Research on Time to Market and Pricing of Platform Products in a Competitive Environment

: Platforms are gradually becoming important business organization models, and platforms with bilateral market characteristics such as payment platforms and online shopping platforms are gradually penetrating people’s lives. Freemium content mostly exists in particular platforms such as online video platforms, etc. Platforms need to balance upstream and downstream markets when formulating strategies. This paper is the ﬁrst to explore the time-to-market and pricing strategies of products in bilateral markets. By connecting upstream and downstream markets through cross-network externalities, we construct a system dynamics model of the problem, simulate the diffusion process of new product launches, and solve the problem of the optimal time to market and optimal pricing of the product. The simulation analyzes the effects of different parameters on the optimal time-to-market and pricing strategies, and comparing the diffusion in a unilateral market, we ﬁnd that in a competitive market environment, the time-to-market and pricing of products are inﬂuenced by exogenous variables such as network externalities, and ﬁrms can promote their products more efﬁciently by changing the marketing mix strategy of platform product beneﬁts and quality reputation. Meanwhile, the results obtained by considering bilateral markets when developing strategies for platform-based companies can lead to higher returns.


Introduction
In the digital network era, platforms are gradually becoming an important business organization model, and payment platforms, online shopping platforms, video software, and other businesses with bilateral market characteristics are gradually penetrating people's lives.For example, on online shopping platforms, the greater the number of sellers, the richer the goods buyers can purchase through the platform, and the greater the number of buyers means the greater the potential demand for sellers' goods, so the increase in the number of buyers and sellers will result in higher value for both parties.Unlike products in a unilateral market, bilateral markets require a balance between upstream and downstream companies.Bilateral market companies cannot adopt targeted pricing strategies based on the different needs of consumers alone and need to consider more complex aspects.
With the development of the platform economy, the freemium model is becoming more and more common, providing free services to users to attract a certain number of consumers, and then charging for value-added services by providing more valuable ones.This model benefits from the characteristics of product network externalities, where free services attract users, and then value-added services are charged.The content of the freemium model mostly exists in some platform enterprises, such as online video platforms, shopping platforms, online games, etc.One method is to launch both free and paid versions of products, for example, online video platforms where one can watch movies for free, but if you want to watch more quantity and higher quality movies, you need to pay; one is to launch free and paid versions of products sequentially, for example, some online games often launch free versions for public testing first and then launch paid versions with perfect functions.
Pricing models are also important, and uncertainty about the degree of product matching in competitive situations is necessary for the design of versioning strategies [1].The free business model first emerged in the 1980s with the development of software with limited functionality, a model distributed on physical CDs [2].The first to name the freemium model, defined as a model that provides a basic service for free, increases the user base, develops user dependency, and then introduces a high-priced value-added service for profit [3].Freemium models have since developed in various industries, such as the application of freemium models in gaming products, where the desire to win or lose by playing the game can be fully utilized to launch a paid model for profit [4].Although freemium products do not charge a fee, their appearance can maximize consumer surplus and social profit.The free sample strategy is more effective for product brands with a high probability of repeat purchases [5].The price of value-added products affects firms' profits, the price of value-added products affects a company's profitability, and a new learning framework can be used to explore the design of freemium model strategies and related pricing strategies [6].Of course, the free strategy for low-quality products will only be adopted if the high-quality products can bring greater benefits to the company [7].The best quality of free products is affected by network externalities in unilateral markets and can indicate the feasible domain of free product quality [8].In a bilateral market, the platform can also earn more profit by investing in value-added services [9].In addition to considering pricing models, attention needs to be paid to consumer purchasing behavior [10], for example, consumers' mismatch and green consumer attitudes towards products [11].
The existence of a platform in a bilateral market means that separate pricing is required for both sides, and the allocation of the price structure in the bilateral market affects the demand for the platform from both sides [12].Market demand in bilateral markets does not exist independently; there are cross-network externalities in bilateral markets, and market demand in bilateral markets can affect each other, and the existence of cross-network externalities leads to different pricing in bilateral markets [13].Pricing is influenced by a variety of factors' self-network externalities, cross-network externalities, and platform pricing all play a role in upstream and downstream user demand on that platform.Different types of platforms should adopt differentiated competitive strategies [14].By analyzing the reasons for the success or failure of the competition between Taobao and eBay and Laikai and WeChat, we summarize that platforms can expand their competitive advantages through strategies such as subsidies and platform investment in the bilateral market competition stage [15].Based on the bilateral market theory, the optimal pricing strategy for the platform to charge membership and transaction fees can be analyzed.Pricing is negatively related to the self-network externality and positively related to the number of the other party [16].The bilateral market can also adopt a free strategy, a platform to implement uniform pricing, free for consumers and part of the free price under the pricing strategy of the user size and profit varies.Enterprises can gradually cultivate consumers' willingness to pay from low to high through the free model, to better occupy the market to obtain higher profits [17].In addition to price, another issue that needs the attention of enterprises is time, which can be studied by the game theory model of vertical differentiation of software products on the design of features and trial time of free software [18].The optimal launch strategy for the product can also be explored using the GBM demand function [19].
Through the study of more than three thousand cases where diffusion patterns were observed, Rogers found that the new technology showed an S-shaped diffusion curve over time, summarizing the process of launching new products into the market.Subsequently, based on the study of the durable goods market, a diffusion model that integrates internal and external influences, namely the Bass model, was proposed [20].Based on the Bass model, the Norton model of product replacement diffusion is constructed by considering the market share of new products as the demand for innovation and the obsolescence of old products [21].Since then, scholars have mostly used this model to study the diffusion of new products, and based on this, they have proposed a generalized Bass model that includes product, price, location, and promotional marketing mix strategies [22].The Bass model does not take into account the repeat purchase behavior of consumers, and subsequent studies have proposed a differential dynamics model of product market diffusion considering the factors of repeat purchase and price [23].The modeling study of the Bass model, using multi-intelligence simulation to build a model, focuses on portraying the interactions between consumers and can simulate and analyze the changes in market line demand of the product in a competitive environment [24].The exploration of the product diffusion model did not stop there, and a new diffusion model suitable for a stepwise diffusion market was proposed from the perspective of regions divided into sub-regions [25].The investment in the product is also a key consideration for the company.A dynamic model that examines the iteration time and pricing of durable goods reveals a correlation between the investment in the product version and the setting of the price [26].Usually, when we set parameters using the Bass model, we cannot fully represent the market.Using statistical and machine learning algorithms can more accurately predict the parameters in the Bass model before a new product is released [27].Pricing strategies for new product launches are not only one kind of Bass model which borrows utility equations to derive the equilibrium pricing decisions of firms by dynamic programming methods but also analyze the equilibrium pricing behavior of firms [28].
To summarize the above literature, it can be seen that previous literature has studied the proliferation of new products from multiple perspectives, and it can be seen that few studies have considered the launch process of bilateral platforms and freemium model products, and most studies have launched free and paid products at the same time.In reality, however, startups tend to take a staged approach to the market launch of their products.In this paper, for the first time, the research considers the situation of new product proliferation of bilateral platform firms and applies the Bass model to the bilateral market competition environment to study the timing of phased product launches and product pricing of platform firms.Firstly, we construct a model of new product diffusion in the downstream market and the utility equation of upstream merchants under the competition of double oligopolistic firms and then analyze the influence of parameters on the firm's revenue.We also explore the influence of external influences on the platform pricing and time-to-market in the process of product diffusion by combining numerical simulations.

