GAME THEORETICAL ANALYSIS OF BUY-IT-NOW PRICE AUCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 557-581 ◽  
Author(s):  
HAI YU ◽  
CHUANGYIN DANG ◽  
SHOU-YANG WANG
Keyword(s):  
Necessary Conditions ◽  
Stackelberg Game ◽  
Common Knowledge ◽  
Risk Averse ◽  
Threshold Strategy ◽  
Price Auction ◽  
Participation Costs ◽  
Expected Revenue ◽  
Starting Price ◽  
Distribution Assumption

We study two kinds of buy-it-now options, temporary and permanent, under a theoretical model of Stackelberg game. In this two-stage game, the bidders, as the followers, use a two-threshold strategy to determine whether to bid or directly buy the item at the posted price, given an auction configuration featured by the seller in the first stage and other common knowledge. Under the uniform distribution assumption for the bidders' valuation, we derive the optimal necessary conditions of the starting price and the buy-it-now price for maximizing the seller's expected revenue. Then, we use two numerical experiments to find some interesting insights, which include that under identical bidders' participation costs, the temporary buy-it-now option can acquire a higher expected revenue for the seller than the permanent option, and a buy-it-now price auction always nontrivially dominates a regular auction in terms of the achieved expected revenue, no matter whether the seller or the bidders are risk-averse.

Why the Reserve Price Should Not Be Kept Secret

2006 ◽  
Vol 6 (1) ◽  
Author(s):  
Karine Brisset ◽  
Florence Naegelen
Keyword(s):  
Price Policy ◽  
Risk Averse ◽  
Relative Risk Aversion ◽  
Reserve Price ◽  
Bayesian Equilibrium ◽  
Ascending Auctions ◽  
Price Auction ◽  
Second Price Auction ◽  
Optimal Reserve ◽  
Secret Reserve Price

This paper considers the optimality of setting a secret reserve price in ascending auctions. Contrary to intuition, an ascending auction is no longer equivalent to a second price auction when the reserve price is secret. We determine the seller's optimal reserve price policy when the bidders' values are private and independently distributed and when the bidders are risk averse. We show that an optimal secret reserve price policy can dominate an optimal public reserve price policy when the bidders' degree of constant relative risk aversion is sufficiently high and when the seller can commit to a reserve price policy before learning her type. In contrast, a secret reserve price policy can never be part of a Bayesian equilibrium when the seller is informed.

scholarly journals On the ratifiability of efficient cartel mechanisms in first-price auctions with participation costs and information leakage

2019 ◽  
Author(s):  
Xiaoyong Cao ◽  
Shao-Chieh Hsueh ◽  
Guoqiang Tian
Keyword(s):  
Information Leakage ◽  
Sealed Bid ◽  
Price Auction ◽  
Participation Costs

Abstract This paper addresses the ratifiability of an efficient cartel mechanism in a first-price auction. When a seller uses a first-price sealed-bid auction, the efficient all-inclusive cartel mechanism will no longer be ratifiable in the presence of both participation costs and potential information leakage. A bidder whose value is higher than a cut-off in the cartel will have an incentive to leave the cartel, thereby sending a credible signal of his high value, which discourages other bidders from participating in the seller’s auction. However, the cartel mechanism is still ratifiable where either the participation cost or information leakage is absent.

Leveling the Playing Field for Risk-Averse Agents in Security-Bid Auctions

2021 ◽  
Author(s):  
Andrés Fioriti ◽  
Allan Hernandez-Chanto
Keyword(s):  
Allocative Efficiency ◽  
Technical Condition ◽  
Risk Averse ◽  
Security Design ◽  
Call Option ◽  
Equilibrium Behavior ◽  
Playing Field ◽  
Price Auction ◽  
Auction Format ◽  
The Relationship

We introduce risk-averse bidders in a security-bid auction to analyze how the security design affects bidders’ equilibrium behavior and, as a result, the revenue and efficiency of the auction. We show that steeper securities provide more insurance because they allow bidders to smooth payoffs across realizations. Such insurance levels the playing field for more-risk-averse bidders, inducing them to bid more aggressively. As a consequence, the auction’s allocative efficiency weakly increases when the seller switches from a flatter to a steeper security. Furthermore, we prove that when bidders are homogeneously and sufficiently risk averse, the only security that guarantees Pareto efficiency is the steepest, that is, a call option. We also determine the relationship between the security design and the auction format. In particular, we show that for convex and superconvex families of securities, the first-price auction yields higher expected revenues, provided a technical condition, whereas for subconvex families, the second price yields higher expected revenues, provided that bidders are moderately risk averse. Finally, we show that steeper securities also attract higher entry from an ex ante perspective, when entry is costly, and discuss the effects that the presence of risk aversion has on informal auctions. This paper was accepted by Gustavo Manso, finance.

scholarly journals Asymmetric Auctions with Resale

2008 ◽  
Vol 98 (1) ◽  
pp. 87-112 ◽  
Author(s):  
Isa Hafalir ◽  
Vijay Krishna
Keyword(s):  
Asymmetric Auctions ◽  
Monopoly Pricing ◽  
General Revenue ◽  
Private Values ◽  
Price Auction ◽  
Second Price Auction ◽  
Expected Revenue ◽  
Second Price Auctions ◽  
Independent Private Values

