R&D with the goal of raising market awareness and attracting manufacturers to adopt the technology earlier (Virki 2010). Motivated by these different strategies in practice, we attempt to explain under what circumstances a technology provider should make an initial demand‐boosting investment herself to encourage all manufacturers to adopt the technology earlier and under what circumstances a technology provider should instead offer an exclusive contract to one of the manufacturers. Finally, we analyze the optimal adoption timing from the system's perspective, and examine the impact of technology provider's intervention on system efficiency.

To address these research questions, we construct a stylized multi‐stage game‐theoretic model with one technology provider and two symmetric downstream manufacturers in the product market, and derive pure‐strategy equilibria for them. We assume that manufacturers pre‐committed their adoption timing at the beginning of the time horizon. In the absence of the technology provider's intervention, we find that when competition—proxied by a function of product substitutability (e.g., Vives 2001)—is very mild, that is, when manufacturers’ products are highly differentiated, in equilibrium both manufacturers adopt the technology simultaneously at the beginning of the time horizon. Otherwise, the adoption will be sequential: The first manufacturer adopts the technology at the beginning of the time horizon, and the second manufacturer strategically delays his adoption so that the first manufacturer has the prospect of collecting enough monopolistic profit and hence is incentivized to make a larger investment.

We find that the equilibrium adoption timing determined by manufacturers’ strategic interaction is not necessarily in line with the technology provider's interest. In particular, under relatively mild competition, the technology provider prefers simultaneous early adoption by both manufacturers, whereas in equilibrium the second manufacturer chooses to delay his adoption; to the contrary under relatively intense competition, the technology provider would prefer the second manufacturer adopting the technology later than when he would have in equilibrium. Inspired by the examples of China Mobile and Apple, we suggest that the technology provider could make an initial investment to boost the market demand when the competition is relatively mild such that both manufacturers are incentivized to adopt the technology early, and when the competition is relatively intense deter the second manufacturer's adoption by offering an exclusive deal to the first manufacturer with a guaranteed monopoly period. Our analyses on system efficiency reveal that, interestingly, the technology provider's “self‐interested” intervention on manufacturers’ adoption timing often improves system efficiency.

Finally, we analyze two extensions of our main model where the effect of manufacturers’ demand‐boosting investments decreases over time, or when the licensing fee is endogenous, and show that our main findings remain robust in both cases. In the latter extension, we also propose a new manipulation that the technology provider can employ to influence manufacturers’ adoption timing.

Literature Review

Our work studies a technology provider's decision to introduce a new technology to downstream manufacturers who are both cooperating and competing in the product market, in the absence of a competing technology.¹ Given the structure of our problem, we will review work that focuses on (a) new technology adoption, which concerns mainly the downstream manufacturers, that focuses on (b) technology introduction, which concerns mainly the technology provider, and that accounts for (c) interactions between technology introduction and technology adoption.

The literature on new technology adoption studies the downstream manufacturers’ timing decisions of when to adopt a new technology—without considering the role of the technology provider. Hoppe (2002) identifies related theoretical models with two distinct foci: those mainly dealing with uncertainty regarding the arrival and value of a new technology (e.g., Balcer and Lippman 1984, Cho and McCardle 2009, McCardle 1985), and those focusing on the strategic interaction in the product market (e.g., Fudenberg and Tirole 1985, Reinganum 1981a,1981b, and more recent work includes Milliou and Petrakis 2011, Whang 2010). Our problem with respect to the downstream manufacturers fits into the latter category, and importantly, our main focus is on the upstream technology provider's decisions. On the other hand, several studies have explored the timing of new product introduction—in the absence of downstream manufacturers’ reactions (e.g., Moorthy and Png 1992, Ramachandran and Krishnan 2008, Savin and Terwiesch 2005). We differ from these works in one important structural aspect: Whereas they consider scenarios where the technology provider and manufacturers are of the same entity, the technology provider in our model introduces the technology to downstream manufacturers—rather than directly to consumers—who adopt the technology into their products, make strategic investment to boost common demand, and compete in the product market.

Finally, a third stream of research investigates the decisions of both the technology provider and downstream manufacturers. This line of work studies new technology introduction to competing downstream manufacturers, and mainly focuses on the licensing decisions of the technology provider (e.g., Erat and Kavadias 2006, Erat et al. 2013, Kamien and Tauman 1986, Kamien et al. 1992). Among them, our work is most related to Erat and Kavadias (2006), who focus on the provider's technology development and pricing decisions. Erat et al. (2013) study a similar setting, but focus on the technology integration process. Different from these two papers which are centered around a technology causing more incremental improvement of the product performance, our technology of interest is more radical and opens up a new market for the manufacturers. Therefore, the downstream manufacturers in our setting not only compete but also cooperate with each other to increase the total demand in the new market. Importantly, this cooperation between manufacturers changes the late adopter's incentive from a lower technology cost to a lower investment in boosting the common demand, and thus significantly impacts manufacturers’ adoption timing decisions. Moreover, as our focus is on technology adoption timing rather than its development or integration, instead of assuming two predetermined points of adoption time as in Erat and Kavadias (2006), we allow manufacturers to adopt the technology at any time in the horizon.

Model

We consider a setting with one technology provider and two symmetric downstream manufacturers, manufacturer a and b. The technology here is broadly defined to include not only patents, copyright, but also know‐how (e.g., expertise, skilled craftsmanship, training capability, etc.; WIPO 2015). The manufacturers pay licensing fee w to the technology provider for each unit of product that carries her technology (e.g., Amir et al. 2014, Lin and Kulatilaka 2006, Sen 2005).²

The time horizon τ is continuous and spans over [0, 1]. At τ = 0, either manufacturer simultaneously decides on an adoption timing and signs a technology transfer agreement with the technology provider (e.g., between China Mobile and Nokia, and between China Mobile and Huawei) that specifies the date starting from which the manufacturer adopts the provider's technology into his product. This static setting follows the open‐loop tradition in dynamic games (e.g., Gaimon 1989, Pacheco‐de Almeida and Zemsky 2012, Reinganum 1981a,1981b), and is consistent with many operations in practice where each manufacturer's adoption timing is bounded by both legally binding contracts and the provision of technology from the technology provider. In addition, once an agreement is reached on the timing of the adoption, the technology provider will need to arrange both human resources (e.g., experts and engineers) and physical equipment accordingly, whose schedules might not be easily altered ex post.³

If manufacturers choose to adopt the technology at different points in time,

τ_{1}

and

τ_{2}

, where

τ_{1}, τ_{2} \in [0, 1]

and

τ_{1} < τ_{2}

, they enter a sequential subgame (Figure 1a). Note that whereas we use a and b to denote the two manufacturers in general, we refer to them as 1 and 2 when we emphasize the adoption order in the sequential subgame. When the first manufacturer adopts the technology at

τ_{1}

, he decides on an investment

Q_{1}

that aims to raise the demand for his product that carries the technology. In addition, he sets up a price

p_{1, I}

for his product, and profits as a monopolist throughout the period

[τ_{1}, τ_{2})

, referred to as period I. At time

τ_{2}

, the second manufacturer adopts the technology and makes a demand‐boosting investment

Q_{2}

, and both manufacturers set their prices,

p_{1, II}

and

p_{2, II}

, for their respective products in this duopoly period

[τ_{2}, 1]

, referred to as period II. Let

t_{I} = τ_{2} - τ_{1}

and

t_{II} = 1 - τ_{2}

be the length of periods I and II, respectively. If manufacturers choose the same adoption time

τ_{a} = τ_{b}

τ_{a}, τ_{b} \in [0, 1]

, they enter a simultaneous subgame (Figure 1b). In this case they decide simultaneously the amount of investments,

Q_{a}

and

Q_{b}

, and the prices,

p_{a}

and

p_{b}

.⁴

Figure 1

Timeline and Sequence of Decisions for the (a) Sequential and (b) Simultaneous Subgames

