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.
