  In real life auctions, a widely observed phenomenon is the winner's curse --
the winner's high bid implies that the winner often over-estimates the value of
the good for sale, resulting in an incurred negative utility. The seminal work
of Eyster and Rabin [Econometrica'05] introduced a behavioral model aimed to
explain this observed anomaly. We term agents who display this bias "cursed
agents". We adopt their model in the interdependent value setting, and aim to
devise mechanisms that prevent the cursed agents from obtaining negative
utility. We design mechanisms that are cursed ex-post IC, that is, incentivize
agents to bid their true signal even though they are cursed, while ensuring
that the outcome is individually rational -- the price the agents pay is no
more than the agents' true value.
  Since the agents might over-estimate the good's value, such mechanisms might
require the seller to make positive transfers to the agents to prevent agents
from over-paying. For revenue maximization, we give the optimal deterministic
and anonymous mechanism. For welfare maximization, we require ex-post budget
balance (EPBB), as positive transfers might lead to negative revenue. We
propose a masking operation that takes any deterministic mechanism, and imposes
that the seller would not make positive transfers, enforcing EPBB. We show that
in typical settings, EPBB implies that the mechanism cannot make any positive
transfers, implying that applying the masking operation on the fully efficient
mechanism results in a socially optimal EPBB mechanism. This further implies
that if the valuation function is the maximum of agents' signals, the optimal
EPBB mechanism obtains zero welfare. In contrast, we show that for sum-concave
valuations, which include weighted-sum valuations and l_p-norms, the welfare
optimal EPBB mechanism obtains half of the optimal welfare as the number of
agents grows large.
