We study in this work the liquidity, defined as the size of the trading volume, in a situation when an infinite number of agents with het- erogeneous beliefs reach a trade-off between cost of a precise estimation (variable depending on the agent) and expected profit from trading at the resulting estimate price. The "true" asset price is not known and the mar- ket price is set at a level that clears the market. We show that under some technical assumptions the model has natural properties such as monotony of offer and demand functions with respect to the price, existence of an overall equilibrium and monotony with respect to cost of information. We also situate our approach within the Mean Field Games (MFG) framework of Lions and Lasry which allows to obtain an interpretation as a limit of Nash equilibrium for an infinite number of players.