Platform Competition Model Construction
Pricing a product is a decision that must be made before the product enters the market.The platform needs to determine the market conditions in advance to determine the optimal strategy.Consider two platforms, A and B. For the upstream market, the platform provides a venue for merchants in the upstream market to promote their products and collect fees.For the downstream market, the platform adopts the strategy of first attracting customers with a free version, creating awareness and then launching a paid version to gain revenue.The decision problem of the firm is the timing of the version launch and the bilateral pricing strategy in a competitive situation, with the decision objective of maximizing the total revenue of the platform.

Hypothesis 1 (Market).
There are only two platform firms A and B in the market.The two platforms are similar and heterogeneous products, and the quality differs mainly in terms of usability, reliability, and functionality.The goods sold by platform A and firm B influence each other.

Hypothesis 2 (Platform).
Two platforms form a duopoly competitive market.Assume that the order of their games is a simultaneous action game, i.e., both set the prices of platform products at the same time.Platforms A and B adopt a freemium model for the downstream market.At the same time, considering the cost characteristics of platform products different from traditional products, the marginal production cost in the process of forming and promoting products and services of platforms A and B is considered as 0, while their fixed costs are not considered.

Hypothesis 3 (Merchants and Consumers
).The Bass diffusion model is divided into those who buy under the external influence and those who buy on the recommendation of consumers who have already bought the product.Consider the "activity" of consumers in the process of use, i.e., some people who have used the product will not have an impact on unused consumers, and will not have an impact on the upstream market.
The meanings of the variables in the model are presented in the following Table 1.

Building the Model
Based on the demand model of products under the duopoly competition proposed by previous authors [18], this paper divides the product launch process into two stages: the first stage is for two firms to provide services to the upstream and downstream markets, and only the free version of the product exists in the downstream market at this stage.The second stage is when both firms launch paid versions of the product to the downstream market at the same time, and the upstream market still provides the same service, at which time there are free and paid versions of the product versions in the downstream market.
The upstream market, by considering the utility gained by the merchant on the platform, determines the choice of firm A or firm B. The model is: The downstream market, based on the classical product diffusion model, takes into account the interaction between bilateral markets.
The classical diffusion model is: where denotes consumers who buy the product due to external influence, q N(t) m [m − N(t)] denotes consumers who are influenced by the people who have already bought the product, p is the external influence factor, and q is the internal influence factor.
Here we consider the competitive strategies of two platform-based firms in the context of bilateral markets, and model the competitive process in the bilateral market taking into account the characteristics of the bilateral market and the total platform revenue as the target, while considering the bilateral market.
Phase I.
In the formula, the utility gained by the upstream market in choosing either firm A or B is the cross-network externality from downstream consumers minus the residual of the mismatch between the service provided by the platform and the price.Assume that the total upstream market is 1, x denotes the proportion of merchants choosing platform A, and 1 − x denotes the proportion of merchants choosing platform B. Downstream market in choosing product A1, ρ 1 β indicates that consumers under bilateral influence choose to use the free version of platform A (denoted by A1).N A1 (t) = kD A1 (t) denotes that consumers will be silenced at 1-k and no longer have any influence on other consumers.α A D A1 (t) (0 < α A < 1) denotes that the remaining consumers are influenced by consumers who have already purchased product A1 and purchased A1 with probability α A and (1 − α B )D B1 (t) (0 < α B < 1) by consumers who have already purchased product B1 and purchased A1 with probability 1 − α B .M 1 − D A1 (t) − D B1 (t) denotes the potential consumers of the market at time t.The negative effect of the price of the product on the demand is introduced and is expressed utilizing a negative index e −p a1 , e −p b1 .
Phase II.

