A.2 Price of Stability: Analysis of Example 2

In this section we prove that in Example 2, the agent takes a1 in all equilibria. The proof relies on
the following Claim.

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Claim 7. Consider Example 2. For every bid proﬁle that incentivizes the agent to take ai for i > 1,
the principal’s expected utility is at most 1 − (cid:15)/(1 − γ).
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