We propose a multi-agents adverse selection version of Townsend's (1979) model of costly audits where the agents' types are correlated. Audits are used because agents have a limited ability to bear risk so that the Full Surplus Extraction (FSE) scheme a la Cremer and McLean (1985,1988) and McAfee and Reny (1992) would be suboptimal here. It is shown that Townsend's result of an optimal marginal arbitrage between rent extraction and efficiency does not hold in the case of perfect correlation: FSE is feasible -- even in dominant strategies -- by devising a contract that put the agents in a prisoner's dilemma. A numerical simulation of the model is performed which suggests that the single agent model is not a good approximation of the multi-agents case.