Hypothesis 4.
Companies A and B launch paid versions with an incremental market share of M 2 (M 2 > M 1 ) in the second phase.
Hypothesis 5.After the launch of the paid version, part of the first phase of potential consumers repeatedly use the free version, and the other part chooses to directly cross over to buy the paid version.
The second stage sales model is constructed based on the previously proposed multigenerational innovative product demand model.

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The utility formula for the upstream market is the same as the principle of stage 1.When the paid version is available in the downstream market, the free version of the product is subject to some impact. 1 . The paid version sales volume adds to the first stage free version model with repeat purchases and crossover purchases by consumers of the first stage free version.
Taking the sales of the paid version launched by company A, D A2 as an example, the first term is the percentage of direct purchases of the second generation D A2 +D B2 M 2 , so the market for the free version of the product narrows 1 . The second term is the same as the first phase of A1 sales, the external impact factor ρ, and the internal impact factor q have changed.
Finally, based on the demand and price of the product, the value of the first stage, the second stage, and the total revenue of the company in both stages can be calculated.The formula is.

System Dynamics Modeling
Based on the previous concepts and formulas, the simulation model for this study was simulated using the system dynamics modeling tool Vensim PLE 7.3.5.
As shown in Figure 1, there existed a portion of potential consumers in the first stage who crossed over and purchased the paid version of the product directly due to the launch of the paid version in the second stage.is the same as the first phase of A1 sales, the external impact factor ρ , and the internal impact factor q have changed.
Finally, based on the demand and price of the product, the value of the first stage, the second stage, and the total revenue of the company in both stages can be calculated.The formula is.

System Dynamics Modeling
Based on the previous concepts and formulas, the simulation model for this study was simulated using the system dynamics modeling tool Vensim PLE 7.3.5.
As shown in Figure 1, there existed a portion of potential consumers in the first stage who crossed over and purchased the paid version of the product directly due to the launch of the paid version in the second stage.The demand model of the second stage is shown in Figure 2, which is similar to the demand model of the free version in the first stage, with the difference that the second stage adds the potential consumers in the first stage of the market to jump the purchase and repeat purchase.According to the previous section, the revenue gained by the company includes the total revenue gained in both phases since the product launch.

Model Simulation
In this paper, we would like to study the optimal time to market and pricing strategy for the platform launch of new products.In this chapter, the system dynamics diffusion model based on new product launches constructed in the previous section is simulated, and the parameters are taken within the range of values that can make the model hold, set as the benchmark model, and the effects of different launch times and changes in the pricing of the platform on the platform profit are considered separately and jointly.

Benchmark Model
The benchmark model was set up as shown in Table 2, and the results of the run are shown in Figure 3.

Model Simulation
In this paper, we would like to study the optimal time to market and pricing strategy for the platform launch of new products.In this chapter, the system dynamics diffusion model based on new product launches constructed in the previous section is simulated, and the parameters are taken within the range of values that can make the model hold, set as the benchmark model, and the effects of different launch times and changes in the pricing of the platform on the platform profit are considered separately and jointly.

Benchmark Model
The benchmark model was set up as shown in Table 2, and the results of the run are shown in Figure 3.
Table 2. Parameter settings of the benchmark model.Both the external and internal factors are 0.5, indicating that both firm A and firm B have comparable competitive strength and there is no market preference at this point.Therefore, the situation of firms A and B are the same, and the demand for the product is analyzed for firm A as an example.The revenue of firm A is Π = 41,842,087, D A1 = 34,945,276, D A2 = 48,552,775.The demand for the product of firm A in different periods can be seen in Figure 3.The demand for the free version of A1 peaked at week 51 from its launch, and the paid version was in the market from week 20 and was still increasing at week 100.Both the external and internal factors are 0.5, indicating that both firm A and firm B have comparable competitive strength and there is no market preference at this point.Therefore, the situation of firms A and B are the same, and the demand for the product is analyzed for firm A as an example.The revenue of firm A is Π = 41,842,087, By modifying the model parameters so that 1 − k = 0, the consumer will always remain active in influencing other consumers, the benefits for firm A are Π = 32,970,712,  By modifying the parameters of the model, it is assumed that the degree of influence of the purchaser of firm A or B on potential consumers increases.The benefits for firm A are = 41,905,902, = 34,945,120, and = 48,632,008.It can be seen that when increasing the attractiveness of the purchaser's potential purchases, the use of the free version decreases, By modifying the model parameters so that 1 − k = 0, the consumer will always remain active in influencing other consumers, the benefits for firm A are Π = 32,970,712, D A1 = 34,997,877, and D A2 = 45,009,681.The demand for firm A's product in different periods can be seen in Figure 4a.The demand for the free version of A1 peaked at week 65 after its launch, and the paid version started to enter the market from week 20 and reached its peak by week 77.Compared with the benchmark model, we can see that when consumers are active all the time, more consumers will stimulate the remaining consumers to use the free version, and the company's revenue will decrease instead.Both the external and internal factors are 0.5, indicating that both firm A and firm B have comparable competitive strength and there is no market preference at this point.Therefore, the situation of firms A and B are the same, and the demand for the product is analyzed for firm A as an example.The revenue of firm A is Π = 41,842,087, By modifying the model parameters so that 1 − k = 0, the consumer will always remain active in influencing other consumers, the benefits for firm A are Π = 32,970,712,  By modifying the parameters of the model, it is assumed that the degree of influence of the purchaser of firm A or B on potential consumers increases.The benefits for firm A are = 41,905,902, = 34,945,120, and = 48,632,008.It can be seen that when increasing the attractiveness of the purchaser's potential purchases, the use of the free version decreases, the use of the paid version increases, and the use of the firm's product as well as the benefits increase.As shown in Figure 4b, the demand for the free version of A1 peaks at week 48 after its launch, and the paid version enters the market from week 20 and still has not peaked by week 100.Compared with the benchmark model, we can see that the company's revenue will increase when the consumer's communication is wider, so the company should provide high-quality services as much as possible to maintain the consumer's "communication".