We first lay out the setup for the sequential subgame. We model the demand for manufacturer i∈{1, 2} in period n∈{I, II} as the product of the respective demand rate and the length of the period, that is,

D_{i, n} = λ_{i, n} t_{n}

, where the demand rate,

λ_{i, n}

, denotes the demand per unit time. Moreover, the demand rate is characterized as a product of two functions: a (i) linear demand function and a (ii) demand‐boosting function. In particular, we adopt the linear demand system proposed in Vives (2001) where the demand for manufacturer i corresponds to a representative consumer's optimal consumption of manufacturer i's product that maximizes the consumer's net utility (for derivation see Vives 2001, p. 145). Variations of this linear demand system have been used in, for example, Godes et al. (2009), Guo et al. (2014), Milliou and Petrakis (2011), Wang et al. (2014), and Wu and Zhang (2014). Moreover, the demand‐boosting function captures the effect that the investment raises market awareness of the technology (Chessa and Murre 2007, Elzinga et al. 2009, Terui et al. 2011) and thereby increases the number of consumers interested in and eventually purchasing the products that carry the technology. This effect of advertising in raising the number of consumers purchasing the products has also been modeled in, for example, Godes et al. (2009) and Villas‐Boas (1993). As a result, multiplying the (i) linear demand and (ii) demand‐boosting function represents the total amount of product i that all consumers will purchase per unit time, which equals the demand per unit time.⁵ Likewise, Lim and Tang (2006) have also employed a similar idea to model demand as the product of the amount of interested consumers and the number of items purchased per consumer. Importantly, as discussed previously, there is a spillover effect of manufacturers’ investments—investment made by one manufacturer raises the awareness of the technology adopted by both manufacturers’ products and thus increases the demand faced by both manufacturers. Hence, the demand‐boosting effect for either manufacturer comes from total investments of both manufacturers (for a similar modelling approach see Krishnamurthy 2000). The demand rates in both periods are then written as:

\begin{matrix} Period I - Monopoly: & λ_{1, I} = (μ - p_{1, I}) g (Q_{1}), λ_{2, II} = 0; \\ Period II - Duopoly: & λ_{i, II} = \frac{1}{1 - γ^{2}} ((1 - γ) μ - p_{i, II} + γ p_{j, II}) g (Q_{1} + Q_{2}), i, j \in {1, 2}, i \neq j . \end{matrix}

Here,

μ - p_{1, I}

and

\frac{1}{1 - γ^{2}} ((1 - γ) μ - p_{i, II} + γ p_{j, II})

, respectively, stand for the linear demand function in monopoly and duopoly period, where μ ≥ 0 denotes a representative consumer's purchasing power per unit time, 0 ≤ γ < 1 the substitutability between manufacturers’ products, and

g (Q_{1})

and

g (Q_{1} + Q_{2})

the respective demand‐boosting functions. To keep the tractability of the analysis, throughout the manuscript, we assume a particular format of

g (Q) = c Q^{1 / 2}

, where c is a positive constant capturing the effectiveness of the investment.

Note that this formulation of demand rate implies that the effect of the demand‐boosting investment does not diminish over time. This is a sound assumption when the time horizon is relatively short. Moreover, in practice advertisement such as TV commercials is often first paid for and then scheduled to be released at multiple points of time (e.g., Bollapragada et al. 2002); similarly, Google Ads can be run automatically over time as long as there is sufficient credit in the client's account. Hence, whereas the investment is made in one shot earlier on, its effect on boosting demand is likely to stay strong over time. In section 7.1, we relax this assumption and consider cases where the effect of manufacturers’ investments is inevitably discounted over time.

The profits for the first and second adopter are as follows (for the ease of display their dependence on

τ_{1}

and

τ_{2}

is omitted for now):

\begin{matrix} π_{1} (p_{1, II}, p_{2, II}, Q_{1}, Q_{2}) & = \\ \frac{t_{II} g (Q_{1} + Q_{2})}{1 - γ^{2}} ((1 - γ) μ - p_{1, II} + γ p_{2, II}) (p_{1, II} - w) \\ + (μ - p_{1, I}) t_{I} g (Q_{1}) (p_{1, I} - w) - Q_{1}, \\ π_{2} (p_{1, II}, p_{2, II}, Q_{1}, Q_{2}) & = \\ \frac{t_{II} g (Q_{1} + Q_{2})}{1 - γ^{2}} ((1 - γ) μ - p_{2, II} + γ p_{1, II}) (p_{2, II} - w) - Q_{2}, \end{matrix}

where the first item in

π_{1} (p_{1, II}, p_{2, II}, Q_{1}, Q_{2})

denotes the first manufacturer's profit over

t_{II}

in the duopolistic period II, and the last two terms denote his profit over

t_{I}

in the monopolistic period I.

In the simultaneous subgame, there only exists a duopoly period and

t_{II} = 1 - τ_{a} = 1 - τ_{b}

. The demand rate is defined accordingly as:

Period II - Duopoly: λ_{i} = \frac{1}{1 - γ^{2}} ((1 - γ) μ - p_{i, II} + γ p_{j, II}) g (Q_{a} + Q_{b}), i, j \in {a, b}, a \neq b,

with manufacturers’ profits from the duopoly period as:

\begin{matrix} π_{a} (p_{a, II}, p_{b, II}, Q_{a}, Q_{b}) & = \frac{t_{II} g (Q_{a} + Q_{b})}{1 - γ^{2}} ((1 - γ) μ - p_{a, II} + γ p_{b, II}) (p_{a, II} - w) - Q_{a}, \\ π_{b} (p_{a, II}, p_{b, II}, Q_{a}, Q_{b}) & = \frac{t_{II} g (Q_{a} + Q_{b})}{1 - γ^{2}} ((1 - γ) μ - p_{b, II} + γ p_{a, II}) (p_{b, II} - w) - Q_{b} . \end{matrix}

Manufacturers’ Problem

In this section, we investigate manufacturers’ pure‐strategy equilibrium in the absence of the technology provider's intervention. We start from backwards with the sequential and the simultaneous investment and pricing subgames, and then analyze equilibrium outcomes of the timing subgame.

Analysis of Investment and Pricing Subgames

Given the adoption timing, manufacturers decide on their investments and prices so as to maximize their own profits. The next proposition characterizes manufacturers’ equilibrium prices, investments, and resulting profits in the sequential and simultaneous subgames. Proofs of the main results are presented in section B of the E‐Companion.

Proposition 1

Define

G_{I} = α t_{I}

and

G_{II} = β t_{II}

, where

α = \frac{c {(μ - w)}^{2}}{8}

β = \frac{c (1 - γ) {(μ - w)}^{2}}{2 (1 + γ) {(2 - γ)}^{2}}

. Under sequential adoption, manufacturers set their equilibrium prices as

p_{1, II}^{*} = p_{2, II}^{*} = \frac{(1 - γ) μ + w}{2 - γ}

and

p_{1, I}^{*} = \frac{μ + w}{2}

. The optimal investments and resulting profits are:

when

G_{I} < \frac{1}{2} G_{II}

Q_{1}^{*} = G_{I}^{2}

Q_{2}^{*} = G_{II}^{2} - G_{I}^{2}

π_{1} = G_{I}^{2} + 2 G_{II}^{2}

, and

π_{2} = G_{I}^{2} + G_{II}^{2}

;

when

G_{I} \geq \frac{1}{2} G_{II}

Q_{1}^{*} = {(G_{I} + G_{II})}^{2}

Q_{2}^{*} = 0

π_{1} = {(G_{I} + G_{II})}^{2}

, and

π_{2} = 2 G_{II} (G_{I} + G_{II})

Under simultaneous adoption, manufacturers set their equilibrium prices as

p_{a, II}^{*} = p_{b, II}^{*} = \frac{(1 - γ) μ + w}{2 - γ}

. The optimal investments and resulting profits are:

Q_{a}^{*} = Q_{b}^{*} = \frac{1}{2} G_{II}^{2}

and

π_{a} = π_{b} = π^{sim} = \frac{3}{2} G_{II}^{2}

Note that α and β, respectively, represent the profitability per unit time in a monopoly and duopoly, and

G_{I}

and

G_{II}

the corresponding cumulative profitability in these two periods. Proposition 1 reveals that under sequential adoption, the first adopter can either invest a relatively small amount,

G_{I}^{2}

, and expects the second adopter to chip in

G_{II}^{2} - G_{I}^{2}

, or invest a relatively large amount,

{(G_{I} + G_{II})}^{2}

, and let the second adopter freeride. Such choice depends on the relative profitability of the monopoly and duopoly periods: If the monopoly period is profitable enough, that is, when

G_{I} \geq \frac{1}{2} G_{II}

, then, despite a freeriding concern, the first adopter is incentivized to make a large investment; otherwise, the first adopter only makes a small investment. Since the magnitudes of

G_{I}

and

G_{II}

depend on the length of the two corresponding periods, intuitively, manufacturers’ preceding timing decisions should have a critical influence on the first adopter's investment decisions.

