Pricing In Two-sided Markets With Users' Expectations

In two-sided markets,platform revenues mainly come from prices charged to users.Pricing problems in two-sided markets are the emphasis of many researcher in this area.Most of these pricing studies are based on complete information,and seldom consider the effect of users' expectations under incomplete information.When information is incomplete,users base expectations on known information,and then decide whether to subscribe to the platform.Ignoring users' expectations may cause startup failure.The structure in the markets is affected by users' expectations as well.Pricing in two-sided markets without considering users' expectations will lead to the reduction of profits,or even business failure whether the market is monopoly or competitive.However,early studies on pricing in two-sided markets rarely analyze users' expectations.This area needs to be enriched.To this end,this paper makes an in-depth and systematic study on the startup problem and market structure,the static and dynamic pricing of a monopoly platform,and the pricing and market entry of competitive platforms while considering users' expectations.This study enriches the theory of platform operation,contributes to the practice of platforms,and has important theoretical and practical significance.Firstly,we study the startup of a monopoly platform with the consideration of users' expectations.It is found that given the platform's pricing,when the numbers of initial users on the two sides are on the critical trajectory,the final equilibrium is unstable.Otherwise,the final equilibrium is stable.Whether in the myopic case or the case with users' expectations,when the numbers of initial users are above the critical trajectory,the platform can reach the equilibrium with high numbers of users,i.e.the platform makes a successful launch,and when the numbers of initial users are below the critical trajectory,the platform makes a failure launch.In addition,when users on one side base decisions more on their beliefs,the launch will be easier if the platform prefers to attract users on this side.The ex post equilibria with fulfilled expectations have nothing to do with the way of users' expectations.However,the way of users' expectations affects the position of the critical trajectory and then influences the final equilibrium.Hence,for the platform manager,in the initial period,he should pay attention to the effect of users' expectations as users' expectations affect the critical trajectory,while in the long term,the platform's profits depend on factors which can improve the users' real utility such as user experience,the platform's service level and information security because the ex post equilibria are not affected by the way of users' expectations.Secondly,we study the structure of two-sided markets under fulfilled expectations equilibrium.We find that users' standalone valuations,which are derived from platform functions or services rather than indirect network effects,can affect the market structure.That the standalone valuation on one side is small has two effects.Firstly,the strength gap between incumbents and inactive platforms based on the same side will be high and then it is difficult for inactive platforms to enter the markets.Secondly,because of indirect network effects,it reduces the strength gap between incumbents and inactive platforms based on the other side and then makes it easy for inactive platforms to enter the markets.Hence,given the ratio of the standalone valuations on the two sides,the market structure is more monopolized if the sum of the two standalone valuations is small,and given the sum of the two standalone valuations,if the difference between the two standalone valuations is big,the market structure is more competitive.In addition,when indirect network effects are strong,the market structure is more monopolized.In competitive bottlenecks,incumbents should pay attention to the standalone valuation on the single-homing side so as to prevent the entry of inactive platforms.Thirdly,we discuss static pricing of a monopoly platform under membership heterogeneity and interaction heterogeneity.We find that when the expectations of users on one side change from passive to responsive(i.e.users on this side will have complete information),under membership heterogeneity(the standalone valuation of users on each side is heterogeneous),the optimal number of users on either side increases,while under interaction heterogeneity(the indirect network effects are heterogeneous),the optimal prices make against users on this side and benefit users on the other side.Under either heterogeneity,when the expectations of users on one side change from passive to responsive,the platform should attract more users on the other side.From the perspective of multiproduct pricing,under membership heterogeneity,users on the two sides are similar to complementary goods,while under interaction heterogeneity,users on the two sides are similar to substitute goods.Fourthly,with the consideration of users' expectations,we study dynamic pricing on a monopoly platform.We find that the optimal prices are affected by marginal costs,indirect network effects and price elasticities.In contrast to the static model in twosided markets,the marginal costs should also include time cost,and the indirect network effects and price elasticities depend on the existing numbers of users rather than on the demands of users.In equilibrium,even though the willingness-to-pay functions and the cost functions are symmetric,skewed pricing may still be optimal.In the complete symmetric case,when users on one side base decisions more on beliefs,the optimal price trajectory increases rapidly in the period when the numbers of users are low,and then converges to the equilibrium with high numbers of users.In addition,when the discount rate is low,the growth rates of users are high,or the marginal costs are low,the optimal price trajectory increases rapidly in the period when the numbers of users are high and then converges to the equilibrium with high numbers of users.Fifthly,we study symmetric equilibrium and asymmetric equilibrium in two-sided markets where platforms enter markets at the same time.In the symmetric equilibrium(users' expectations for the two platforms are the same),whether users single-home or multi-home,when the expectations of users on one side change from expectations to responsive,the platform should set low prices for users on the other side.In contrast to two-sided single-homing,in competitive bottlenecks,the platform's profits may be lower.In the asymmetric equilibrium(users' expectations for the two platforms are different),when the expectations of users on one side change from passive to responsive,the superior platform for which users hold high expectations and the inferior platform for which users hold low expectations should set high prices for users on this side and set low prices for users on the other side when users on the two sides single-home.In addition,in competitive bottlenecks,asymmetric equilibrium may not exist,and in the case where it exists,in contrast to two-sided single-homing,the inferior platform's profits increase and the profit gap between the superior platform and the inferior platform decreases.Finally,we study competition between an incumbent and an entrant.We find that with the change of the parameters of indirect network effects,for the incumbent,the optimal strategies are the seesaw principle on the numbers of users,i.e.,the platform will increase the number of users on one side and decrease the number of users on the other side;for the entrant,the optimal strategies are opposite to the incumbent on the single-homing side and have nothing to do with the incumbent on the multi-homing side.In the case with two-sided single-homing,the profits of the entrant decrease with the difference between the parameters of indirect network effects on the two sides.In competitive bottlenecks,compared with two-sided single-homing,the entrant's profits may be lower in the Stackelberg model,while in the Cournot model,the profits of the entrant increase and the profits of the incumbent decrease.In addition,in contrast to the Stackelberg model,in the Cournot model,the profits of the incumbent decrease and the profits of the entrant increase.