First-price Sealed-bid Auctions with Smoothly Ambiguity Averse Bidders
Tianyu Ma and Frank Riedel
We study first-price sealed-bid auctions with two risk-neutral bidders who have independent private
values but are smoothly ambiguity averse about the distribution of their opponents' valuations. Adopting
the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji (2005), we separate ambiguity attitudes
from risk and establish existence and uniqueness of a symmetric, non-decreasing equilibrium. Although the
primitives feature independent private values, we show that equilibrium bidding is observationally
equivalent to that in a subjective expected utility auction with correlated private values: there exists a
correlated-values environment whose interim beliefs reproduce the same bidding function, and under
constant relative ambiguity aversion these effective beliefs become type independent. Greater ambiguity
aversion induces more aggressive bidding, and as ambiguity aversion tends to infinity the equilibrium
converges to the maxmin expected utility benchmark of Lo (1998). Finally, smooth ambiguity breaks the
standard ranking between first-price and second-price auctions: the first-price format narrows the
seller's revenue range across priors, while bidder welfare admits no uniform ranking and may favor either
format depending on ambiguity attitudes.
Ambiguous Contracts with an \(\alpha\)-MEU Agent
Tianyu Ma
We study ambiguous contracts in a finite moral-hazard principal-agent model in which the agent has
\(\alpha\)-MEU preferences (Ghirardato, Maccheroni, and Marinacci, 2004). Dütting, Feldman, Peretz,
and Samuelson (2024) show that under maxmin expected utility (Gilboa and Schmeidler, 1989) ambiguity
can enlarge the set of implementable actions and that, under consistency, optimal ambiguous contracts
admit a single-outcome-payment (SOP) structure. We show that these conclusions are not robust to
moderate ambiguity attitudes. When \(\alpha < 1\), consistency is no longer without loss of generality:
an inconsistent set of payment functions can strictly improve the principal's payoff, so consistency
becomes a substantive credibility restriction. Imposing consistency, we derive sharp thresholds for
implementability. If the target action is dominated by a mixture of \(d\) actions, then no consistent
contract can \(\alpha\)-implement it when \(\alpha \le 1/d\); under full dimensionality, this threshold
is sharp. We also show that if \(\alpha \le 1/(n-1)\), every consistent \(\alpha\)-incentive-compatible
set of payment functions is equivalent to a classic contract. Finally, the SOP characterization fails in
general for \(\alpha \in (0,1)\), although any consistent incentive-compatible ambiguous contract can
still be reduced to at most \(n-1\) payment functions.