Bidders Face Research Articles

Convexity in Real-time Bidding and Related Problems

We study problems arising in real-time auction markets, common in e-commerce and computational advertising, where bidders face the problem of calculating optimal bids. We focus upon a contract management problem where a demand aggregator is subject to multiple contractual obligations requiring them to acquire items of heterogeneous types at a specified rate and where they will seek to fulfill these obligations at minimum cost. Our main results show that, through a transformation of variables, this problem can be formulated as a convex optimization problem, for both first and second price auctions. The resulting duality theory admits rich structure and interpretations. Additionally, we show that the transformation of variables can be used to guarantee the convexity of optimal bidding problems studied by other authors, who did not leverage convexity in their analysis. The main point of our work is to emphasize that the natural convexity properties arising in first and second price auctions are not being fully exploited. Finally, we show direct analogies to problems in financial markets: the expected cost of bidding in second price auctions is formally identical to certain transaction costs when submitting market orders, and that a related conjugate function arises in dark pool financial markets.

Post-auction investment by financially constrained bidders

This study examines auctions in which the value of goods is endogenously determined by ex post investment while bidders face financial constraints. The main results are twofold. First, we characterize performance comparisons on revenue and investment between standard auctions. When the valuation is linear in investment, we have the equivalence theorem with respect to the seller's expected revenue and the winner's expected investment. When the valuation is concave in investment, the first-price auction yields higher expected revenue than the second-price auction. In addition, under additional conditions, the expected investment is larger in the second-price auction. Second, we analyze mechanisms other than simple auctions when sellers aim to promote investment. Scoring auctions increase the winner's investment at the expense of a decrease in revenue compared to price-only auctions.

Political Risk and Deal Completion Likelihood

This study examines the impact of political risk on the likelihood of takeover completion and on deal duration. Using a sample of US deals between 2002 and 2019, we find a negative and significant relationship between the takeover completion likelihood and the bidder’s political risk. Our findings also suggest that firms take more time to complete deals when the bidders face higher political risk. As firm-level political risk breeds uncertainty, bidders faced with higher political risk are more likely to cancel bids before closing and delay deal completion. Political shocks can expose acquirers to default risk and make it costly for bidders to raise external funds to undertake mergers and acquisitions (M&As). Our results are robust, after controlling for potential endogeneity concerns.

Does Bilateral Trust Matter During Mergers and Acquisitions Negotiations?

AbstractWe examine the effect of bilateral trust on cross‐border mergers and acquisitions (M&As). Using a large European M&A sample, we find that bilateral trust facilitates deal announcement and completion. Bidder and target bilateral trusts towards each other are both important for deal announcement, but only bidder trust towards the target firm matters for deal completion. The effect of bilateral trust on deal completion is amplified in more complex transactions and when bidders face severe liability of foreignness. Moreover, bilateral trust between the parties is also associated positively with merger performance. These results support the importance of bilateral trust as a deal facilitator in negotiation settings characterized by contract incompleteness and liability of foreignness.

Risk aversion and auction design: Theoretical and empirical evidence

Auctions are inherently risky: bidders face uncertainty about their prospects of winning and payments, while sellers are unsure about revenue and chances of a successful sale. Auction rules influence the allocation of risk among agents and the behavior of risk-averse bidders, leading to a breakdown of payoff and revenue equivalence and a heightened significance of auction design decisions by sellers. In this paper, we review the literature on risk aversion in auctions, with an emphasis on what can be learned about auction design from theoretical modeling and empirical studies. We survey theoretical results relating to the behavior of risk-averse agents in auctions, the comparison of standard auction formats in the presence of risk aversion and implications for auction design. We discuss standard and more recent approaches to identifying risk preferences in empirical studies and evidence for the significance of risk aversion in auction applications. Finally, we identify areas where existing evidence is relatively scant and ask what questions empirical research might ask given the theory and where further theoretical research may be beneficial given existing empirical results.

Robust bidding and revenue in descending price auctions

We study the properties of Dutch auctions in an independent private value setting, where bidders face uncertainty over the type distribution of their opponents and evaluate their payoffs by the worst case from a set of probabilistic scenarios. In contrast to static auction formats, participants in the Dutch auction gradually learn about the valuations of other bidders. We show that the transmitted information can lead to changes in the worst-case distribution and thereby shift a bidder's payoff maximizing exit price over time. We characterise the equilibrium bidding function in this environment and show that the arriving information leads bidders to exit earlier at higher prices. As a result, the Dutch auction systematically generates more revenue than the first-price auction.