Proposition 1 also shares similar insights as findings in Krishnamurthy (2000) where firms sharing the same market decide on their generic advertising investments to enlarge the common demand. It is shown that, if there is only one dominant firm, like in our case (ii), then in equilibrium only the dominant firm contributes to the generic advertising, and if there are multiple dominant firms, more similar to our case (i), then these firms share the responsibility.

Analysis of the (Static) Timing Subgame

At time zero, the technology provider engages both manufacturers in simultaneously committing to an adoption timing. To obtain the timing equilibria, we first specify one adopter's best response to the other's timing decision. Let manufacturer b adopt at

τ_{b}

, and manufacturer a can be (i) the first adopter by adopting at

τ_{a} < τ_{b}

(if

τ_{b} > 0

), (ii) the second adopter by adopting at

τ_{a} > τ_{b}

(if

τ_{b} < 1

), or (iii) involved in the simultaneous subgame by adopting at

τ_{a} = τ_{b}

. The following two lemmas characterize manufacturer a's timing responses if he chooses to be in cases (i) and (ii).

Lemma 1

Given that the second manufacturer adopts the technology at time

τ_{2} \in (0, 1]

, the first manufacturer's optimal adoption timing is

τ_{1}^{*} (τ_{2}) = 0

Lemma 2

Define

θ = \frac{4 (1 - γ)}{(1 + γ) {(2 - γ)}^{2}} = \frac{β}{α} \in (0, 1]

and

\underset{̲}{θ} = \frac{2}{5}

. Given that the first manufacturer adopts the technology at time

τ_{1} \in [0, 1)

, the second manufacturer's optimal adoption timing is

τ_{2}^{*} (τ_{1}) = 1_{0 < θ < \underset{̲}{θ}} \frac{τ_{1} + (1 - 2 θ)}{2 (1 - θ)} + 1_{\underset{̲}{θ} \leq θ \leq 1} \frac{2 τ_{1} + θ}{2 + θ};

moreover, in either region of θ,

τ_{2}^{*} (τ_{1})

is such that

G_{I} \geq \frac{1}{2} G_{II}

, that is,

\frac{t_{I}}{t_{II}} \geq \frac{θ}{2}

By definition, θ strictly decreases in the product substitutability γ, and hence θ represents market competitiveness (Vives 2001): the smaller the θ, the higher the product substitutability, the more competitive the market is, and vice versa. Combining with Proposition 1, Lemma 2 shows that, had the manufacturer chosen to be the second mover, his optimal adoption timing is always such that

G_{I} \geq \frac{1}{2} G_{II}

, that is, he always strategically postpones his adoption to allow the first adopter more time to exploit the monopoly profit, such that he can freeride on the first adopter's investment.

In addition, θ also equals the ratio of per‐unit‐time profitability in the duopoly, β, to that in the monopoly period, α, where a large θ indicates relatively similar per‐unit‐time profitabilities in the duopoly and the monopoly period, and a small θ points to a relatively large difference. The next proposition describes θ's role in manufacturers’ adoption timing equilibrium.

Proposition 2

Define

\bar{θ} = 2 \sqrt{2} - 2

. Manufacturers’ equilibrium adoption timing is

τ_{1}^{*} = 0 and τ_{2}^{*} = 1_{0 < θ < \underset{̲}{θ}} {\hat{τ}}_{2} + 1_{\underset{̲}{θ} \leq θ < \bar{θ}} {\bar{τ}}_{2},

where

{\bar{τ}}_{2} = \frac{θ}{2 + θ}

{\hat{τ}}_{2} = \frac{1 - 2 θ}{2 (1 - θ)}

. (This implies that when

\bar{θ} \leq θ \leq 1

τ_{2}^{*} = 0

; moreover, by symmetry either manufacturer can be the first or second adopter.)

Proposition 2 reveals three timing equilibria in different market conditions.⁶ As illustrated in Figure 2, when

θ \geq \bar{θ}

, the per‐unit‐time profitabilities of the monopoly and the duopoly periods are relatively similar, and manufacturers are more incentivized to stay in the duopoly period together; by contrast, when

θ < \bar{θ}

, the monopoly period becomes a lot more lucrative than the duopoly period, which urges one of the two manufacturers to adopt earlier.

Figure 2

Second Manufacturer's Adoption Timing in Equilibrium [Color figure can be viewed at wileyonlinelibrary.com]

Proposition 2 also illustrates the role of θ in the second manufacturer's adoption timing under sequential adoption. When θ is relatively small, the second adopter's equilibrium timing reflects an optimal balance between adopting earlier to exploit the duopoly profit and adopting later to elicit a larger investment from the first adopter. The former consideration dominates the latter one when the duopoly period is lucrative, in which case θ is large; and vice versa. Therefore,

τ_{2}^{*}

decreases in θ. When θ is relatively large,

τ_{2}^{*}

represents a “freeriding threshold” above which the first adopter earns sufficient monopoly profit to justify a large investment for the second to freeride on. Hence, a smaller θ, that is, a higher monopoly per‐unit‐time profitability, requires a shorter monopoly period to reach the threshold. Therefore,

τ_{2}^{*}

increases in θ in this case.

By allowing manufacturers to adopt at any time, we contribute new insights into how the speed of adoption is affected by the level of competition in the product market. In particular, were manufacturers’ adoption timing predetermined at two points in time, we would have reached the conclusion that increased competition results in staggered adoption. Instead, we have shown that the adoption speed is not monotonic in the level of competition. Prior empirical findings on the effect of competition (measured by market concentration) on adoption speed are mixed; for example, Levin et al. (1987), Hannan and McDowell (1984), Escuer et al. (1991), and Karshenas and Stoneman (1993), respectively, have found a positive, negative, inverted‐U shape, and non‐significant relationship. These conflicting findings have been attributed to their idiosyncrasies in entry and product introduction strategies or industrial structures (e.g., Escuer et al. 1991, Seim and Vaiard 2011). Our model, accommodating various relationships between competition and adoption speed, offers an alternative explanation that these mixed empirical findings might have been driven by different intervals of competition intensity in each study sample.

Finally, by Proposition 2 manufacturers’ equilibrium adoption timing will not be affected by the technology provider's licensing fee, w. In section 7.2, we analyze an alternative setting where the technology provider assigns two different licensing fees to the monopoly and duopoly periods, and thus is able to influence manufacturers’ adoption timing by manipulating these two fees.

