Theoretical Economics 13 (2018), 553–578

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### Computational principal agent problems

*Pablo D. Azar, Silvio Micali*

#### Abstract

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 Îµ > 0, the principal canâ€”
by learning a single component x1 of xâ€”incentivize the agent to report the correct value
f(x) with accuracy Îµ.

Keywords: Principal agent problems, computational complexity

JEL classification: D82,D86

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