This paper is available on arxiv under CC 4.0 license.

**Authors:**

(1) Kiriaki Frangias;

(2) Andrew Lin;

(3) Ellen Vitercik;

(4) Manolis Zampetakis.

## Table of Links

Warm-up: Agents with known equal disutility

Agents with unknown disutilites

Conclusions and future directions, References

B Omitted proofs from Section 2

C Omitted proofs from Section 3

D Additional Information about Experiments

## C Omitted proofs from Section 3

We similarly handle the second case, in which the agent does not exert effort, this time noting that the agent does not experience disutility:

For agent a*i* to be incentivized to exert effort, the payment needs to be such that:

Using E[|C*i*|] < d and simplifying we get the lower bound:

To satisfy individual rationality, we require the following:

which holds if and only if:

which is always satisfied as long as constraint 12 is satisfied.

where the first inequality follows from above. Therefore the optimization problem for a suitable *g*∗ is the following:

such that:

*This paper is available on Arxiv under CC 4.0 license.*