We study first- and second-price auctions with resale in a model with independent private values. With asymmetric bidders, the resulting inefficiencies create a motive for post-auction trade which, in our model, takes place via monopoly pricing—the winner makes a take-it-or-leave-it offer to the loser. We show (a) a first-price auction with resale has a unique monotonic equilibrium; and (b) with resale, the expected revenue from a first-price auction exceeds that from a second-price auction. The inclusion of resale possibilities thus permits a general revenue ranking of the two auctions that is not available when these are excluded. (JEL D44)

Sequential Bidding in Asymmetric First Price Auctions

2017 ◽  
Vol 18 (1) ◽  
Author(s):  
Gal Cohensius ◽  
Ella Segev
Keyword(s):  
The Other ◽  
Expected Payoff ◽  
First Order ◽  
Uniform Distributions ◽  
Price Auction ◽  
Second Price Auction ◽  
Expected Revenue ◽  
Sequential Bidding

AbstractWe study asymmetric first price auctions in which bidders place their bids sequentially, one after the other and only once. We show that, when bidders’ values are drawn from uniform distributions and are asymmetric, i.e., there is a strong bidder and a weak bidder (the strong bidder’s distribution first order stochastically dominates that of the weak bidder’s), the expected revenue in the sequential bidding first price auction (when the strong bidder bids first) may be higher than in the simultaneous bidding first price auction as well as the simultaneous bidding second price auction. The expected payoff of the weak bidder is also higher in the sequential first price auction. Therefore a seller interested in increasing revenue facing asymmetric bidders may find it beneficial to order them and let them bid sequentially instead of simultaneously.

scholarly journals Stackelberg Game of Buyback Policy in Supply Chain with a Risk-Averse Retailer and a Risk-Averse Supplier Based on CVaR

PLoS ONE ◽  
2014 ◽  
Vol 9 (9) ◽  
pp. e104576 ◽  
Author(s):  
Yanju Zhou ◽  
Qian Chen ◽  
Xiaohong Chen ◽  
Zongrun Wang
Keyword(s):  
Supply Chain ◽  
Stackelberg Game ◽  
Risk Averse

scholarly journals Mixed Mechanisms for Auctioning Ranked Items

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2227
Author(s):  
Estrella Alonso ◽  
Joaquín Sánchez-Soriano ◽  
Juan Tejada
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Point Of View ◽  
Uniform Price Auction ◽  
Keyword Auctions ◽  
The Family ◽  
Discriminatory Price ◽  
Auction Mechanisms ◽  
Price Auction ◽  
Expected Revenue

This paper deals with the problem of designing and choosing auctioning mechanisms for multiple commonly ranked objects as, for instance, keyword auctions in search engines on Internet. We shall adopt the point of view of the auctioneer who has to select the auction mechanism to be implemented not only considering its expected revenue, but also its associated risk. In order to do this, we consider a wide parametric family of auction mechanisms which contains the generalizations of discriminatory-price auction, uniform-price auction and Vickrey auction. For completeness, we also analyze the Generalized Second Price (GSP) auction which is not in the family. The main results are: (1) all members of the family satisfy the four basic properties of fairness, no over-payment, optimality and efficiency, (2) the Bayesian Nash equilibrium and the corresponding value at risk for the auctioneer are obtained for the considered auctions, (3) the GSP and all auctions in the family provide the same expected revenue, (4) there are new interesting auction mechanisms in the family which have a lower value at risk than the GSP and the classical auctions. Therefore, a window opens to apply new auction mechanisms that can reduce the risk to be assumed by auctioneers.

Decision policies on players’ different risk combination under supplier encroachment

2020 ◽  
Vol 54 (4) ◽  
pp. 1057-1075
Author(s):  
Ping Chen ◽  
Bo Li ◽  
Huafei Huang
Keyword(s):  
Supply Chain ◽  
Risk Taking ◽  
Numerical Experiments ◽  
Stackelberg Game ◽  
Risk Preferences ◽  
Management Problem ◽  
Risk Averse ◽  
Optimal Decisions ◽  
Decision Policies ◽  
The Impact

Literature concerning about the supply chain management problem is usually based on perfect rationality. However, risk preferences have been proved to be an important role which influences managers’ decisions significantly. This paper investigates a risk combination problem under supplier encroachment with different risk preferences players. Assuming that the supply chain players may be risk-averse, risk-neutral and risk-taking, we build a Stackelberg game model to explore the optimal decisions and the impact of different risk combinations, respectively. We focus on two scenarios: the consumers perceive uniform quality between the two channels and perceive differentiated quality between the two channels. We find that the retailer always prefers a risk-averse supplier, while the supplier always prefers a risk-taking retailer. But the combination of a risk-averse supplier and a risk-taking retailer is not always beneficial to the whole supply chain. Further, we conduct numerical experiments to explore the risk combinations and the impacts of players’ selfish, aggressive and altruistic behaviors on optimal decisions.

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