Liquidity generated by heterogeneous beliefs and costly estimations

We study the liquidity, de ned as the size of the trading volume, in a situation where an in nite number of agents with heterogeneous beliefs reach a trade-o between the cost of a precise estimation (variable depending on the agent) and the expected wealth from trading. The \true" asset price is not known and the market 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 supply and demand functions with respect to the price, existence of an equilibrium and monotony with respect to the marginal 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 in nite number of agents.