In this paper, a price mechanism for a competitive market possibly possessing a coupled dynamics of price and demand is considered from the control theoretic viewpoint. In particular, an application of Linear Quadratic controller is proposed as a price adjusting algorithm to regulate both price and demand to the unknown equilibrium. To design such a controller, the market operator needs to know the full characterization of the market, which is available only locally. Using a heuristics involving l1 norm optimization, we propose a method for local agents to select "minimum but important" information describing themselves and send it to the market operator, with which a better controller design is possible. This gives a novel and practical way for the price mechanism design using reduced information about the market.