Technology Provider's Problem

The technology provider obtains w from manufacturers for each unit of their products that carries her technology. Moreover, we assume that the technology provider incurs a unit cost of m ≥ 0. Depending on manufacturers’ adoption timing, the technology provider's profit can be written as the marginal profit of providing the technology, w − m, multiplied by the total amount of products that carry the technology, which equals the total demand faced by both manufacturers.

\begin{matrix} Sequential Adoption: Π_{p}^{seq} & = (w - m) (D_{1, II} + D_{2, II} + D_{1, I}) \\ = (w - m) (\frac{2 t_{II} g (Q_{1} + Q_{2}) (μ - w)}{(1 + γ) (2 - γ)} + \frac{t_{I} g (Q_{1}) (μ - w)}{2}); \\ Simultaneous Adoption: Π_{p}^{sim} & = (w - m) (D_{a, II} + D_{b, II}) \\ = (w - m) \frac{2 t_{II} g (Q_{a} + Q_{b}) (μ - w)}{(1 + γ) (2 - γ)} . \end{matrix}

It is conceivable that, having a different objective, the technology provider might prefer that manufacturers adopt the technology at different times than they would in equilibrium. The next proposition first describes the adoption timing that is optimal for the technology provider given manufacturers’ equilibrium investment and pricing decisions.

Proposition 3

Manufacturers’ adoption timing preferred by the technology provider is

τ_{1 p}^{*} = 0 a n d τ_{2 p}^{*} = 1_{0 < θ < {\underset{̲}{θ}}_{p}} {\hat{τ}}_{2 p} + 1_{{\underset{̲}{θ}}_{p} \leq θ < {\bar{θ}}_{p}} {\bar{τ}}_{2},

where

{\bar{τ}}_{2}

is as defined in Proposition 2 and

{\hat{τ}}_{2 p}

{\underset{̲}{θ}}_{p}

, and

{\bar{θ}}_{p}

are defined in the proof; in addition,

\underset{̲}{θ} < {\underset{̲}{θ}}_{p} < {\bar{θ}}_{p} < \bar{θ}

, and

{\underset{̲}{θ}}_{p}

and

{\bar{θ}}_{p}

are solved to be approximately 0.64 and 0.67, respectively. (This implies that when

{\bar{θ}}_{p} \leq θ \leq 1

τ_{2 p}^{*} = 0

.) Moreover, we have that

{\hat{τ}}_{2 p} > {\hat{τ}}_{2}

and

{lim}_{θ \to 0} {\hat{τ}}_{2 p} = 1

Comparing Proposition 3 to Proposition 2, we find that manufacturers’ adoption timing preferred by the technology provider shares a similar pattern as that in equilibrium—a simultaneous adoption when competition is mild and a sequential one as competition intensifies. However, there exist important distinctions. On the one hand, we note that

{\hat{τ}}_{2 p} > {\hat{τ}}_{2}

, indicating that when competition is sufficiently intense the technology provider, like in the case of Apple from our motivating example, prefers the second manufacturer to adopt the technology even later than in equilibrium; in the extreme case where manufacturers’ products are perfect substitutes, the technology provider actually prefers only one adopter for the entire horizon. On the other hand,

{\bar{θ}}_{p} < \bar{θ}

indicates that there is a wider region of θ where simultaneous adoption is preferred; that is, the technology provider, like in the case of China Mobile, is more likely to desire an early adoption by all manufacturers. A comparison between these two patterns is summarized in Corollary 1 and illustrated in Figure 3.

Figure 3

Second Manufacturer's Adoption Timing in Un‐Intervened Equilibrium (Dashed Line) and Optimal for Technology Provider (Solid Line) [Color figure can be viewed at wileyonlinelibrary.com]

Corollary 1

When

{\bar{θ}}_{p} \leq θ < \bar{θ}

, the technology provider prefers simultaneous adoption at time zero, whereas in equilibrium manufacturers choose to adopt sequentially at

τ_{1}^{*} = 0

and

τ_{2}^{*} = {\bar{τ}}_{2}

. Moreover, when

0 < θ < {\underset{̲}{θ}}_{p}

, the technology provider prefers sequential adoption with the second manufacturer adopting the technology at

τ_{2 p}^{*} = {\hat{τ}}_{2 p}

, whereas in equilibrium the second manufacturer chooses to adopt earlier at either

τ_{2}^{*} = {\bar{τ}}_{2}

τ_{2}^{*} = {\hat{τ}}_{2}

Whereas in equilibrium either manufacturer is only concerned of maximizing his own profit, the provider needs to take into consideration both manufacturers’ demands. When profitabilities in both periods are relatively similar, implying a larger θ, the technology provider is better off when the second manufacturer adopts earlier, which simply brings in an additional source of demand earlier. By contrast, when the profitability in the monopoly period is sufficiently high, the provider prefers a postponed adoption by the second manufacturer because this will motivate the first manufacturer to make an even larger investment to boost the demand, which in turn benefits the technology provider.

Given such discrepancy in the adoption timing preference, we next investigate the technology provider's optimal actions that would align manufacturers’ incentives with that of the provider. Inspired by the motivating examples of China Mobile and Apple, we propose two types of manipulations under different market conditions: making an initial investment to encourage both manufacturers to adopt the technology earlier, or offering an exclusive contract to one of the manufacturers such that the other is barred from adoption for a certain period of time.

Technology Provider's Demand‐Boosting Investment

We suggest that in the case of

{\bar{θ}}_{p} \leq θ \leq \bar{θ}

, the technology provider can make an initial investment of

Q_{p}

to encourage both manufacturers to adopt simultaneously at time zero. In particular, we assume that the technology provider makes an initial investment at time zero, such that the demand‐boosting effect becomes

g (Q_{1} + Q_{p})

in the monopoly period, and

g (Q_{1} + Q_{2} + Q_{p})

in the duopoly period. The rest of the timeline and sequence of decisions remain the same. The next proposition summarizes manufacturers’ equilibrium adoption timing under the initial investment

Q_{p}

Proposition 4

Define

{\underset{̲}{θ}}_{p}^{Q} = \frac{1}{2}

and

{\bar{θ}}_{p}^{Q} = \frac{\sqrt{69}}{3} - 2

; hence,

{\underset{̲}{θ}}_{p}^{Q} < {\underset{̲}{θ}}_{p} < {\bar{θ}}_{p} < {\bar{θ}}_{p}^{Q}

. Under the technology provider's initial investment

Q_{p}

, manufacturers’ equilibrium adoption timing is

τ_{1}^{*} (Q_{p}) = 0 a n d τ_{2}^{*} (Q_{p}) = 1_{(θ, Q_{p}) \in Ω_{p 4}} {\hat{τ}}_{2} + 1_{(θ, Q_{p}) \in Ω_{p 3}} {\bar{τ}}_{2} + 1_{(θ, Q_{p}) \in Ω_{p 2}} {\underset{̲}{τ}}_{2} (Q_{p}),

where

{\bar{τ}}_{2}

and

{\hat{τ}}_{2}

are as defined in Proposition 2, and

{\underset{̲}{τ}}_{2} (Q_{p})

and regions

Ω_{pi}

, i = 1, 2, 3, 4, are defined in the proof. (This implies that when

(θ, Q_{p}) \in Ω_{p 1}

τ_{2}^{*} (Q_{p}) = 0

.) Moreover, manufacturers’ equilibrium pricing remains the same as in Proposition 1 and optimal investments under sequential‐ and simultaneous‐adoption equilibrium are, respectively,

\begin{matrix} Q_{1}^{*} (Q_{p}) & = α^{2} {(θ + (1 - θ) τ_{2}^{*} (Q_{p}))}^{2} - Q_{p}, Q_{2}^{*} (Q_{p}) = 0, a n d \\ Q_{a}^{*} (Q_{p}) & = Q_{b}^{*} (Q_{p}) = 1_{0 \leq Q_{p} < α^{2} θ^{2}} \frac{1}{2} (α^{2} θ^{2} - Q_{p}) . \end{matrix}

A comparison of Proposition 4 to Proposition 2 reveals that the technology provider's investment has significantly altered the landscape of manufacturers’ equilibrium adoption timing. The new equilibria, as illustrated in Figure 4 (its 3D version is provided in section A of the E‐Companion), are the same as those in Proposition 2 when

Q_{p} = 0

, and as

Q_{p}

increases,

τ_{2}^{*} (Q_{p})

becomes zero for a larger range of θ. Importantly, for any given θ, the technology provider can always incentivize both manufacturers to adopt the technology from time zero.

