Latent Dirichlet Allocation for Internet Price War

Internet market makers are always facing intense competitive environment, where personalized price reductions or discounted coupons are provided for attracting more customers. Participants in such a price war scenario have to invest a lot to catch up with other competitors. However, such a huge cost of money may not always lead to an improvement of market share. This is mainly due to a lack of information about others' strategies or customers' willingness when participants develop their strategies. In order to obtain this hidden information through observable data, we study the relationship between companies and customers in the Internet price war. Theoretically, we provide a formalization of the problem as a stochastic game with imperfect and incomplete information. Then we develop a variant of Latent Dirichlet Allocation (LDA) to infer latent variables under the current market environment, which represents the preferences of customers and strategies of competitors. To our best knowledge, it is the first time that LDA is applied to game scenario. We conduct simulated experiments where our LDA model exhibits a significant improvement on finding strategies in the Internet price war by including all available market information of the market maker's competitors. And the model is applied to an open dataset for real business. Through comparisons on the likelihood of prediction for users' behavior and distribution distance between inferred opponent's strategy and the real one, our model is shown to be able to provide a better understanding for the market environment. Our work marks a successful learning method to infer latent information in the environment of price war by the LDA modeling, and sets an example for related competitive applications to follow.