Expectations-Based Loss Aversion in Auctions with Interdependent Values: Extensive vs. Intensive Risk

We analyze the bidding behavior of expectations-based loss-averse bidders in auctions with interdependent values. We emphasize the difference between the risk bidders face over whether they win the auction (extensive risk) and the risk they face over the value of the prize conditional on winning (intensive risk). The extensive risk creates an “attachment” effect, whereas the intensive risk operates via a “comparison” effect. How loss-averse bidders react to these different risks depends on whether they incorporate their bid into their reference point. Under “unacclimating personal equilibrium” (UPE), where bidders keep their expectations fixed when choosing their bids, both the extensive and intensive risks induce them to bid more aggressively. Moreover, bidders are exposed to the “winner’s curse” and a seller can attain higher revenue by hiding information in order to leverage the intensive risk. By contrast, under “choice-acclimating personal equilibrium” (CPE), where a bid determines both the reference lottery and the outcome lottery, the intensive risk creates a “precautionary bidding” effect that pushes bidders to behave less aggressively; whether this effect is reinforced or undermined by the extensive risk depends on a bidder’s likelihood of winning the auction. Furthermore, bidders are less aggressive than under UPE and can be subject to a “loser’s curse.” Yet, by committing to bidding less aggressively, such as by engaging in proxy bidding, loss-averse bidders are better off under CPE than UPE. This paper was accepted by Ilia Tsetlin, decision analysis.

Mergers and Acquisitions: The Role of Ambiguity

Firms that face high ambiguity—Knightian uncertainty—reduce organic investments and increase the likelihood, count, and dollar value of merger and acquisition bids. Conversely, firms that face low ambiguity are likely targets. The probability and speed of deal completion increase in the spread between bidder and target ambiguity. All-stock deals are less likely when bidders face high ambiguity, and all-cash deals are less likely when targets face high ambiguity. Bidder ambiguity declines following deal completion, and bidders that face higher ambiguity have larger abnormal announcement returns that decrease in target ambiguity.

Hypothetical thinking and the winner’s curse: an experimental investigation

There is evidence that bidders fall prey to the winner’s curse because they fail to extract information from hypothetical events—like winning an auction. This paper investigates experimentally whether bidders in a common value auction perform better when the requirements for this cognitive issue—also denoted by contingent reasoning—are relaxed, leaving all other parameters unchanged. For my underlying research question, I used a lab experiment with two stages. In stage I, the subjects participate in a non-standard common value auction, called the wallet game, in which a naive bidding strategy can lead to both winner’s curse and loser’s curse. In stage II, the subjects in the treatment group learn whether their initial bid was the winning bid or not and they get the opportunity to change this bid. In this sense, the bidders face the same decision problems as in stage I again, but the need for hypothetical thinking is reduced in stage II. The overall pattern of the data suggests that the problem of irrational over- and underbidding can be weakened by giving the subjects ex ante feedback about their bid, but unlike related studies I also find negative effects of additional information.

Empirical relevance of ambiguity in first-price auctions

We study the identification and estimation of first-price auctions with independent private values if bidders face ambiguity about the valuation distribution and have maxmin expected utility. Using variation in the number of bidders we nonparametrically identify the true valuation distribution and the lower envelope of the set of prior beliefs. We also allow for CRRA and unobserved auction heterogeneity, and propose a Bayesian estimation method based on Bernstein polynomials. Monte Carlo experiments show that our estimator performs well, and incorrectly ignoring ambiguity induces bias and loss of revenue. We find evidence of ambiguity in timber auctions in the Pacific Northwest.

Wholesale Price Auctions for Dual Sourcing under Supply Risk

ABSTRACTWholesale price bids commonly occur in procurement auctions where dual sourcing is usually employed to mitigate supply risks. When at most two winners are required, unreliable wholesale price bidders face the unique trade‐off between unit margin and quantity allocation that depends on both winners' bids and the reliabilities. Motivated by above facts and considerations, we investigate several auction formats accommodating wholesale price bids for dual sourcing under newsvendor market, with unreliable suppliers possessing private costs. Generalized first‐price auction (GFA) is designed under known cost distribution, while generalized English auction (GEA) and optimal auction with learning (OAL) are examined under unknown distribution. Through a preannounced allocation rule to curb the bidding behavior, both GFA and OAL balance information rent and quantity allocation and generate various diversification degrees. Information asymmetry under GFA depresses the quantity proportion for high‐cost winner, because he charges higher unit information rent than low‐cost winner does. In contrast, two winners in GEA collude at the same price and thus split the order quantity evenly. The full diversification possibly enables GEA to generate higher service level than GFA under high supply risk, although the expected output quantity of GEA is always lower. Regarding the practical requirement for auction format choice, when the costs of implementation and distribution acquisition are not negligible, the previous analysis suggests that the favorable format is driven from GFA or OAL to GEA, as supply risk or the number of bidders increases, or as retail price exceeds a threshold. We also extend to multisourcing cases and examine the impacts of salvage and lost sale on auction format choice.