Figure 4

Four Cases of Equilibrium Adoption Timing Under Technology Provider's Investment

Q_{p}

Moreover, a new sequential‐adoption equilibrium,

τ_{1}^{*} (Q_{p}) = 0

and

τ_{2}^{*} (Q_{p}) = {\underset{̲}{τ}}_{2} (Q_{p})

, emerges when

Q_{p} > 0

. This happens in the region

Ω_{p 2}

, where market competition is neither too intense nor too mild, and the technology provider's investment is neither too large nor too small. Different from when

Q_{p} = 0

where the second manufacturer always adopts late enough such that the first manufacturer makes a large investment (Lemma 2), in the region

Ω_{p 2}

the second manufacturer's equilibrium adoption time is less than the “freeriding threshold,” that is,

{\underset{̲}{τ}}_{2} (Q_{p}) < {\bar{τ}}_{2}

for any

Q_{p} > 0

, resulting in a relatively short monopoly period for the first manufacturer; the second manufacturer instead freerides on the technology provider's initial investment and still invests nothing himself.

We now turn to the technology provider's investment decision. Despite the flexibility of making an initial investment to incentivize both manufacturers to adopt the technology at time zero, intuitively, the technology provider might not always find it beneficial to do so since the investment itself is costly. The next proposition presents conditions under which it is beneficial to do so.

Proposition 5

Define

ν = \frac{w - m}{μ - w} \in [0, \infty)

. When

{\bar{θ}}_{p} \leq θ < \bar{θ}

, the technology provider should make an initial investment

Q_{p}^{*} = {\underset{̲}{Q}}_{p} (θ)

to incentivize manufacturers to adopt at time zero if and only if

ν \geq \frac{{(2 + θ)}^{2} {\underset{̲}{Q}}_{p} (θ)}{4 α^{2} θ^{2} (\frac{2 - γ}{1 - γ} (θ^{2} + 4 θ - 2) - 3)},

where the right‐hand side decreases in θ;

{\underset{̲}{Q}}_{p} (θ)

is defined in the proof.

Here, ν represents the marginal profit of the technology provider relative to that of the manufacturers. The technology provider's decision to make an initial investment is affected by both the internal operational structure, ν, and the external market condition, θ. Intuitively, for a given market condition, the technology provider has a stronger incentive to invest when she enjoys a higher profit margin, so that the increased total demand resulting from her investment will have a higher impact on her profit. Moreover, the less competitive the market is, the easier it is for the technology provider to attenuate the second manufacturer's incentive of adopting late and freeriding on the first manufacturer's investment, and thereby to align manufacturers’ preferences with her own.

Technology Provider's Exclusivity Offer

In the case of

0 < θ < {\underset{̲}{θ}}_{p}

, in order to keep the second manufacturer from adopting the technology too early, we suggest that the technology provider offers one of the manufacturers an exclusive contract over the period

τ \in [0, τ_{p}]

, during which time the other manufacturer is barred from adoption.

Marvel (1982)'s seminal work defines an exclusive deal as a contractual requirement by which retailers promise a supplier that they will not handle goods of competing producers. Such contracts can also be used by a market incumbent to bar new entrants (Aghion and Bolton 1987), by a seller to protect his relationship‐specific investment on the buyer (Segal and Whinston 2000), by a supplier to induce revenue sharing with his retailers (Cai et al. 2012), etc. Our work establishes another rationale—to align preferences on technology adoption timing. Like Aghion and Bolton (1987), our exclusive contract is aimed at barring new “entrants,” but instead of being offered by one of the competing manufacturers to the technology provider, it is offered the other way around, such that the adoption timing of the two competing manufacturers aligns with the one desired by the technology provider. The next proposition examines manufacturers’ response under

τ_{p}

Proposition 6

Under the offer of an exclusive period

[0, τ_{p}]

, the first manufacturer adopts the technology at

τ_{1}^{*} (τ_{p}) = 0

and the second adopts at

τ_{2}^{*} (τ_{p}) = 1_{0 < θ < \underset{̲}{θ}} max (τ_{p}, {\hat{τ}}_{2}) + 1_{\underset{̲}{θ} \leq θ < \bar{θ}} max (τ_{p}, {\bar{τ}}_{2}) .

(This implies that when

\bar{θ} \leq θ \leq 1

τ_{2}^{*} (τ_{p}) = 0

By Proposition 6, the second adopter reacts to the

τ_{p}

restriction in a straightforward fashion: If, in the absence of the restriction, he had intended to adopt any time earlier than

τ_{p}

, he now adopts as soon as the restriction is over; otherwise, the restriction would not have any effect on him.

Given this response, the optimal length of the exclusive period follows naturally. In particular, in the case of

0 < θ < {\underset{̲}{θ}}_{p}

where the technology provider prefers the second manufacturer adopting at

{\hat{τ}}_{2 p}

whereas the second manufacturer himself prefers an earlier adoption at

{\bar{τ}}_{2}

{\hat{τ}}_{2}

, the technology provider can sign an exclusive contract with one manufacturer, blocking the second adoption until

τ_{p}^{*} = {\hat{τ}}_{2 p}

. Since

{\hat{τ}}_{2 p} \geq max ({\bar{τ}}_{2}, {\hat{τ}}_{2})

, by Proposition 6, it is optimal for the second manufacturer to adopt as soon as the exclusivity is over.

Corollary 2

When

0 < θ < {\underset{̲}{θ}}_{p}

, the technology provider should offer an exclusive contract to one of the manufacturers over the period

[0, τ_{p}^{*}]

, where

τ_{p}^{*} = {\hat{τ}}_{2 p}

. Under this exclusive contract, in equilibrium, the first manufacturer adopts at

τ_{1}^{*} = 0

, and the second adopts at

τ_{2}^{*} = {\hat{τ}}_{2 p}

Corollary 2 and Proposition 5 imply a consistent story with our two motivating examples.⁷ As handsets tend to have more features to distinguish themselves than networks, they are less substitutable, implying a higher θ in the handset market. Hence, it is plausible that the example of Apple corresponds to the range

0 < θ < {\underset{̲}{θ}}_{p}

whereas that of China Mobile coincides with

{\bar{θ}}_{p} \leq θ < \bar{θ}

, and thus our findings from Proposition 5 and Corollary 2 are consistent with actions taken by China Mobile and Apple. Although our model does not cover the full spectrum of factors that were taken account into either China Mobile's initial investment or Apple's exclusive contract decision, our results shed light on one potential motive behind these decisions—to align downstream manufacturers’ technology adoption timing with the technology provider's preference.

System Efficiency

In this section, we investigate manufacturers’ adoption timing that is optimal for an ecosystem comprised of the two manufacturers and the technology provider; the system profit is then simply the sum of profits from all parties. Given the optimal prices and investments from Proposition 1, the next proposition depicts the adoption timing that is optimal for the ecosystem.

Proposition 7

Manufacturers’ adoption timing optimal for the system is

τ_{1 s}^{*} = 0 a n d τ_{2 s}^{*} = 1_{(θ, ν) \in Ω_{s 4}} + 1_{(θ, ν) \in Ω_{s 3}} {\hat{τ}}_{2 s} + 1_{(θ, ν) \in Ω_{s 2}} {\bar{τ}}_{2},

where

{\hat{τ}}_{2 s}

is defined in the proof and

{\bar{τ}}_{2}

as defined in Proposition 2. (This implies that when

(θ, ν) \in Ω_{s 1}

τ_{2 s}^{*} = 0

.) The regions

Ω_{si}

, i = 1, 2, 3, 4, are defined in the proof and illustrated in Figure 5.

