Optimal Timings Of Two-sided Platforms’ Pricing Games Under Different Expectations

The paper studys the two-sided platforms’ optimal timings of pricing game between two sides of market under different users’ expectations.Two-sided platforms need to complete pricing games with both sides for equilibriums,because users’ benefits in each side depend on number of users in the other side.There are three possible timings of two-sided platforms’ pricing games which are playing game with both sides simultaneously,playing game with one side before the other and the reversed order.Platforms may choose any timing of them and the timings can influence the users’ decisions,but the past researches about two-sided markets only consider the games with simultaneous timing,so we can not judge that which timing is optimal for the platforms.Meanwhile,the expectation of users is also an important factor for demands of two-side markets and the effects of timings to decisions of users depend on the users’ expectations.The past researches about two-sided markets have studied three types of expectations which are responsive expectation,passive expectation and wary expectation.The paper introduces the adaptive and dynamic equilibrium model to two-sided markets,study the optimal timings of pricing games under three different expectations which are active expectation,passive expectation and adaptive expectation through the comparison of equilibrium profits of platforms based on equilibrium model framework of two-sided markets.Moreover,we consider three types of market structure which are monopoly(monopoly in both sides),competitive bottlenecks(monopoly in one sides and differentiated competition in the other)and duopoly(differentiated competition in both sides)The main contributions of the paper are as following conclusions:(1)Optimal timings in monopoly market.Simultaneous game is optimal if users are all form active expectation and any of two sequential games is more profitable than simultaneous game if users all form passive expectation.The result is uncertain,but simultaneous game is worst in most of simulation samples if users all form adaptive expectation.(2)Optimal timings in competitive bottlenecks market.The paper turn to the market which is differentiated and competitive with fixed capacity in one side and monopolistic in the other side.It is optimal to play game with monopolistic side before competitive side if users are all form active expectation.It is optimal to play game with competitive side firstly with active users only if the differentiation between platforms is very weak.On the contrary,simultaneous game is optimal if users all form passive expectation.The result is uncertain,but playing game with monopoly side is optimal in most of simulation samples if users all form adaptive expectation.(3)Optimal timings in duopoly market.It is the market which is differentiated and competitive with fixed capacities in both sides.It is optimal to play game firstly with the side which is weaker in differentiation and stronger in cross-group externalities than the other side if users are all form active expectation.On the contrary,simultaneous game is optimal if users all form passive expectation.The result is uncertain,simultaneous game is optimal in most of simulation samples with short termination time and the advantage to other timings vanishes along with grown of termination time if users all form adaptive expectation.(4)Pricing strategies under adaptive expectation.The paper obtains the sequences of dynamic optimal prices under adaptive expectation in monopoly,competitive bottlenecks and duopoly markets through dynamic equilibrium model and Optimal Control Method.The paper also verify the rationality of a common strategy for devloping two-sided markets which is attracting users by lower prices before earning profit by rising prices.(5)Comparison of expectations.The profits with active expectation users are higher than with passive expectation users in monopoly market and it is reversed in other two competitive markets regardless of timings.Finally,the results above are all based on conditions that cross-group network externalities are positive and all of the equilibriums are existent,unique and valid.The later condition exists only if the cross-group network externalities are relatively weaker in monopoly market and only if the cross-group network externalities are weaker relative to the differentiations in other two types of market.