Computational principal agent problems

Collecting and processing large amounts of data is becoming increasingly crucial in our society. We model this task as evaluating a function f over a large vector x = (x1, . . . , xn), which is unknown, but drawn from a publicly known distribution X. In our model learning each component of the input x is costly, but computing the output f(x) has zero cost once x is known. We consider the problem of a principal who wishes to delegate the evaluation of f to an agent, whose cost of learning any number of components of x is always lower than the corresponding cost of the principal. We prove that, for every continuous function f and every ε > 0, the principal can— by learning a single component xi of x—incentivize the agent to report the correct value f(x) with accuracy ε. ∗Email: [email protected]. Address: MIT Economics. 77 Massachusetts Ave. E52-300, Cambridge MA, 02139. †Email: [email protected]. Address: MIT Electrical Engineering and Computer Science. 32 Vassar Street, Cambridge, MA 02139.