Figure 5

Four Cases of Manufacturers’ Adoption Timing Optimal for the System

Proposition 7 indicates a similar pattern to those described in Propositions 2 and 3—sequential adoption in a competitive market and simultaneous adoption if the competition is mild. There are, however, two important distinctions. First, the system‐optimal adoption timing is determined not only by the external market condition, θ, but also by the ecosystem's internal operational structure, ν. Moreover, observe that when

(θ, ν) \in Ω_{s 4}

τ_{2 s}^{*} = 1

, indicating that even when the two manufacturers’ products are not perfect substitutes, the system might still prefer a monopoly manufacturer for the entire time horizon.

We next consider the impact of the technology provider's interventions—making an initial investment or offering an exclusive contract—on the system profit. Denote

Π_{s}

as the system profit and ρ the relative impact of the interventions; in particular,

ρ = (Π_{s} under technology provider interventions - Π_{s} under equilibrium) / (Π_{s} under system optimal - Π_{s} under equilibrium) \times 100 %,

where in general a positive ρ indicates a positive impact from the technology provider's interventions on the system profit, and vice versa. Figure 6 illustrates ρ as a function of θ and the unit price w. It shows that—except in regions where manufacturers’ equilibrium adoption timing coincides with the preference of the technology provider or the system and ρ becomes either zero or undefined—the technology provider's interventions often result in an improvement of the system profit; a negative impact is only possible in the small range when

\frac{5}{8} < θ < {\underset{̲}{θ}}_{p}

. Interestingly, the technology provider's actions to maximize her own profit often help to improve system efficiency.

Figure 6

Technology Provider's Relative Impact on System Profit

Extensions

In this section, we individually relax two assumptions in our main model, that the effect of manufacturers’ investments stay constant over time, or that the licensing fee is exogenously given.

Discounted Demand‐Boosting Effect over Time

We first consider the case where the demand‐boosting effect of manufacturers’ investments decay over time; the general setup and timeline of events remain the same. In particular, we not only allow the demand‐boosting effect to be exponentially discounted over time with rate η ≥ 0, but also allocate a smaller weight to the first manufacturer's investment when we are considering the demand‐boosting effect in the duopoly period of the sequential subgame, that is, we now assume that

g (Q) = g (r Q_{1} + Q_{2})

, where 0 < r ≤ 1 is a constant. It would have been more realistic to have r discounted over time as well; nevertheless, the current setup captures the fact that the effect of the first manufacturer's earlier investment at

τ_{1}

becomes weaker by the time of

τ_{2}

, and then the effect of both investments still exponentially decays over time from

τ_{2}

on. For the ease of reference, we refer to the first discount associated with η as time discount, and the second associated with r as weight discount, where a larger time discount corresponds to a larger η and a larger weight discount corresponds to a smaller r. Note that when η = 0 and r = 1, the current setting degenerates to the previous case without any discount.

The profits for the first and second manufacturers in the sequential subgame now become:

\begin{matrix} π_{1}^{d} (p_{1, II}, p_{2, II}, Q_{1}, Q_{2}) & = \frac{\int_{τ_{2}}^{1} g (r Q_{1} + Q_{2}) e^{- η (t - τ_{2})} d t}{1 - γ^{2}} ((1 - γ) μ - p_{1, II} + γ p_{2, II}) (p_{1, II} - w) \\ + \int_{τ_{1}}^{τ_{2}} g (Q_{1}) e^{- η (t - τ_{1})} d t \cdot (μ - p_{1, I}) (p_{1, I} - w) - Q_{1}, \\ π_{2}^{d} (p_{1, II}, p_{2, II}, Q_{1}, Q_{2}) & = \frac{\int_{τ_{2}}^{1} g (r Q_{1} + Q_{2}) e^{- η (t - τ_{2})} d t}{1 - γ^{2}} ((1 - γ) μ - p_{2, II} + γ p_{1, II}) \times (p_{2, II} - w) - Q_{2}, \end{matrix}

where the first item in

π_{1}^{d} (p_{1, II}, p_{2, II}, Q_{1}, Q_{2})

denotes the first manufacturer's discounted profit in the duopolistic period II, and the last two terms denote his profit in the monopolistic period I. In the simultaneous subgame, manufacturers’ discounted profits are:

\begin{matrix} π_{a}^{d} (p_{a}, p_{b}, Q_{a}, Q_{b}) & = \frac{\int_{τ_{a}}^{1} g (Q_{a} + Q_{b}) e^{- η (t - τ_{a})} d t}{1 - γ^{2}} ((1 - γ) μ - p_{a} + γ p_{b}) (p_{a} - w) - Q_{a}, \\ π_{b}^{d} (p_{a}, p_{b}, Q_{a}, Q_{b}) & = \frac{\int_{τ_{b}}^{1} g (Q_{a} + Q_{b}) e^{- η (t - τ_{b})} d t}{1 - γ^{2}} ((1 - γ) μ - p_{b} + γ, p_{a}) (p_{b} - w) - Q_{b}, τ_{a} = τ_{b} . \end{matrix}

The next proposition shows that with discount, manufacturers’ equilibrium prices, investments, and resulting profits remain in similar formats as those characterized in Proposition 1. Proofs of results in the extensions are presented in section C of the E‐Companion.

Proposition 8

Define

G_{I}^{d} = \frac{α (1 - e^{- η (τ_{2} - τ_{1})})}{η}

and

G_{II}^{d} = \frac{β (1 - e^{- η (1 - τ_{2})})}{η}

, where

α = \frac{c {(μ - w)}^{2}}{8}

β = \frac{c (1 - γ) {(μ - w)}^{2}}{2 (1 + γ) {(2 - γ)}^{2}}

. Manufacturers’ equilibrium prices remain the same as in Proposition 1. Moreover, under sequential adoption manufacturers’ optimal investments and resulting profits are:

G_{I}^{d} < \frac{2 - r}{2 \sqrt{r}} G_{II}^{d}

Q_{1}^{d *} = {(G_{I}^{d})}^{2}

Q_{2}^{d *} = {(G_{II}^{d})}^{2} - {(G_{I}^{d})}^{2}

π_{1}^{d} = {(G_{I}^{d})}^{2} + 2 {(G_{II}^{d})}^{2}

π_{2}^{d} = r {(G_{I}^{d})}^{2} + {(G_{II}^{d})}^{2}

;

G_{I}^{d} \geq \frac{2 - r}{2 \sqrt{r}} G_{II}^{d}

Q_{1}^{d *} = {(G_{I}^{d} + \sqrt{r} G_{II}^{d})}^{2}

Q_{2}^{d *} = 0

π_{1}^{d} = {(G_{I}^{d} + \sqrt{r} G_{II}^{d})}^{2}

π_{2}^{d} = 2 \sqrt{r} G_{II}^{d} (G_{I}^{d} + \sqrt{r} G_{II}^{d})

Under simultaneous adoption, manufacturers’ optimal investments and resulting profits are:

Q_{a}^{d *} = Q_{b}^{d *} = \frac{1}{2} {(G_{II}^{d})}^{2}

and

π_{a}^{d} = π_{b}^{d} = \frac{3}{2} {(G_{II}^{d})}^{2}

Importantly, Proposition 8 shows that, despite the discount, the second manufacturer is still able to freeride on the first manufacturer's investment. The next proposition characterizes timing equilibria under discount.