Time-to-Market for Phase II
In the benchmark model, the time to market for the second-generation product is set to T = 20 and both companies market the paid version at the same time.
3.2.1.Two Companies Entered the Second Phase at the Same Time Suppose two firms, A and B, launch their paid versions simultaneously as T A = T B = T and explore the optimal time to market for both firms.The graph of the relationship between the revenue earned by firms and the time to market is obtained.From Figure 5a, it is clear that the revenue of the firms decreases as they delay the launch of the paid version.The decrease is relatively smooth until 60 weeks, and from 60 weeks onward the firm's revenue drops sharply.
efits increase.As shown in Figure 4b, the demand for the free version of A1 peaks at week 48 after its launch, and the paid version enters the market from week 20 and still has not peaked by week 100.Compared with the benchmark model, we can see that the company's revenue will increase when the consumer's communication is wider, so the company should provide high-quality services as much as possible to maintain the consumer's "communication".

Time-to-Market for Phase II
In the benchmark model, the time to market for the second-generation product is set to T = 20 and both companies market the paid version at the same time.

Two Companies Do Not Enter the Second Stage at the Same Time
Suppose two firms A and B do not launch the paid version at the same time, explore the relationship between the revenue of platform A and the optimal time to market obtained by simulation when the time to enter the second phase of the other firm is known, as shown in Figure 5b.It can be seen that before week 20, platform A has higher revenue than B. After week 20, the return of platform B is higher than that of A. As the time to market is delayed, the return of platform A decreases accordingly.Platform B's returns increase as the time to market the paid version of A is delayed.In the game between the two sides, the platform company that launches the paid version first has more advantages.

Platform Optimal Pricing Strategy
Based on the benchmark model, the pricing problem of the firms is explored, and the platform firms face the pricing problem in the upstream and downstream bilateral markets.The pricing of both firms in the bilateral market in the benchmark model is the same, and firm B can be set as the control group and firm A as the experimental group.

Two Companies Do Not Enter the Second Stage at the Same Time
Suppose two firms A and B do not launch the paid version at the same time, explore the relationship between the revenue of platform A and the optimal time to market obtained by simulation when the time to enter the second phase of the other firm is known, as shown in Figure 5b.It can be seen that before week 20, platform A has higher revenue than B. After week 20, the return of platform B is higher than that of A. As the time to market is delayed, the return of platform A decreases accordingly.Platform B's returns increase as the time to market the paid version of A is delayed.In the game between the two sides, the platform company that launches the paid version first has more advantages.

Platform Optimal Pricing Strategy
Based on the benchmark model, the pricing problem of the firms is explored, and the platform firms face the pricing problem in the upstream and downstream bilateral markets.The pricing of both firms in the bilateral market in the benchmark model is the same, and firm B can be set as the control group and firm A as the experimental group.

Optimal Pricing for Downstream Consumers
In this paper, we consider that the platform enterprises all adopt the freemium model, so it is the price of the paid version that needs to be discussed in the downstream market.To explore the trend when the price changes on the enterprise's revenue, we plot the relationship between the revenue of enterprise A and the price of the downstream paid version, as shown in Figure 6a.When platform A has low charges for downstream consumers, the usage of downstream consumers is higher than that of house B, but the low price leads to less revenue than platform firm B.
In this paper, we consider that the platform enterprises all adopt the freemium model, so it is the price of the paid version that needs to be discussed in the downstream market.To explore the trend when the price changes on the enterprise's revenue, we plot the relationship between the revenue of enterprise A and the price of the downstream paid version, as shown in Figure 6a.When platform A has low charges for downstream consumers, the usage of downstream consumers is higher than that of house B, but the low price leads to less revenue than platform firm B.

Optimal Pricing for Upstream Merchants
In this paper, we assume that firm B's pricing upstream is always constant and analyze the graph between firm A's revenue and upstream price, as shown in Figure 7a.With p s1 as the independent variable, p s1 < p s2 , π a > π b .Firms in a duopoly competitive environment have higher returns to the side that prices the upstream market.Observing the usage as shown in Figure 7b, it can be seen that as p s1 increases, D A1 , D A2 gradually decreases, and when D B1 D B2 gradually increases, p s1 < p s2 , D A2 > D B2 .When platform A has low charges for upstream merchants, the usage of downstream consumers is higher than that of enterprise B. At this time, the gain of platform enterprise A is larger than that of enterprise B. market.To explore the trend when the price changes on the enterprise's revenue, we plot the relationship between the revenue of enterprise A and the price of the downstream paid version, as shown in Figure 6a.When platform A has low charges for downstream consumers, the usage of downstream consumers is higher than that of house B, but the low price leads to less revenue than platform firm B.

