Sequential First-Price Auction with Randomly Arriving Buyers

2018 ◽  
Vol 6 (1) ◽  
pp. 29-34
Author(s):  
Shulin Liu ◽  
Xiaohu Han
Keyword(s):  
Dynamic Model ◽  
Equivalence Theorem ◽  
Bidding Strategy ◽  
Revenue Equivalence ◽  
Dynamic Markets ◽  
Differentiated Goods ◽  
Price Auction ◽  
Second Price Auction ◽  
Equilibrium Bidding ◽  
Model Setting

AbstractIn this paper we reanalyze Said’s (2011) work by retaining all his assumptions except that we use the first-price auction to sell differentiated goods to buyers in dynamic markets instead of the second-price auction. We conclude that except for the expression of the equilibrium bidding strategy, all the results for the first-price auction are exactly the same as the corresponding ones for the second-price auction established by Said (2011). This implies that the well-known “revenue equivalence theorem” holds true for Said’s (2011) dynamic model setting.

scholarly journals A measure of the variability of revenue in auctions: A look at the revenue equivalence theorem

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Fernando Beltrán ◽  
Natalia Santamaría
Keyword(s):  
Equivalence Theorem ◽  
Auction Theory ◽  
Two Dimensions ◽  
Revenue Equivalence ◽  
Extensive Simulation ◽  
Value Set ◽  
Equilibrium Bidding ◽  
The One

One not-so-intuitive result in auction theory is the revenue equivalence theorem, which states that as long as an auction complies with some conditions, it will on average generate the same revenue to an auctioneer as the revenue generated by any other auction that complies with them. Surprisingly, the conditions are not defined on the payment rules to the bidders but on the fact that the bidders do not bid below a reserve value—set by the auctioneer—the winner is the one with the highest bidding and there is a common equilibrium bidding function used by all bidders. In this paper, we verify such result using extensive simulation of a broad range of auctions and focus on the variability or fluctuations of the results around the average. Such fluctuations are observed and measured in two dimensions for each type of auction: as the number of auctions grows and as the number of bidders increases.

Soft Floors in Auctions

2019 ◽  
Vol 65 (9) ◽  
pp. 4204-4221 ◽  
Author(s):  
Robert Zeithammer
Keyword(s):  
The Other ◽  
Symmetric Equilibrium ◽  
Revenue Equivalence ◽  
Bidding Strategies ◽  
Reserve Prices ◽  
Private Values ◽  
Price Auction ◽  
Winning Bidder ◽  
Second Price Auction ◽  
Independent Private Values

Several of the auction-driven exchanges that facilitate programmatic buying of internet display advertising have recently introduced “soft floors” in addition to standard reserve prices (called “hard floors” in the industry). A soft floor is a bid level below which a winning bidder pays his own bid instead of paying the second-highest bid as in a second-price auction most ad exchanges use by default. This paper characterizes soft floors’ revenue-generating potential as a function of the distribution of bidder independent private values. When bidders are symmetric (identically distributed), soft floors have no effect on revenue, because a symmetric equilibrium always exists in strictly monotonic bidding strategies, and standard revenue-equivalence arguments thus apply. The industry often motivates soft floors as tools for extracting additional expected revenue from an occasional high bidder, for example a bidder retargeting the consumer making the impression. Such asymmetries in the distribution of bidder preferences do not automatically make soft floors profitable. This paper presents two examples of tractable modeling assumptions about such occasional high bidders, with one example implying low soft floors always hurt revenues because of strategic bid-shading by the regular bidders, and the other example implying high soft floors can increase revenues by making the regular bidders bid more aggressively. This paper was accepted by Juanjuan Zhang, marketing.

scholarly journals Strategies for Making Best Offers on eBay

2017 ◽  
Vol 14 (3) ◽  
Author(s):  
William Britt ◽  
William Gryc ◽  
Jamie Oliva ◽  
Brittney Tuff ◽  
Charli White
Keyword(s):  
Optimal Strategies ◽  
Bidding Strategy ◽  
Model Risk ◽  
Know How ◽  
Bayesian Nash Equilibrium ◽  
Sealed Bid ◽  
Risk Neutral ◽  
Price Auction ◽  
Equilibrium Bidding ◽  
Best Offer

We model for “Buy-It-Now or Best Offer” auctions on eBay using two different models. In the first model, risk-neutral bidders submit bids in serial and try to surpass a stochastic seller threshold while taking into account how many previous failed bids were made by other bidders. We compute optimal strategies for this model and show that bidder expected surplus decreases in the number of previous failed bids. In the second model we assume bidders do not know how many previous failed bids have been made, and instead use a first-price sealed-bid mechanism with a buy-out price where bidders serially submit bids with the knowledge that no previous bidders have used the buy-out price. We derive a unique equilibrium bidding strategy for risk-neutral bidders in this serial model, show that any equilibrium in a similar parallel bidding model is the same as the equilibrium in the serial model, and compute seller revenue. In particular, under certain circumstances, bidders will bid more in this format than they would in a standard first-price sealed-bid auction, but that a seller maximizes expected revenue by setting a buy-out price higher than any bidder is willing to pay thereby making the auction essentially a first-price auction. KEYWORDS: Auction Theory; eBay; Buy-It-Now or Best Offer; Symmetric Bayesian Nash Equilibrium; Buy-Out Price; First-Price Sealed-Bid

Optimal Bidding Decision of Bidders in Homogeneous Goods Procurement

2013 ◽  
Vol 415 ◽  
pp. 726-729
Author(s):  
Zhong Wen Chen
Keyword(s):  
Optimal Decision ◽  
Bidding Strategy ◽  
Uniform Price Auction ◽  
Uniform Price ◽  
Nonlinear Equilibrium ◽  
Price Auction ◽  
Optimal Bidding ◽  
Equilibrium Bidding ◽  
Divisible Goods ◽  
Optimal Decision Making

In this paper, a uniform price auction mechanism for procuring homogeneous divisible goods is studied, and both nonlinear bidding strategy and linear bidding strategy of symmetric bidders are analyzed. And then the dominant relationship is discussed deeply between the two kinds of equilibrium bids. The results show that the nonlinear equilibrium bidding strategy dominates linear ones. Based on this analysis, several suggestions are given on how to make optimal decision making on bidding strategy choice for bidders.

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