Proposition 9

Under discount, manufacturers’ equilibrium adoption timing is:

when

r_{0}^{d} \leq r \leq 1

τ_{1}^{d *} = 0

and

τ_{2}^{d *} = 1_{0 < θ < {\underset{̲}{θ}}^{d}} {\hat{τ}}_{2}^{d} + 1_{{\underset{̲}{θ}}^{d} \leq θ < {\bar{θ}}^{d}} {\bar{τ}}_{2}^{d}

;

when

0 < r < r_{0}^{d}

τ_{1}^{d *} = 0

and

τ_{2}^{d *} = 1_{0 < θ < {\hat{θ}}^{d}} {\hat{τ}}_{2}^{d}

where

{\hat{τ}}_{2}^{d}

{\bar{τ}}_{2}^{d}

{\underset{̲}{θ}}^{d}

{\bar{θ}}^{d}

{\hat{θ}}^{d}

, and

r_{0}^{d}

are defined in the proof. (This implies that when

{\bar{θ}}^{d} \leq θ \leq 1

{\hat{θ}}^{d} \leq θ \leq 1

τ_{2}^{d *} = 0

.) Moreover, both

{\hat{τ}}_{2}^{d}

and

{\bar{τ}}_{2}^{d}

are such that

G_{I}^{d} \geq \frac{2 - r}{2 \sqrt{r}} G_{II}^{d}

Proposition 9 shows a consistent pattern with results in the main model: a simultaneous adoption when the level of market competition is low, and a sequential one when the market is highly competitive; importantly, the second manufacturer always strategically delays his adoption such that he is able to freeride on the first manufacturer's investment. In addition, we find that when the weight discount is relatively small (i.e., a large r), the timing equilibria remain the same pattern as those described in Proposition 2 in the absence of discount. We note that the weight discount plays a more important role than the time discount; intuitively, this is because whereas the time discount is applied to both manufacturers’ investments, the weight discount is asymmetrically applied to only that of the first manufacturer—directly affecting how much the second manufacturer is able to freeride and thereby the timing equilibria.

Endogenous Licensing Fee

In this section, we consider the technology provider's decision to optimize the licensing fee. In particular, we investigate two cases, where there is a single licensing fee, w, as described in section 3, or two licensing fees,

w_{1}

and

w_{2}

, offered to the monopoly and duopoly periods, respectively.⁸

Single Licensing Fee

We first consider the case where the technology provider optimizes her profit over a single licensing fee, w, w∈[m, μ). As we have previously discussed, since manufacturers’ equilibrium adoption timing is not a function of the single licensing fee, manipulating w would not affect manufacturers’ timing decisions. The next proposition describes the optimal licensing fee for the technology provider, taking into consideration manufacturers’ equilibrium solutions characterized in section 4.

Proposition 10

Given manufacturers’ equilibrium adoption timing, investments, and prices, the technology provider's optimal licensing fee that maximizes her profit is

w^{*} = \frac{μ + 3 m}{4}

Two‐Part Licensing Fee

In this section, we consider the case where the technology provider can offer two licensing fees,

w_{1}

and

w_{2}

, respectively, to the monopoly and duopoly periods, where

w_{1}, w_{2} \in [m, μ)

. The next proposition shows that manufacturers’ optimal investments and prices follow the same formats as those described in Proposition 1.

Proposition 1′

Define

G_{I}^{'} = α^{'} t_{I}

and

G_{II}^{'} = β^{'} t_{II}

, where

α^{'} = \frac{c {(μ - w_{1})}^{2}}{8}

β^{'} = \frac{c (1 - γ) {(μ - w_{2})}^{2}}{2 (1 + γ) {(2 - γ)}^{2}}

. Under sequential adoption, manufacturers set their equilibrium prices as

p_{1, II}^{' *} = p_{2, II}^{' *} = \frac{(1 - γ) μ + w_{2}}{2 - γ}

and

p_{1, I}^{' *} = \frac{μ + w_{1}}{2}

. The optimal investments and resulting profits are:

when

G_{I}^{'} < \frac{1}{2} G_{II}^{'}

Q_{1}^{' *} = G_{I}^{' 2}

Q_{2}^{' *} = G_{II}^{' 2} - G_{I}^{' 2}

π_{1}^{'} = G_{I}^{' 2} + 2 G_{II}^{' 2}

, and

π_{2}^{'} = G_{I}^{' 2} + G_{II}^{' 2}

;

when

G_{I}^{'} \geq \frac{1}{2} G_{II}^{'}

Q_{1}^{' *} = {(G_{I}^{'} + G_{II}^{'})}^{2}

Q_{2}^{' *} = 0

π_{1}^{'} = {(G_{I}^{'} + G_{II}^{'})}^{2}

, and

π_{2}^{'} = 2 G_{II}^{'} (G_{I}^{'} + G_{II}^{'})

Under simultaneous adoption, manufacturers set their equilibrium prices as

p_{a, II}^{' *} = p_{b, II}^{' *} = \frac{(1 - γ) μ + w_{2}}{2 - γ}

. The optimal investments and resulting profits are:

Q_{a}^{' *} = Q_{b}^{' *} = \frac{1}{2} G_{II}^{' 2}

and

π_{a}^{'} = π_{b}^{'} = π^{s i m'} = \frac{3}{2} G_{II}^{' 2}

We next look at manufacturers’ equilibrium adoption timing.

Proposition 2′

Let

θ^{'} = θ {(\frac{μ - w_{2}}{μ - w_{1}})}^{2} = \frac{β^{'}}{α^{'}}

. Manufacturers’ equilibrium adoption timing is

τ_{1}^{' *} = 0 and τ_{2}^{' *} = 1_{0 < θ^{'} < \underset{̲}{θ}} {\hat{τ}}_{2}^{'} + 1_{\underset{̲}{θ} \leq θ^{'} < \bar{θ}} {\bar{τ}}_{2}^{'},

where

{\bar{τ}}_{2}^{'} = \frac{θ^{'}}{2 + θ^{'}}

and

{\hat{τ}}_{2}^{'} = \frac{1 - 2 θ^{'}}{2 (1 - θ^{'})}

, and

\underset{̲}{θ}

and

\bar{θ}

are as defined in Lemma 2 and Proposition 2, respectively. (This implies that when

\bar{θ} \leq θ^{'} \leq 1

τ_{2}^{' *} = 0

; moreover, by symmetry either manufacturer can be the first or second adopter.)

Proposition

2^{'}

shows that as different fees are assigned to the monopoly and duopoly periods, the equilibrium adoption timing no longer stays independent from licensing fees. In particular, whereas the threshold market conditions, θ and

\bar{θ}

stay the same as those with a single fee, the ratio of unit‐time‐profitability in the duopoly and monopoly period,

\frac{β^{'}}{α^{'}}

, is now determined not only by the market condition θ, but also by the two licensing fees

w_{1}

and

w_{2}

. As a result, by adjusting the relation between

w_{1}

and

w_{2}

, the technology provider could manipulate how and when the two manufacturers adopt the technology. For example, given a market condition θ, the technology provider could induce both manufacturers to simultaneously adopt her technology at time zero by adjusting

w_{1}

and

w_{2}

such that

θ {(\frac{μ - w_{2}}{μ - w_{1}})}^{2} \geq \bar{θ}

; alternatively, the technology provider could also postpone the second manufacturer's adoption by tuning down

{(\frac{μ - w_{2}}{μ - w_{1}})}^{2}

such that

{\hat{τ}}_{2}^{'}

becomes larger.

Finally, we investigate the technology provider's problem. The technology provider obtains

w_{1}

from the first manufacturer for each unit of his products that carries her technology during the monopoly period, and

w_{2}

from both manufacturers during the duopoly period. In addition, the provider incurs a unit cost of m ≥ 0. Depending on manufacturers’ adoption timing, the technology provider's profit under sequential and simultaneous adoption can be respectively written as follows.

\begin{matrix} Sequential Adoption : Π_{p}^{s e q^{'}} & = (w_{1} - m) D_{1, I}^{'} + (w_{2} - m) (D_{1, II}^{'} + D_{2, II}^{'}) \\ = (w_{1} - m) \frac{t_{I} g (Q_{1}) (μ - w_{1})}{2} + (w_{2} - m) \frac{2 t_{II} g (Q_{1}, Q_{2}) (μ - w_{2})}{(1 + γ) (2 - γ)}; \\ Simultaneous Adoption : Π_{p}^{s i m^{'}} & = (w_{2} - m) (D_{a}^{'} + D_{b}^{'}) = (w_{2} - m) \frac{2 t_{II} g (Q_{a}, Q_{b}) (μ - w_{2})}{(1 + γ) (2 - γ)} . \end{matrix}

Taking into consideration manufacturers’ equilibrium adoption timing under any given licensing fees, the next proposition presents the technology provider's optimal licensing fees.

