First‐price auctions with resale and with outcomes robust to bid disclosure

Although there exists a pure separating equilibrium of the two‐bidder first‐price auction with resale when the bids are kept secret, the ratchet effect prevents the existence of such an equilibrium if the bidders are heterogeneous and the bids are fully disclosed. Nevertheless, we construct a behavioral equilibrium under full disclosure that is equivalent to the pure separating equilibrium under no disclosure. Thus, if the bidders follow this equilibrium, the choice of the disclosure regime does not affect the final allocation of the item nor the expected payoffs.