Time-to-Market and Pricing Joint Strategy
The timing of the launch of the second stage and the bilateral pricing strategy are analyzed separately above, and the joint strategy of timing and pricing will be analyzed below, still with B as the control group unchanged and changing the indicators of A.
Varying the time to market makes a graph of the relationship between optimal pricing and time to market.As can be seen from Figure 8a, as the time to market keeps pushing back, its pricing for the upstream market has a slight decrease, and the downstream pricing remains the same, when the later the product is introduced to the market, its impact on the downstream consumers is smaller than that on the upstream merchants.Under optimal pricing, firm A enters the second stage at different times with the benefits shown in Figure 8b.It can be found that platform B maintains the same pricing strategy as the time to market is gradually delayed, and its revenue gradually decreases as the time to market is delayed.Platform A, on the other hand, can better capture the market and obtain higher returns by changing its pricing strategy promptly in a competitive environment.
ing and time to market.As can be seen from Figure 8a, as the time to market keeps pushing back, its pricing for the upstream market has a slight decrease, and the downstream pricing remains the same, when the later the product is introduced to the market, its impact on the downstream consumers is smaller than that on the upstream merchants.Under optimal pricing, firm A enters the second stage at different times with the benefits shown in Figure 8b.It can be found that platform B maintains the same pricing strategy as the time to market is gradually delayed, and its revenue gradually decreases as the time to market is delayed.Platform A, on the other hand, can better capture the market and obtain higher returns by changing its pricing strategy promptly in a competitive environment.

Sensitivity Analysis
This chapter examines the impact of exogenous variables such as version differentiation strategies and network externalities on platform pricing and time to market.Firm A is used as the experimental group and B is the control group.The effect of changes in different factors of the firm on the optimal pricing, the optimal time to market, and the total revenue of the firm is studied.The firm's returns are expressed as a return ratio (based on the total returns of the benchmark model Π = 41,842,087).The return of firm A is the return after the optimal solution is brought in under different scenarios, and the return of firm B is the return that maintains the same values taken in the benchmark model.

Analysis of the Impact of Product Versions on Consumers in the Downstream Market
For comparison purposes, the impact of the free and paid versions of the product on consumers is set to 0 1 1 2 , q q θ θ .As the impact of the free version increases, the time to mar- ket of the paid version first remains constant and then plummets to 0. That is, the impact of the free version increases when the time to market of the paid version increases, thereby attracting more consumers in the first stage.As the time to market is delayed, the revenue of the company decreases.When the degree of influence of the free version continues to increase, to avoid consumers preferring to use the free version, the platform can only reduce the time to market the paid version until it is listed at the same time.There is some fluctuation in pricing for the upstream and downstream markets, but the change is not significant.Overall, the platform's revenue still increases as the impact level increases.See Figure 9.

Sensitivity Analysis
This chapter examines the impact of exogenous variables such as version differentiation strategies and network externalities on platform pricing and time to market.Firm A is used as the experimental group and B is the control group.The effect of changes in different factors of the firm on the optimal pricing, the optimal time to market, and the total revenue of the firm is studied.The firm's returns are expressed as a return ratio (based on the total returns of the benchmark model Π = 41,842,087).The return of firm A is the return after the optimal solution is brought in under different scenarios, and the return of firm B is the return that maintains the same values taken in the benchmark model.

Analysis of the Impact of Product Versions on Consumers in the Downstream Market
For comparison purposes, the impact of the free and paid versions of the product on consumers is set to θ 0 q 1 , θ 1 q 2 .As the impact of the free version increases, the time to market of the paid version first remains constant and then plummets to 0. That is, the impact of the free version increases when the time to market of the paid version increases, thereby attracting more consumers in the first stage.As the time to market is delayed, the revenue of the company decreases.When the degree of influence of the free version continues to increase, to avoid consumers preferring to use the free version, the platform can only reduce the time to market the paid version until it is listed at the same time.There is some fluctuation in pricing for the upstream and downstream markets, but the change is not significant.Overall, the platform's revenue still increases as the impact level increases.See Figure 9.
The revenue of both firms A and B tends to increase and then decrease as the impact of the free version increases.As the impact of the free version increases, the strategy is to launch the paid version as early as possible, otherwise, the majority of the market will use the free version, resulting in a decrease in the use of the paid version.
As the degree of impact of paid versions increases, the time to market paid versions gradually lengthens.See Figure 10.Revenues also show a trend of increasing and then decreasing as they gradually lengthen.Pricing shows a trend of gradually increasing, with revenue increasing as the price increases.The company's strategy is to postpone the time to market to increase revenue as the impact of the paid version increases, but not all the time, otherwise potential consumers will lose the desire to buy, which leads to a decrease in the profit revenue of the paid version.
The revenue of both firms A and B tends to increase and then decrease as the impact of the free version increases.As the impact of the free version increases, the strategy is to launch the paid version as early as possible, otherwise, the majority of the market will use the free version, resulting in a decrease in the use of the paid version.As the degree of impact of paid versions increases, the time to market paid versions gradually lengthens.See Figure 10.Revenues also show a trend of increasing and then decreasing as they gradually lengthen.Pricing shows a trend of gradually increasing, with revenue increasing as the price increases.The company's strategy is to postpone the time to market to increase revenue as the impact of the paid version increases, but not all the time, otherwise potential consumers will lose the desire to buy, which leads to a decrease in the profit revenue of the paid version.

Market Volume Ratio
In the benchmark model, the second stage market volume

Market Volume Ratio
In the benchmark model, the second stage market volume M 2 is approximately 1.3 times the first stage market volume M 1 .Define M 2 = θ 3 M 1 , and observe the effect of the size M 2 on the firm's revenue when the market volume M 1 is constant.See Figure 11.
(c) (d) . Impact of the parameter 2 q on business decisions and earnings: (a) optimal time to mar- ket; (b) firm returns under optimal time to market for firm A and benchmark time to market for firm B; (c) optimal pricing; (d) firm returns under optimal pricing for firm A and benchmark pricing for firm B.

