Revenues in discrete multi-unit, common value auctions: a study of three sealed-bid mechanisms

This paper proposes a discrete bidding model for both quantities and pricing. It has a two-unit demand environment where subjects bid for contracts with an unknown redemption value, common to all bidders. Prior to bidding, the bidders receive private signals of information on the (common) value. The relevant task is to compare the equilibrium strategies and the seller’s revenue of the three most common auction formats with two players. The result is that the Vickrey auction always gives the most revenue to the seller, the discriminatory auction follows closely and the uniform auction clearly is the worst due to demand reduction.

Liquidity provision vs. deposit insurance: preventing bank panics without moral hazard

Equilibrium bidding strategies under most multi-unit auction rules cannot be obtained as closed form expressions. Research in multi-unit auctions has, therefore, depended on implicit characterization of equilibrium strategies using the first-order conditions of the bidders’ expected payoff maximization problem. In this paper we consider the pay-as-bid auction with diminishing marginal values for two units and show that any symmetric equilibrium in continuous strategies has the necessary properties to allow such a characterization. Moreover, any increasing solution to the system of differential equations that is used to characterize the equilibrium strategies describes an equilibrium strategy.Generous suggestions and comments from Richard Engelbrecht-Wiggans, Charles M. Kahn, and an anonymous referee are gratefully acknowledged.     

Survival auctions

Dynamic clock auctions with drop-out information typically yield outcomes closer to equilibrium predictions than do comparable sealed-bid auctions. However, clock auctions require congregating bidders for a fixed time interval, which has limited field applicability and introduces inefficiencies of its own given the time cost of congregating bidders. In this experiment we explore the effects of removing these inefficiencies through survival auctions—a multi-round sealed-bid auction which is theoretically isomorphic to the dynamic clock auction with drop-out information. Kagel’s research was partially supported by National Science Foundation Grants No. 0136925 and 0136928. Any opinions, findings, and conclusions or recommendations in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We thank the associate editor, an anonymous referee, seminar participants at Purdue University, especially Tim Cason, participants at International Industrial Organization April 2004 Conference, the ESA June 2003 meetings, and our discussant, Tim Salmon, for valuable comments. Kirill Chernomaz provided valuable research assistance. The usual caveat applies.     

三种国债拍卖方式的拍卖收入比较研究

国债拍卖主要有美国式拍卖、荷兰式拍卖与混合式拍卖三种,但究竟哪一种拍卖方式的拍卖收入最大?学术界迄今尚无定论。文章对W-Z模型进行扩展,并在此基础上通过结合不同市场利率环境下投标者的不同风险偏好进行比较研究。结果表明:(1)当市场利率趋升时,若非竞争性投标量较大,则混合式拍卖收入最大;若非竞争性投标量较小,但竞争性投标者较少,且市场利率上升趋势极强,则同样是混合式拍卖收入最大,反之则荷兰式拍卖收入最大。(2)当市场利率趋降时,美国式拍卖收入最大。(3)当市场利率平稳时,何种拍卖方式收入最大无法确定。     

An experimental investigation of soft price caps in uniform price auction markets for wholesale electricity

This paper presents the results from an auction experiment using industry professionals and student participants who compete in a simulated wholesale market for electricity. Motivated by the intervention by FERC in response to the “meltdown” of the California spot market, we investigate the effect of including a “soft” price cap in a uniform price auction as a means of mitigating high prices. When prices are driven above the soft cap, offer curves become flat, in contrast to the hockey stick shape observed in a typical uniform price auction for electricity. This flat offer curve leads to market prices that are relatively insensitive to both generation costs and demand reductions.      

Commitment in sequential auctioning: advance listings and threshold prices

This paper models sequential auctioning of two perfect substitutes by a strategic seller, who learns about demand from the first-auction price. The seller holds the second auction only when the remaining demand is strong enough to cover her opportunity cost. Bidding in anticipation of such a contingent future auction is characterized, including a sufficient condition for existence of an invertible (increasing symmetric pure-strategy) bidding equilibrium that facilitates the seller’s learning. A unique invertible bidding equilibrium exists for the Dutch auction format, but only when the second auction is sufficiently discounted by the bidders. In the equilibrium, high-valuation bidders shade their bids down as if the second auction were guaranteed. To counter such strategic bidding, the seller would value ex-ante commitment to hold the second auction less often. Three forms of such commitment are analyzed: commitment to list future auctions in advance, commitment to not hold the second auction unless the first price exceeds a publicly announced threshold, and commitment to a reserve-price in the second auction. I would like to thank Georgios Katsenos, Thomas Jeitschko, Miguel Villas-Boas, George Deltas, and an anonymous referee for thorough and insightful feedback.     