Proposition 11

Given manufacturers’ equilibrium prices, investments, and adoption timing described in Proposition 1′ and

2^{'}

, the technology provider's optimal licensing fees are

\begin{matrix} w_{1}^{*} & = 1_{0 < θ < θ_{1}} m + 1_{θ_{1} \leq θ \leq 1} (μ - \frac{3 (μ - m)}{4 \sqrt{\bar{θ} / θ}}), a n d \\ w_{2}^{*} & = 1_{0 < θ < θ_{2}} {\hat{w}}_{2 b} + 1_{θ_{2} \leq θ < θ_{1}} {\hat{w}}_{2 a} + 1_{θ_{1} \leq θ \leq 1} \frac{μ + 3 m}{4}, \end{matrix}

where

{\hat{w}}_{2 a}

{\hat{w}}_{2 b}

θ_{1}

, and

θ_{2}

are defined in the proof;

θ_{1}

and

θ_{2}

are solved to be around 0.86 and 0.82, respectively. Consequently, manufacturers follow a sequential adoption when

0 < θ < θ_{1}

and a simultaneous one otherwise.

Note that when

θ_{1} \leq θ \leq 1

, any

w_{1} \geq μ - \frac{3 (μ - m)}{4 \sqrt{\bar{θ} / θ}}

is optimal; we take the minimum value such that it is best for the manufacturers while not affecting the technology provider. Consistent with our previous findings, Proposition 11 shows that it is optimal for the technology provider to induce a sequential adoption when the market is relatively competitive, and a simultaneous adoption when the market competition is relatively mild. In general, different from the case of single fee, manipulating either licensing fee might be serving the purpose of incentivizing manufacturers to adopt at a certain time, as well as maximizing the provider's corresponding profit given manufacturers’ adoption timing; in addition, since the licensing fees are imbedded in the provider's profit, it is no longer feasible to disentangle what the technology provider desires and what external actions (e.g., initial investment or exclusive contract) she could employ to fulfill her preference. Therefore, we refrain from over‐interpreting the implications of each optimal licensing fee.

Conclusion

In this work, we study the interplay between a technology provider who introduces a new technology and downstream manufacturers who adopt the technology into their products. We find that in the un‐intervened equilibrium, manufacturers prefer simultaneous adoption when the competition is mild, and sequential adoption otherwise; in the latter case the second manufacturer strategically defers his technology adoption in order to freeride on the first manufacturer's demand‐boosting investment. We show that this pattern of adoption timing deviates from that preferred by the technology provider in two cases, and we propose strategies for the technology provider to cope with the mis‐alignment. In the region where market competition is mild, we propose that the technology provider could make an initial investment to incentivize an earlier adoption of the second adopter. In the other case where manufacturers in the un‐intervened equilibrium adopt simultaneously at time zero, we suggest that the technology provider offer an exclusive period to one of the manufacturers to bar the other from adopting the technology early. Our analyses on system efficiency reveal that the technology provider's “selfish” actions to maximize her own profit are often not inefficient from the system's perspective. Finally, we individually relax two assumptions in the main model: that the demand‐boosting effect of manufacturers’ investments stay constant over time, and that the licensing fee is exogenous. We show that our main results are robust to these considerations; in the latter extension, we also propose an alternative manipulation for the technology provider to influence manufacturers’ adoption timing—by offering a two‐part licensing fee scheme.

Limitations and Future Work

Our work has several limitations that provide good venues for future research. We have assumed that consumer demand is only affected by external factors such as demand‐boosting investments and prices. In practice, consumer demand is also likely to be influenced by dynamics within the consumer body such as network externalities or market diffusion. In particular, the diffusion of consumer demand (Bass 1969) is particularly applicable to our setting that focuses on the introductory stage of a new technology, where imitator consumers are more likely to purchase the product carrying the new technology when more people have already done so. Under this new setting, our demand rate function, which is currently constant over time, would instead first increase and then decrease in time. This new curvature of demand should make the monopoly period relatively less profitable and duopoly period more so, and thereby narrow the gap of profitability between these two periods. We expect that this might expand the region of simultaneous‐adoption equilibrium. A comprehensive model that takes into account consumer demand diffusion would be not only interesting but also instrumental in analyzing the technology provider's corresponding actions.

Similarly, we have also assumed in our main model that the demand‐boosting effect of manufacturers’ investments is constant over time. In practice although advertisement could be paid for upfront and scheduled at regular hours after the payment, consumers can still develop fatigue toward repeated promotions (e.g., Shah 2017), or their circumstances might change over time (e.g., Sahni et al. 2019), such that the demand‐boosting effect of manufacturers’ investments decreases over time. Whereas we have attempted to capture this discounted effect of investments in a relatively simple fashion in section 7.1, a more fine‐grained characterization might yield new insights.

In addition, whereas we have analyzed a two‐part licensing fee scheme in section 7.2 under which different licensing fees are assigned to the monopoly and duopoly periods, other fee schemes as a function of time can also be considered (e.g., Hu and Tang 2021, Tang and Girotra 2017); in addition, fees can also be contingent on manufacturers’ demand‐boosting investment. It will be interesting to see how these fee schemes are able to manipulate manufacturers’ adoption timing and be optimized to serve the technology provider.

Finally, whereas our work has been focusing on the adopting‐earlier‐or‐later tradeoff in the absence of demand uncertainty, adding uncertainty to demand can introduce new tradeoffs; in particular, the late adopter will be able to observe the early adopter's profit stream and thereby enjoy information advantage (e.g., Agrawal et al. 2016, Kwon et al. 2016). It is intriguing to analyze the technology provider's actions in this case.

Footnotes

Acknowledgment

Open access funding enabled and organized by Project DEAL.

We do not consider between‐technology competition (e.g., Farrell and Saloner 1986, Hu et al. 2017, Katz and Shapiro ).

We also considered a proportional price scheme (e.g., Cai et al. 2012, Stasik 2010, Yoffie and Slind ), where the technology provider charges a unit price that is proportional to the selling price of manufacturers’ products, and find that our main results can be extended to this alternative price scheme (see section F in the E‐Companion).

We analyze a closed‐loop version (e.g., Fudenberg and Tirole ) in section E of the E‐Companion on cases where interactions among the technology provider and manufacturers are not bounded by contracts or technology provision, and show that in equilibrium both manufacturers adopt the technology simultaneously at time zero.

Note that the second adopter in the sequential subgame invests

Q_{2}

after observing

Q_{1}

whereas

Q_{a}

and

Q_{b}

in the simultaneous subgame are made simultaneously; hence, these two subgames need to be analyzed separately.

We explore another type of investment in section G of the E‐Companion that, instead of raising market awareness, increases the “willingness‐to‐pay” of each consumer. Consistently, the timing equilibria are then determined by c, representing the effectiveness of the investment on increasing demand; other findings remain qualitatively the same.

Consistent with what we have pointed out earlier, the simultaneous‐adoption equilibrium is not a special case of a sequential adoption at

τ_{2} \to 0

. In particular, by Propositions 1 and

, when

τ_{1} = 0

and

τ_{2} \to 0

manufacturers’ investments are

Q_{1}^{*} = 0

and

Q_{2}^{*} = β^{2}

, whereas under the simultaneous adoption

Q_{a}^{*} = Q_{b}^{*} = \frac{1}{2} β^{2}

when

τ_{a} = τ_{b} = 0

Figure 2 in the appendix offers a summary of these two corresponding scenarios.

We also explored an alternative adopter‐specific scheme in section D of the E‐Companion, where

w_{1}

and

w_{2}

are respectively assigned to the first and second adopter, and show that similar to the current period‐specific scheme, the provider is also able to manipulate manufacturers’ adoption timing through endogenous licensing fees.

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