Market Volume Ratio
In the benchmark model, the second stage market volume  As can be seen from Figure 11, when the market volume ratio between the second stage and the first stage gradually increases, the time to market gradually shortens to zero; as the audience of the paid version increases, the firm can appropriately advance the time to market of the paid version.At the same time, although the optimal pricing for the upstream market decreases as the market volume increases, the revenue of the company keeps increasing.
When the market volume difference between the second stage and the first stage is large, the company can appropriately advance the listing of the paid version, and the pricing for the upstream market can be moderately reduced.

Mismatch Influence Degree Analysis
Let the mismatch between the consumer's service offered to the upstream merchant be 4 θ λ , and make a graph of the relationship between the mismatch and the firm's opti- mal pricing and revenue for the upstream.It can be seen that as the mismatch increases, the firm's pricing for the upstream shows a trend of constant and then increasing.When the mismatch does not change much, it does not affect the change of optimal pricing.When the mismatch continues to increase, the pricing for the merchant increases.In the process of 4   θ change, the revenue ratio shows a trend of increasing and then decreasing, and it can be seen from the figure that when 4   θ takes the optimal price in a certain range, all of them are higher than the revenue of the benchmark model, and the closer to 1, the As can be seen from Figure 11, when the market volume ratio between the second stage and the first stage gradually increases, the time to market gradually shortens to zero; as the audience of the paid version increases, the firm can appropriately advance the time to market of the paid version.At the same time, although the optimal pricing for the upstream market decreases as the market volume increases, the revenue of the company keeps increasing.
When the market volume difference between the second stage and the first stage is large, the company can appropriately advance the listing of the paid version, and the pricing for the upstream market can be moderately reduced.

Mismatch Influence Degree Analysis
Let the mismatch between the consumer's service offered to the upstream merchant be θ 4 λ, and make a graph of the relationship between the mismatch and the firm's optimal pricing and revenue for the upstream.It can be seen that as the mismatch increases, the firm's pricing for the upstream shows a trend of constant and then increasing.When the mismatch does not change much, it does not affect the change of optimal pricing.When the mismatch continues to increase, the pricing for the merchant increases.In the process of θ 4 change, the revenue ratio shows a trend of increasing and then decreasing, and it can be seen from the figure that when θ 4 takes the optimal price in a certain range, all of them are higher than the revenue of the benchmark model, and the closer to 1, the larger the ratio is.When the platform firm A takes the optimal pricing under different mismatch degrees, while B remains unchanged, it can be seen that the gain of firm A is larger than that of B. Meanwhile, in the competitive process, as the mismatch degree of its service provision increases, the platform's gain will show a slight increase under normal circumstances.When one of the two competing parties changes its pricing with the mismatch degree, the profit gain of the changing party will increase and the degree of increase decreases with the increase of the mismatch degree, and the gain of the unchanging party will also increase but to a small extent in the competitive process.See Figure 12.When the mismatch between the services proposed by platform for upstream markets and the expectations of the upstream merchants themselves increases, companies may resort to increasing their pricing to upstream markets to compensate for the total revenue of the company.

The Degree of Influence of Upstream Merchants on Consumers after the Start of the Second Phase
Assuming that upstream merchants use paid versions for consumers is θ 5 times the impact of the free version, observe the impact of the size of ρ n 1 on business revenue when the market volume ρ m 1 is constant.See Figure 13.As can be seen from Figure 13, as the ratio of upstream merchants' influence on consumers' use of the paid version to the free version of the product increases, the optimal time to market for the paid version gradually lengthens, and the platform's optimal pricing for the upstream market decreases somewhat.The platform's adoption of the optimal pricing strategy at different degrees of influence can bring higher revenue to the company.
When the upstream merchants of a platform company have a greater impact on consumers' use of the paid version versus the free version of the product, the company can reduce pricing and delay the launch of the paid version to obtain higher revenue.When the upstream merchants of a platform company have a greater impact on consumers' use of the paid version versus the free version of the product, the company can reduce pricing and delay the launch of the paid version to obtain higher revenue.

Model Comparative Analysis
Solve for the optimal pricing strategy of the model in the unilateral market and the revenue under this strategy, compare the optimal strategy of the model in the unilateral and bilateral markets, and analyze the feasibility of considering the bilateral market.The platform needs to consider the mutual influence between bilateral markets, so they have a different strategy in pricing than in unilateral markets.In this paper, we establish the relationship by considering the influence between bilateral markets as external factors in the Bass model in the study of product diffusion.It is assumed that platform firms consider only unilateral utility,  is considered a constant in the model of this pa- per. The implication is the effect of advertising and promotion means on consumers' use of platform A.

Model Comparative Analysis
Solve for the optimal pricing strategy of the model in the unilateral market and the platform revenue under this strategy, compare the optimal strategy of the model in the unilateral and bilateral markets, and analyze the feasibility of considering the bilateral market.The platform needs to consider the mutual influence between bilateral markets, so they have a different strategy in pricing than in unilateral markets.In this paper, we establish the relationship by considering the influence between bilateral markets as external factors in the Bass model in the study of product diffusion.It is assumed that platform firms consider only unilateral utility, β is considered a constant in the model of this paper.β The implication is the effect of advertising and promotion means on consumers' use of platform A.
At this point, the first stage is modeled as: Still assuming that the paid version is brought to market in week 20, the model for phase 2 is: The revenue model of the platform is: Under this model, simulating different β values and the rest of the variables taking the same values, the usage of platform A and the revenue at 100 weeks are simulated as shown in the Table 3.Using the benchmark model as a comparison, the revenue of firm A is Π = 41,842,087, D A1 = 34,945,276, and D A2 = 48,552,775.It can be seen that although the usage of the paid version under the bilateral is not as much as under the unilateral market only, the usage of the free version is more and the revenue is greater when considering the bilateral market.When considering pricing and time-to-market decisions, the platform should focus more on the bilateral market to bring more revenue.