An ascending double auction

We show why the failure of the affiliation assumption prevents the double auction from achieving efficient outcomes when values are interdependent. This motivates the study of an ascending price version of the double auction. It is shown that when there is a sufficiently large, but still finite, number of sellers, this mechanism has an approximate perfect Bayesian equilibrium in which traders continue bidding if and only if their true estimates of the ‘value’ of the object being traded exceed the current price. This equilibrium is ex post efficient and has a rational expectations property in the sense that along the equilibrium path traders appear to have made the best possible trades conditional on information revealed by the trading process. We thank two anonymous referees and Dan Kovenock, the Editor, whose detailed comments and suggestions have allowed us to substantially improve the paper. We also thank seminar participants at University of Toronto, University of Wisconsin-Madison, Summer 2003 North American Meetings of the Econometric Society, 2004 NSF Decentralization Conference for their comments.     

Characterizing the Vickrey combinatorial auction by induction

This note studies the allocation of heterogeneous commodities to agents whose private values for combinations of these commodities are monotonic by inclusion. This setting can accommodate the presence of complementarity and substitutability among the heterogeneous commodities. By using induction logic, we provide an alternative proof of Holmstrom’s (Econometrica 47:1137–1144, 1979) characterization of the Vickrey combinatorial auction as the unique efficient, strategy-proof, and individually rational allocation rule on a smoothly connected domain of value profiles. Our approach is elementary, not involving smoothness, and intuitive in the sense that familiar properties of the single-item second-price auction provide the first step in our induction on the number of auctioned items. Moreover, our method of proof can be applied to domains which may not be smoothly connected, including nonconvex ones. The authors acknowledge the helpful comments of anonymous referee. Serizawa greatly benefited from discussion with Rajat Deb.     

Equilibrium uniqueness with perfect complements

The present note analyzes the simultaneous ascending-bid auction with arbitrarily many asymmetric bidders with decreasing marginal valuations under complete information. We show that the game is solvable by iterated elimination of weakly dominated strategies if the efficient allocation assigns at least one unit to every player and if bid increments are sufficiently small. In that unique equilibrium, bidders immediately reduce their demand to the efficient allocation, and the auction ends in the first round of bidding.We would like to thank seminar participants at UC Davis, in particular Klaus Nehring and Louis Makowski for comments. Financial support by the Alexander–von–Humboldt Foundation through a Feodor–Lynen grant and by the Deutsche Forschungsgemeinschaft, SFB Transregio 15, “Governance and Efficiency of Economic Systems” is gratefully acknowledged.     

Comparing competition and collusion: a numerical approach

Summary. Collusion is a serious problem in many procurement auctions. In this research, I study a model of first price sealed bid procurement auctions with asymmetric bidders. I demonstrate that the equilibrium to the model is unique and describe three algorithms that can be used to compute the inverse equilibrium bid functions. I then use the computational algorithms to compare competitive and collusive bidding. The algorithms are useful for structural estimation of auction models and for assessing the damages from bid-rigging. Received: January 14, 2000; revised version: February 28, 2001     

The multiple unit auction with variable supply

Summary. The theory of multiple unit auctions traditionally assumes that the offered quantity is fixed. I argue that this assumption is not appropriate for many applications because the seller may be able and willing to adjust the supply as a function of the bidding. In this paper I address this shortcoming by analyzing a multi-unit auction game between a monopolistic seller who can produce arbitrary quantities at constant unit cost, and oligopolistic bidders. I establish the existence of a subgame-perfect equilibrium for price discriminating and for uniform price auctions. I also show that bidders have an incentive to misreport their true demand in both auction formats, but they do that in different ways and for different reasons. Furthermore, both auction formats are inefficient, but there is no unambiguous ordering among them. Finally, the more competitive the bidders are, the more likely the seller is to prefer uniform pricing over price discrimination, yet increased competition among bidders may or may not enhance efficiency. Received: June 18, 1998; revised version: January 13, 1999     

Banning Bidders from All-pay Auctions

We consider an all-pay auction with complete information among the bidders; the seller does not observe the bidders’ values. We show that for some information structures in which the seller has a small uncertainty about the valuations, it is profitable for him to exclude from the auction all but two (randomly selected) bidders even though the latter are ex ante identical from his point of view.I am grateful to Paolo Bertoletti who introduced me to this topic and provided useful comments. I also thank Dan Kovenock (Co-Editor) and two anonymous referees for suggestions which considerably improved the exposition.     

Optimal sale across venues and auctions with a buy-now option

We characterize the optimal selling mechanism for a seller who faces demand demarcated by a high and a low end and who can access an (online) auction site (by paying an access cost) in addition to using his own store that can be used as a posted price selling venue. We first solve for the optimal mechanism of a direct revelation game in which there is no venue-restriction constraint. We find that the direct optimal mechanism must necessarily incorporate a certain kind of pooling. We then show that even with the venue constraint, the seller can use a two stage indirect mechanism that implements the allocation rule from the optimal direct mechanism, and uses the venues in an optimal fashion. The first stage of the indirect mechanism is a posted price at the store. If the object is not sold, we move to stage two, which involves an auction at the auction site. A feature of this auction is a buy-now option which is essential for implementing the pooling feature of the optimal direct mechanism. We also show that the buy-now option in the optimal mechanism is of a “temporary” variety, and that a “permanent” buy-now option, in contrast, cannot implement the optimal mechanism. Auctions with a temporary buy-now option are in widespread use on eBay. We thank the Associate Editor, George Deltas, for his insightful comments. We also thank seminar participants at the University of Basel and the SAET conference 2007.     

