Contracts with Endogenous Information

I derive a general formulation of a Bayes Nash revelation game in a linear environment with endogenous information, whose precision depends on a covert choice of effort. I show that in nonstochastic mechanisms the first order approach to reporting (the Mirrless approach) can be complemented by a first order approach to effort spent on information acquisition if and only if i) the agent's posterior is independent of the agent's effort, ii) an increase in the agent's effort increases the risk (in the sense of Rothschild and Stiglitz (1970) in the ex ante distribution of the posterior mean, and iii) does so at a decreasing rate. Experiment structures with these characteristics arise when posteriors resulting from high (low) signals are higher (lower) for more informative signals (i.e., in monotone environments). The marginal value of information is ambiguous. Sufficient conditions for a negative or positive marginal value are derived. Contracts that encourage (discourage) information acquisition are more (less) sensitive to the agent's information than their counterparts for exogenous information structures. Distortions at the top arise if the agent may choose the precision of information directly.