Discussion and Conclusions
Platforms face bilateral markets, where their profits are no longer purely consumer profits, but the sum of bilateral profits is considered comprehensively.In this paper, we consider that the size of upstream companies also has an impact on platform pricing for consumers.The impact of the bilateral market is considered to study the bilateral pricing strategy under the maximization of the total revenue of the platform.
Most of the existing literature on the diffusion process of innovative products into the market has been studied in unilateral markets, however, in reality, more and more platforms are choosing to adopt freemium models when launching into the market.When two platforms are competing in the market and when adopting freemium models to the consumer side, it is important to study how platforms enter the market as well as the time difference between free and paid versions of the market launch and the pricing mix strategies of platforms under different circumstances.This should be added to existing studies.
The use of the Bass model is mostly in the unilateral market, and network externalities are introduced into the model to improve the model to make it suitable for modeling the diffusion process of platforms in bilateral markets.A comprehensive consideration of network externalities is informative in studying the necessary conditions for platform entry into the market.The application of the Bass model has been extended.This study is the first attempt to investigate the time-to-market and pricing issues of a freemium version of a product under a bilateral platform considering the competition between the two platforms.Using cross-network externalities, the innovation diffusion model used in the unilateral case is applied to the bilateral market.In the bilateral market, upstream merchants can choose to access either platform A or platform B, and downstream consumers can choose to use either the free or paid version of platform A or platform B. The platform chooses the time to market for the free and paid versions and the pricing for the bilateral.Firstly, we simulated the diffusion process of a new product launch based on the Bass model and borrowed the system dynamics to build a model for simulation, which simulated the process and results of market demand change of versioned products in the process of platform competition.Secondly, the benchmark model is set up and the effects of exogenous variables on the optimal pricing, the optimal time to market, and revenue of the product are analyzed by modifying the model parameters.Ultimately, the management insights of bilateral platforms in a competitive market environment are obtained.
(1) In a competitive market environment, external factors have an impact on the market share and revenue of a company, and companies should try to stimulate the "excitement" of consumers and maintain the "communication" of consumers so that they can capture the market faster and gain higher This will lead to faster market capture and higher revenues.
(2) In a competitive market environment, the difference in the timing of the firm's entry into the second stage affects the firm's returns.When two firms delay their launch at the same time, the impact on the revenue between platforms is not significant.However, when two firms do not enter the second stage at the same time, the platform firm that launches the paid version into the second stage first has a more competitive advantage.
(3) In a competitive market environment, although the revenue of the platform increases with higher prices, they should not pursue low or high prices.Lower prices in the upstream market will lead to higher revenues because lower fees for upstream merchants will affect the usage of the downstream market through cross-network externalities, thus increasing the revenue of the platform.Higher prices in the downstream market lead to higher revenues, but also affect the market share of the paid version.
(4) Exogenous variables.When the influence of free product versions on consumers increases, enterprises should list paid versions as early as possible.When the influence of paid version on consumers increases, the listing time can be postponed to increase the revenue, which can reduce the pressure of platform product development; when the market volume difference is large, enterprises can list paid versions earlier and reduce the pricing to the upstream market; when the mismatch of the platform in the upstream market increases, enterprises can increase the pricing in the upstream market; when the upstream merchants have a large influence on consumers' choice of different versions, in case of a large difference in consumer choice, the company can adopt the strategy of lowering the price and delaying the launch of the paid version to obtain higher revenue.
(5) Companies adopt a marketing mix strategy of platform product benefits and quality word-of-mouth to be able to promote their products more efficiently.When developing strategies, enterprises can consider bilateral markets can be greater than considering the total use of the two versions of the unilateral market, but also can bring more revenue for the enterprise.
We investigate the process of launching a new product in a bilateral market by a platform.The platform adopts a single pricing strategy for the upstream market and a freemium model for the downstream market, with a "free" and then "fee" approach.We propose the optimal pricing strategy for the platform in the bilateral market and the optimal time to market for the paid version in the downstream market, as well as the optimal combination strategy for the platform in different market environments, which provides a theoretical basis for the competitive combination strategy of the platform.This paper integrates the effects of network externalities and quality version differences.In reality, there are other influencing factors, such as competing platforms offering different product qualities, which can be studied in the future.

Figure 1 .
Figure 1.Demand model of the first stage product.The demand model of the second stage is shown in Figure2, which is similar to the demand model of the free version in the first stage, with the difference that the second

Figure 1 .
Figure 1.Demand model of the first stage product.

Sustainability 2023 ,Figure 2 .
Figure 2. Demand model of the second stage product.(a) is when platforms A and B in the market are offered only in the free version, (b) both free and paid versions are present in the market.

Figure 2 .
Figure 2. Demand model of the second stage product.(a) is when platforms A and B in the market are offered only in the free version, (b) both free and paid versions are present in the market.
,552,775.The demand for the product of firm A in different periods can be seen in Figure3.The demand for the free version of A1 peaked at week 51 from its launch, and the paid version was in the market from week 20 and was still increasing at week 100.