Option to wait in a search model

We consider a standard search model with buyers and sellers. Upon meeting the buyers make a take-it-or-leave-it offer, but the sellers have an option not to trade immediately but wait for more agents to appear. If more buyers come, there is excess demand, and the buyers engage in auction to get the good. Analogously, if more sellers come, the sellers engage in a Bertrand-type pricing game to sell the object. The option to wait restricts the price offer of the buyer; in an equilibrium in which trades are consummated without delay there is a unique price offer for the buyer.JEL Classification: C78, D44, D831     

附加职工安置约束的国企产权拍卖机制研究

The transfer of SOE’s property right involves benefits readjustment of its stakeholders; therefore the design of the trading mechanism is not only to sell the SOE with a high price but also to realize other non-price objectives such as rearrangement of original employees, further development of the enterprise etc. This paper constructs a bidding mechanism with the constraint of accommodating employees to analyze the tradeoff between maximizing SOE auction revenue and minimizing induced unemployment. By adding that the winner is required to settle down a certain quantity of former SOE employees in the new enterprise, this mechanism brings on the competition among prospective investors in both the price and the quantity of employment, which can help the government to balance the different objectives more efficiently. However, the constraint will only work under the condition that the government has stressed sufficiently on the employees’ rearrangement and set the best constraint threshold. Moreover, the government should set an explicit compensation standard for the induced lay-offs to eliminate the investors’ accommodating cost dispersion and introduce more strategic investors with considerable heterogeneity to participate in the bidding. __________ Translated from Jingji yanjiu 经济研究 (Economic Research Journal), 2007, (10):115–125     

Policy Bias Equivalence under Common Agency

This paper studies interest group influence on policy making. Lobbying occurs in a first price auction where an interest group wins with certainty, if her bid exceeds the loser’s bid by the policy maker’s valuation for the socially best policy. Otherwise the latter implements the privately known best policy. In equilibrium the size of the policy maker’s valuation does not matter for the size of the policy bias. The idea is to construct a “reference game” and to shift the support of the equilibrium mixed strategies into the original game, without altering the structure of the densities.     

The private value single item bisection auction

In this paper we present a new iterative auction, the bisection auction, that can be used for the sale of a single indivisible object. The bisection auction has fewer rounds than the classical English auction and causes less information to be revealed than the Vickrey auction. Still, it preserves all characteristics the English auction shares with the Vickrey auction: there exists an equilibrium in weakly dominant strategies in which everyone behaves truthfully, the object is allocated in accordance with efficiency requirements to the buyer who has the highest valuation, and the price paid by the winner of the object equals the second-highest valuationElena Grigorieva acknowledges support by the Dutch Science Foundation NWO through grant 401-01-101. Jean-Jacques Herings acknowledges support by the Dutch Science Foundation NWO through a VICI-grant. Rudolf Müller acknowledges support by European Commission through funds for the International Institute of Infonomics     

Bidding for nothing? The pitfalls of overly neutral framing

Neutral framing is a standard tool of experimental economics. However, overly neutral instructions, which lack any contextual clues, can lead to strange behaviour. In a contextless second-price auction for a meaningless good, a majority of subjects enter positive bids – likely a case of cognitive experimenter demand effect. Subjects may interpret the lack of context as being tasked with bidding in the experiment. Adding another auction that has a context drastically reduces the positive bids in the meaningless auction.     

License prices for financially constrained firms

It is often alleged that high auction prices inhibit service deployment. We investigate this claim under the extreme case of financially constrained bidders. If demand is just slightly elastic, auctions maximize consumer surplus if consumer surplus is a convex function of quantity (a common assumption), or if consumer surplus is concave and the proportion of expenditure spent on deployment is greater than one over the elasticity of demand. The latter condition appears to be true for most of the large telecom auctions in the US and Europe. Thus, even if high auction prices inhibit service deployment, auctions appear to be optimal from the consumers’ point of view.      

Researching Preferences,Valuation and Hypothetical Bias

A number of recent papers in environmental economics have focused on the process of researching preferences – agents are uncertain about preferences but with effort may narrow their uncertainty. This issue has arisen in formulating bids in contingent valuation (CV) as well as the debate over the divergence between WTP and WTA. In the context of CV, it has been suggested that the hypothetical nature of the preference elicitation process biases responses. This paper provides both a theoretical model and experimental evidence to contribute to this debate. The model is a model of competitive bidding for a private good with two components that are particularly relevant to the debate. The first component is that bidders are unsure of their own value for the private good but may purchase information about their own value (researching preferences). The second component is that there is a probability that the auction is hypothetical – that the winning bidder will not get the private good and will not pay the winning bid. The experiment tests this theoretical model of bidding equilibrium and analyzes the effects of variations in the parameters (hypotheticalness, information costs and number of agents) on the endogenous variables (such as the proportion of bidders who become informed and the winning bid). Experimental results suggest that an increase in the hypotheticalness of an auction tends to decrease the likelihood that bidders pay for information on their valuation with an ambiguous effect on the winning bid.