适应性预期条件下的双边平台动态最优价格研究

The Dynamic Optimal Prices of Two-sided Platform with Adaptive Expectations

本文研究了当市场两边的用户序贯加入时,在先加入一边的用户对后加入一边的用户的数量形成适应性预期的条件下,双边平台的动态最优价格。本文建立了适应性预期的双边市场最优控制模型,在垄断和双寡头两种市场结构中分别使用欧拉方程和拉格朗日乘子法求解出了两种不同表现形式的最优价格序列,前者表现为任意一期最优价格与以往最优价格之间的关系,后者表现为从初始期到终止期的最优价格的完整序列,分别适用于解决平台在以往最优价格已知或以往最优价格未知但终止时间既定这两种情况下的定价问题。最终根据后一种价格序列进行了数值仿真。

We study the dynamic optimal prices of two-sided platforms which the two sides of users sequentially join and the users of firstly joining side form adaptive expectations to the quantity of the users of secondly joining side. We build up the optimum control model of two-sided market based on adaptive expectation and respectively solve the model through Euler equation and Lagrangian multiplier method in order to obtain two optimal prices sequences which differ in the types of expression in each of the monopoly and duopoly market. The two sequences, which the former one is shown as the relation between the optimal prices of the current period and the optimal prices of past periods and the later one is shown as the complete optimal prices sequence from initial period to terminal period, would respectively apply to the pricing problem of platforms under different conditions that the optimal prices of past periods are given or the time of termination is given rather than that of the past optimal prices. Finally, we simulate the numerical values of optimal prices based on the later sequence.