Conjugate information disclosure in an auction with learning

Abstract

We consider a single-item, independent private value auction environment with two bidders: a leader, who knows his valuation, and a follower, who privately chooses how much to learn about his valuation. We show that, under some conditions, an ex-post efficient revenuemaximizing auction-which solicits bids sequentially-partially discloses the leader's bid to the follower, to influence his learning. The disclosure rule that emerges is novel; it may reveal to the follower only a pair of bids to which the leader's actual bid belongs. The identified disclosure rule, relative to the first-best, induces the follower to learn less when the leader's valuation is low and more when the leader's valuation is high. JEL codes: D82, D83 certain region. The pool of bidders typically includes an incumbent operator and potential entrants. The bidders' valuations of the franchise vary depending on the bidder's operating costs.The incumbent is likely to know its costs from past experience, whereas the entrants are poorly informed and must perform due diligence to evaluate the purchase opportunity. This paper is a step towards understanding what a profit-maximizing government should reveal to potential entrants about the well-informed incumbent's intended bid in order to influence their due diligence.The paper formulates a model that captures the essential features of the government's informationdisclosure problem. A seller sells an item by sequentially bargaining with two bidders: the leader, who knows its valuation, and the follower, who must exert costly effort to better estimate his valuation. The bidders' valuations are private and statistically independent.The seller maximizes his revenue by designing, announcing, and committing to a mechanism.He is restricted to choosing a mechanism with an ex-post efficient allocation rule, which must assign the item to the bidder with the higher expected valuation (conditional on the bidders' information). The focus on ex-post efficient allocation rules is restrictive and is motivated primarily by tractability, as well as by the desire to isolate the distortions due to information disclosure from the distortions due to the allocation rule. 1 In addition, in some applications, the violation of expost efficiency is politically costly or outright infeasible. 2 We also restrict attention to mechanisms that rule out the sale of information about already collected bids; only in such mechanisms is there room for strategic disclosure.The paper's main result is the rule according to which the seller partially obfuscates the bid he receives from the leader before passing this information on to the follower, who then decides how much to learn. 3 In particular, the seller optimally partitions the leader's possible types (i.e., valuations, reported as bids) into singletons and pairs of so-called conjugate types. Thus, the seller may disclose to the follower just a pair to which the leader's type belongs, without revealing that type. Figure 1 illustrates.The seller's strategic disclosure distorts the fol...

Assortative Information Disclosure

“…6 Related notions include "conjugate" disclosure rules in Nikandrova and Pancs (2017) and "ppairwise" information structures in Terstiege and Wasser (2020).…”

“…Now consider the separable case with the additional assumption that G is uniform. This is the main specification considered by Rayo and Segal (2010), as well as by Nikandrova and Pancs (2017) in their study of information disclosure in sequential auctions. Under this extra assumption, unitary single-dipped disclosure is optimal if w is convex, and unitary single-peaked disclosure is optimal if w is concave.…”

The Persuasion Duality

“…This special case has been studied by Rayo and Segal (2010) and Nikandrova and Pancs (2017) under the assumption that the set Ω is a finite set and a strictly convex curve, respectively. They derive certain necessary properties of an optimal solution.…”

“…Because the function v is Lipschitz continuous on any compact domain, it follows from Proposition 4 in Appendix A that the persuasion problem is regular. This special case has been studied by Rayo and Segal (2010) and Nikandrova and Pancs (2017) under the assumption that the set Ω is a finite set and a strictly convex curve, respectively. They derive certain necessary properties of an optimal solution.…”

Buyer-Optimal Robust Information Structures

“…3 The key difference is that the buyer eventually learns his valuation perfectly, whereas in our paper the seller endogenously decides how much information to add. Nikandrova and Pancs (2017) consider sequential two-bidder auctions with information acquisition. When recommending information acquisition to the second bidder, the auctioneer optimally pools high and low bids of the first bidder to mitigate incentive constraints.…”