On the Uniqueness of Bayesian Coarse Correlated Equilibria in Standard First-Price and All-Pay Auctions
CoRR(2024)
摘要
In first-price and all-pay auctions under the standard symmetric independent
private-values model, we show that the unique Bayesian Coarse Correlated
Equilibrium with symmetric, differentiable and strictly increasing bidding
strategies is the unique strict Bayesian Nash Equilibrium. Interestingly, this
result does not require assumptions on the prior distribution. The proof is
based on a dual bound of the infinite-dimensional linear program. Numerical
experiments without restrictions on bidding strategies show that for
first-price auctions and discretisations up to 21 of the type and bid space,
increasing discretisation sizes actually increase the concentration of Bayesian
Coarse Correlated Equilibrium over the Bayesian Nash Equilibrium, so long as
the prior c.d.f. is concave. Such a concentration is also observed for all-pay
auctions, independent of the prior distribution. Overall, our results imply
that the equilibria of these important class of auctions are indeed learnable.
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