Private Information In Sequential Common-Value Auctions (original) (raw)

Sequential Common-Value Auctions with Asymmetrically Informed Bidders

Review of Economic Studies, 2008

We study an infinitely repeated first-price auction with common values. We focus on one-sided incomplete information, in which one bidder learns the objects' value, which itself does not change over time. Learning by the uninformed bidder occurs only through observation of the bids. The proprietary information is eventually revealed, and the seller extracts essentially the entire rent (for large discount factors). Both players' pay-offs tend to 0 as the discount factor tends to 1. However, the uninformed bidder does relatively better than the informed bidder. We discuss the case of two-sided incomplete information and argue that, under a Markovian refinement, the outcome is pooling as information is revealed only insofar as it does not affect prices.

Private Information In Repeated Auctions

Levine's Bibliography, 2003

We study an infinitely repeated two-player game with incomplete information, where the stage game is a first-price auction with pure common values. Before playing, the bidders receive affiliated private signals about the value, which itself does not change over time. Items sold in such an auction environment include bonds, wine, neighboring oil tracts, and wholesale fish. In this setting, learning occurs only through observation of the bids. We show that in the case of one-sided incomplete information, this information is eventually revealed and the seller extracts essentially the entire rent (for large enough discount factors). In contrast, the unique equilibrium with patient players under two-sided incomplete information is purely pooling: no information is ever revealed. In the special case with only two types of each bidder, we are able to fully characterize the equilibrium for all values of the discount factor and all priors. 1 information, even when their estimate is high, and prefer to win half of the time at such a low price, rather than break the tie in their favor and divulge thereby some of their information.

Conjugate information disclosure in an auction with learning

Journal of Economic Theory

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.

The Non-Existence of Equilibrium in Sequential Auctions When Bids Are Revealed

Journal of Electronic Commerce Research, 2007

Sequential auctions of homogeneous objects are common in public and private marketplaces. Weber derived equilibrium results for what is now a classic model of sequential auctions. However, Weber’s results are derived in the context of two particular price quote assumptions. In this paper, we examine a model of sequential auctions based on online auctions, in which, after each auction, all bids are revealed. We show that a pure-strategic, symmetric equilibrium does not exist, regardless of whether the auctions are first- or second-price, if all bids are revealed at the end of each auction.

An Experimental Study on Sequential Auctions with Privately Known Capacities

We experimentally study bidding behavior in sequential first-price procurement auctions where bidders' capacity constraints are private information. Treatment differs in the ex-ante probability distribution of sellers' capacities and in the (exogenous) probability that the second auction is actually implemented. Our results show that: (i) bidding behavior in the second auction conforms with sequential rationality; (ii) while first auction's bids negatively depend on capacity, bidders seem unable to recognize this link when, at the end of the first auction, they state their beliefs on the opponent's capacity. To rationalize this inconsistency between bids and beliefs, we conjecture that bidding in the first auction is also affected by a hidden, behavioral type - related to the strategic sophistication of bidders - that obfuscates the link between capacity and bids. Building on this intuition, we show that a simple level-k model may help explain the inconsistency.

Multi-unit auctions with private information: an indivisible unit continuous price model

Economic Theory, 2010

We construct a model of multi-unit auctions in which I bidders bid for two indivisible units of a common value good. Using a first-order approach, we find that there are equilibria in which bidders bid the same price for both units in the discriminatory auction, but not in the uniform auction. When there are only two bidders, under certain conditions there are linear equilibria for both the discriminatory and the uniform auction formats. In all equilibria, bidders equalize the expected marginal benefit of bidding to the marginal costs of bidding. We show that comparison of the seller's expected revenue across auction formats depends only on the ratio of the precision of private information to the precision of public information.

Information disclosure by a seller in sequential first-price auctions

International Journal of Game Theory

I study sequential first-price auctions where two items are sold to two bidders with private binary valuations. A seller, prior to the second auction, can publicly disclose some information about the outcome of the first auction. I characterize equilibrium strategies for various disclosure rules when the valuations of bidders are either perfectly positively or perfectly negatively correlated across items. I establish outcome equivalence between different disclosure rules. I find that it is optimal for the seller to disclose some information when the valuations are negatively correlated, whereas it is optimal not to disclose any information when the valuations are positively correlated. For most of the parameter values, the seller’s expected revenue is higher if the losing bid is disclosed. When only the winner’s identity is disclosed, the equilibrium is efficient whether the valuations are positively or negatively correlated.

Sequential all-pay auctions with noisy outputs

Journal of Mathematical Economics, 2014

We study a sequential all-pay auction with two contestants who are privately informed about a parameter (ability) that affects their cost of effort. Contestant 1 (the first mover) exerts an effort in the first period which translates into an observable output, but with some noise, and contestant 2 (the second mover) observes this noisy output. Then, contestant 2 exerts an effort in the second period, and wins the contest if her output is larger than or equal to the observed noisy output of contestant 1; otherwise, contestant 1 wins. We study two variations of this model: one in which both contestants do not know the realization of the noise when they exert their effort (symmetric information), and another in which contestant 1 knows the realization of the noise when exerting her effort, while contestant 2 does not (asymmetric information). For both variations, we characterize the subgame perfect equilibrium and examine the effect of a random noise on the contestants' equilibrium outputs. In particular we show that contestants' equilibrium behavior in our model is robust to the existence of a small noise.

Information Disclosure by a Seller in a Sequential First-Price Auction

RePEc: Research Papers in Economics, 2017

I study sequential first-price auctions where two items are sold to two bidders with private binary valuations. A seller, prior to the second auction, can publicly disclose some information about the outcome of the first auction. I characterize equilibrium strategies for various disclosure rules when the valuations of bidders are either perfectly positively or perfectly negatively correlated across items. I establish outcome equivalence between different disclosure rules. I find that it is optimal for the seller to disclose some information when the valuations are negatively correlated, whereas it is optimal not to disclose any information when the valuations are positively correlated. For most of the parameter values, the seller's expected revenue is higher if the losing bid is disclosed. When only the winner's identity is disclosed, the equilibrium is efficient whether the valuations are positively or negatively correlated.

Working Paper No . E 2017 / 2 Information Disclosure by a Seller in a Sequential First-Price

2017

I study a sequential first-price auction where two items are sold to two bidders with private binary valuations. A seller, prior to the second auction, can publicly disclose some information about the outcome of the first auction. I characterize equilibrium strategies for various disclosure rules when the valuations of bidders are either perfectly positively or perfectly negatively correlated across items. I establish outcome equivalence between different disclosure rules. I find that it is optimal for the seller to disclose some information when the valuations are negatively correlated, whereas it is optimal not to disclose any information when the valuations are positively correlated. For most of the parameter values, the seller’s revenue is higher if the losing bid is disclosed. When only the winner’s identity is disclosed, the equilibrium is efficient whether the valuations are positively or negatively correlated.