Abstract: Amidst escalating societal competition and improving living standards, there is an increasing demand for various paid knowledge services, leading to the thriving development of online knowledge service markets. However, this development also faces challenges, such as the varying quality of knowledge services, making it difficult for consumers to identify high-quality service providers. As an intangible product, it is challenging for consumers to judge the quality or intrinsic utility of knowledge services based on their external characteristics. Serious information asymmetry exists between consumers and service providers, with consumers only able to reduce uncertainty about the quality of knowledge services after experiencing them. Therefore, many knowledge service providers reduce this uncertainty by offering a limited duration of free services to attract consumers to purchase paid knowledge services.
This “limited-time free service” strategy may impact the profitability of knowledge service providers in several ways. Firstly, offering limited-time free knowledge services can help reduce consumers’ perceived uncertainty about service quality, enhance perceived utility and attract more consumers to purchase paid knowledge services. Secondly, providing time-limited free knowledge services may cannibalize consumers who initially intend to purchase paid knowledge services. For instance, if consumers find that free knowledge services meet their consultation needs, they may not continue to purchase paid knowledge services. Finally, if competing knowledge service providers offer free knowledge services, there is a possibility of potential consumers attracted by competitors’ free service strategies, resulting in loss of consumers for themselves. Therefore, in a competitive environment, knowledge service providers may adopt strategies with a certain duration of free services or purely paid service. This paper poses two research questions under duopoly competition: What is the optimal pricing for knowledge service providers under different strategic scenarios? Under what conditions is the strategy of limited-time free knowledge services superior to the strategy of purely paid knowledge services?
Regarding the decision-making problems of service providers offering limited-time free services and purely paid services, this paper studies the strategic choice game process of service providers under duopoly competition and analyzes equilibrium prices and profits under four scenarios. Nash equilibria under different scenarios are derived using backward induction.
The study finds that: First, the optimal pricing of service providers under the free service strategy is influenced by consumers’ mismatched costs, the duration of free services provided, the difference between the actual service quality of service providers and consumers’ perceived service quality before the free trial, the difference between competitors’ actual service quality and consumers’ perceived service quality before the free trial, and the unit service costs of both competitors. Second, the longer the duration of free services provided by service providers, the higher the optimal pricing for their paid knowledge services; when the duration of free services exceeds a certain threshold, the optimal pricing of competitors’ paid knowledge services decreases with increasing duration of free services. Third, when the service cost of service providers is low, they tend to choose the strategy of offering limited-time free services.
This paper makes the following theoretical contributions. Firstly, unlike previous literature on information products, this paper considers the service provider’s service cost when providing services in the theoretical model. Secondly, this study explores the free service strategy choices and paid service pricing strategies of service providers under competitive situations, complementing research related to the “free trial” strategy of individual service providers under monopoly situations.

Key words: knowledge paid services, limited-time free service strategy, duopoly pricing strategy

摘要： 随着知识付费服务的兴起,部分知识服务者会采取提供一定时长免费服务来达到营销的目的。针对服务者提供有限时长免费服务以及纯粹付费服务的决策选择问题,本文研究了双寡头竞争情形下的服务者策略选择博弈过程,分析了四种情形下的均衡价格和利润,使用逆向归纳法求得了不同情形下的纳什均衡。研究发现:(1)服务者在提供免费服务策略下的最优付费服务定价会受到消费者的不匹配成本、提供免费服务的时长、服务者真实服务质量和消费者在免费试用前感知服务质量之差、竞争者真实服务质量和消费者在免费试用前感知服务质量之差、竞争者双方的单位服务成本的影响。(2)服务者提供的免费服务时长越长,则其付费知识服务的最优定价越高;当免费服务时长超过一定阈值时,其竞争对手的最优付费知识服务定价随免费时长的增加而降低。(3)当服务者的服务成本较小时,会选择采用有限时长免费的服务策略。

关键词: 知识付费服务, 有限时长免费服务策略, 双寡头定价策略