Auctions with Dynamic Populations: Efficiency and Revenue Maximization (original) (raw)
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Auctions with Dynamic Populations: Efficiency and Revenue Maximization,” Unpublished manuscript
2009
ABSTRACT: We examine an environment where goods and privately informed buyers ar-rive stochastically to a market. A seller in this setting faces a sequential allocation problem with a changing population. We characterize the set of incentive compatible allocation rules and provide a generalized revenue equivalence result. In contrast to a static setting where incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object, in this dynamic setting, incentive compatibility implies that higher-valued buyers have a greater likelihood of receiving an object sooner. We also characterize the set of efficient allocation rules and show that a dynamic Vickrey-Clarke-Groves mechanism is efficient and dominant strategy incentive compatible. We then derive an optimal direct mechanism. We show that the revenue-maximizing direct mechanism is a pivot mechanism with a reserve price. Finally, we consider sequential ascending auctions in this setting, both wi...
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.
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.
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.
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.
Optimal auction mechanisms with private values
Ekonomski anali, 2010
This paper reviews equilibrium behavior in different auction mechanisms. We will deal with two types of open auctions, English and Dutch, and two types of sealed-bid auctions, first-price and second-price, when there is a single object for sale and bidders have private values. We show that under certain conditions all four auctions yield the same expected revenue to the seller, but once these assumptions are relaxed revenue equivalence does not hold. We will also study auctions by using standard tools from demand theory. Finally, we will analyze collusive behavior of bidders. The two goals that an auction mechanism has to achieve are efficient allocation and maximization of the seller's expected revenue.
Private Information In Sequential Common-Value Auctions
CMS-EMS …, 2006
We study an infinitely$repeated first$price auction with common values. Initially, bid$ ders receive independent private signals about the objectslvalue, which itself does not change over time. Learning occurs only through observation of the bids. Under one$sided incomplete ...
Econometrica, 2002
An analogue of multi-unit auction is provided when bidders have interdependent values and one-dimensional private information. The analogue is strategically equivalent to a collection of two-bidder single-unit second-price auctions and it possesses an e¢cient ex-post equilibrium.
SSRN Electronic Journal, 2010
We consider a two good world where an individual i with income m i has utility function u (x, y), where x ∈ [0, ∞) and y ∈ {0, 1}. We first derive the valuation (maximum price that he is willing to pay for the object) for good y as a function of his income. Then we consider the following problem. Suppose good x is available in a store at a fixed price 1. Good y can be obtained in an auction. In such a situation we show that bidding ones own valuation is an equilibrium in a second-price auction. With risk neutral bidders and high enough incomes we derive the symmetric equilibrium in first-price and all-pay auctions and show that revenue equivalence fails to hold. With risk neutrality we also show that under mild restrictions, the revenue maximising reserve price is zero for all the three auctions and the all-pay auction with zero reserve price fetches the highest expected revenue. With low enough incomes, we show that under some restrictions, bidding ones own valuation is a symmetric equilibrium even for first-price and all-pay auctions. Here also, the expected revenue is the highest with all-pay auctions.
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.