1 AD
= 34,997,877, and 2 A D = 45,009,681.The demand for firm A's product in different periods can be seen in Figure 4a.The demand for the free version of A1 peaked at week 65 after its launch, and the paid version started to enter the market from week 20 and reached its peak by week 77.Compared with the benchmark model, we can see that when consumers are active all the time, more consumers will stimulate the remaining consumers to use the free version, and the company's revenue will decrease instead.(a) (b)

Figure 4 .
Figure 4. (a) Sales of products when consumers are completely undamaged; (b) sales of products when consumer influence increases.
,552,775.The demand for the product of firm A in different periods can be seen in Figure3.The demand for the free version of A1 peaked at week 51 from its launch, and the paid version was in the market from week 20 and was still increasing at week 100.

1 ADFigure 4 .
Figure 4. (a) Sales of products when consumers are completely undamaged; (b) sales of products when consumer influence increases.By modifying the parameters of the model, it is assumed that the degree of influence of the purchaser of firm A or B on potential consumers increases.The benefits for firm A are = 41,905,902, = 34,945,120, and = 48,632,008.It can be seen that when increasing the attractiveness of the purchaser's potential purchases, the use of the free version decreases,

Figure 4 .
Figure 4. (a) Sales of products when consumers are completely undamaged; (b) sales of products when consumer influence increases.

3. 2 . 1 .Figure 5 .
Figure 5. (a) Graph of the relationship between firm earnings and time to market; (b) graph of earnings when two firms do not enter the second stage at the same time.

Figure 5 .
Figure 5. (a) Graph of the relationship between firm earnings and time to market; (b) graph of earnings when two firms do not enter the second stage at the same time.

Figure 6 ..Figure 7 .
Figure 6.(a) Revenue of enterprise A versus the price of downstream paid version; (b) product usage versus the price of the downstream paid version.3.3.2.Optimal Pricing for Upstream MerchantsIn this paper, we assume that firm B's pricing upstream is always constant and analyze the graph between firm A's revenue and upstream price, as shown in Figure7a.With 1 p s as

Figure 6 .
Figure 6.(a) Revenue of enterprise A versus the price of downstream paid version; (b) product usage versus the price of the downstream paid version.

Figure 6 ..Figure 7 .
Figure 6.(a) Revenue of enterprise A versus the price of downstream paid version; (b) product usage versus the price of the downstream paid version.3.3.2.Optimal Pricing for Upstream MerchantsIn this paper, we assume that firm B's pricing upstream is always constant and analyze the graph between firm A's revenue and upstream price, as shown in Figure7a.With 1 p s as

Figure 7 .
Figure 7. (a) Graph comparing revenue and upstream price of firm A; (b) graph comparing product usage and upstream price.

Figure 8 .
Figure 8.(a) Optimal pricing corresponding to a different time to market; (b) product revenue of firm A and firm B under a joint decision.

Figure 8 .
Figure 8.(a) Optimal pricing corresponding to a different time to market; (b) product revenue of firm A and firm B under a joint decision.

Figure 9 .
Figure 9. Impact of the parameter 1 q on business decisions and earnings: (a) optimal time to mar- ket; (b) firm returns under optimal time to market for firm A and benchmark time to market for firm B; (c) optimal pricing; (d) firm returns under optimal pricing for firm A and benchmark pricing for firm B.

Figure 9 .
Figure 9. Impact of the parameter q 1 on business decisions and earnings: (a) optimal time to market; (b) firm returns under optimal time to market for firm A and benchmark time to market for firm B; (c) optimal pricing; (d) firm returns under optimal pricing for firm A and benchmark pricing for firm B.

Figure 10 .
Figure 10.Impact of the parameter 2 q on business decisions and earnings: (a) optimal time to market; (b) firm returns under optimal time to market for firm A and benchmark time to market for firm B; (c) optimal pricing; (d) firm returns under optimal pricing for firm A and benchmark pricing for firm B.

2 M is approximately 1. 3 times the first stage market volume 1 M
. Define

2 M
on the firm's revenue when the market volume 1 M is constant.See Figure11.

Figure 10 .
Figure10.Impact of the parameter q 2 on business decisions and earnings: (a) optimal time to market; (b) firm returns under optimal time to market for firm A and benchmark time to market for firm B; (c) optimal pricing; (d) firm returns under optimal pricing for firm A and benchmark pricing for firm B.

2 M is approximately 1. 3 times the first stage market volume 1 M
. Define

Figure 11 .
Figure 11.Impact of the parameter M 2 on business decisions and earnings: (a) optimal time to market; (b) firm returns under optimal time to market for firm A and benchmark time to market for firm B; (c) optimal pricing; (d) firm returns under optimal pricing for firm A and benchmark pricing for firm B.

Figure 12 .
Figure 12.Effect of the parameter on business decisions and earnings: (a) Upstream market optimal pricing; (b) upstream market optimal pricing and firm returns at benchmark pricing.

4. 4 . 1 n ρ on business revenue when the market volume m 1 ρFigure 12 .
Figure 12.Effect of the parameter on business decisions and earnings: (a) Upstream market optimal pricing; (b) upstream market optimal pricing and firm returns at benchmark pricing.

Figure 13 . 1 
Figure 13.Impact of the parameter m 1  on business decisions and earnings: (a) optimal time to market; (b) firm returns under optimal time to market for firm A and benchmark time to market for firm B; (c) optimal pricing; (d) firm returns under optimal pricing for firm A and benchmark pricing for firm B.

Figure 13 .
Figure 13.Impact of the parameter ρ m 1 on business decisions and earnings: (a) optimal time to market; (b) firm returns under optimal time to market for firm A and benchmark time to market for firm B; (c) optimal pricing; (d) firm returns under optimal pricing for firm A and benchmark pricing for firm B.

Table 1 .
Variables and their meanings in the model.

Table 2 .
Parameter settings of the benchmark model.

Table 3 .
Diffusion of products in unilateral markets at different β values.