A Comparison of Bidding Strategies for Online Auctions Using Fuzzy Reasoning and Negotiation Decision Functions

Bidders often feel challenged when looking for the best bidding strategies to excel in the competitive environment of multiple and simultaneous online auctions for same or similar items. Bidders face complicated issues for deciding which auction to participate in, whether to bid early or late, and how much to bid. In this paper, we present the design of bidding strategies, which aim to forecast the bid amounts for buyers at a particular moment in time based on their bidding behavior and their valuation of an auctioned item. The agent develops a comprehensive methodology for final price estimation, which designs bidding strategies to address buyers’ different bidding behaviors using two approaches: Mamdani method with regression analysis and negotiation decision functions. The experimental results show that the agents who follow fuzzy reasoning with a regression approach outperform other existing agents in most settings in terms of their success rate and expected utility.

Pay-As-Bid vs. First-Price Auctions: Similarities and Differences in Strategic Behavior

Pay-as-bid auctions extend the rules of the well-known first-price auction to the sale of multiple units of the same good. According to a common understanding of the recent literature, strategic incentives in pay-as-bid auctions differ from those in the first-price auctions when bidders have multi-unit demand. I show that each of N symmetrically informed bidders shades his bid for 1 of N shares of a perfectly divisible good in a pay-as-bid auction as if he competed with (N-1)N bidders for one indivisible good in a first-price auction. This analogy carries over to environments where bidders have pri- vate information if equilibrium demand schedules are additively separable in the type but breaks otherwise. Whether bidding in pay-as-bid auctions is more complex than in first-price auctions thus depends on the type of uncertainty bidders face.

Self-confirming price-prediction strategies for simultaneous one-shot auctions

Bidding in simultaneous auctions is challenging because an agent's value for a good in one auction may depend on the outcome of other auctions; that is, bidders face an exposure problem. Previous works have tackled the exposure problem with heuristic strategies that employ probabilistic price predictions—so-called price-prediction strategies. We introduce a concept of self-confirming prices, and show that within an independent private value model, Bayes–Nash equilibrium can be fully characterized as a profile of optimal price-prediction strategies with self-confirming prices. We operationalize this observation by exhibiting a practical procedure to compute near-self-confirming price predictions given a price-prediction strategy. An extensive empirical game-theoretic analysis demonstrates that bidding strategies that use such predictions are effective in simultaneous auctions with both complementary and substitutable preference structures. In particular, we produce one such strategy that finds near-optimal bids, thereby outperforming all previously studied bidding heuristics in these environments.

Second-price common value auctions with uncertainty, private and public information: Experimental evidence

We conduct a laboratory experiment of second-price sealed bid auctions of a common value good with two bidders. Bidders face three different types of information: common uncertainty (unknown information), private information (known by one bidder) and public information (known by both bidders), and auctions differ on the relative importance of these three types of information. We find that subjects barely differentiate between private and public information and deviate from the theoretical predictions with respect to all three types of information. There is under-reaction to both private and public information and systematic overbidding in all auctions above and beyond the standard winner’s curse. The Cursed Equilibrium and Level-k models successfully account for some features of the data but others remain largely unexplained.

The nature of information and its effect on bidding behavior: Laboratory evidence in a first price common value auction

We study in the laboratory a series of first price sealed bid auctions of a common value good. Bidders face three types of information: private information, public information and common uncertainty. Auctions are characterized by the relative size of these three information elements. Only half of our subjects bid differently depending on whether the last piece of information obtained is private or public but they do not react to each type of information as predicted by theory. The other half of the subjects do not distinguish between private and public information and either consistently underbid or consistently overbid.

How Much is Too Much? Large Termination Fees and Merger Outcomes

We investigate the use and impact of large target termination fees in acquisitions. Large termination fees are associated with more post-bid competition and lower completion rates, suggesting high fees do not effectively lock-in friendly bidders. Large termination fees are more common in deals with small and distressed targets and deals with high advisory fees. Switching regression estimates predict that high-fee deals would receive lower premiums with reduced termination fees. Overall, our evidence suggests that targets use large termination fees to overcome contracting problems when bidders face high transaction costs and information risk. In contrast to prior literature, there is limited evidence that managerial self-interest motivates high fees, as target managers in these deals are not more likely to receive severance packages or employment with the bidder in high-fee deals.

Assigning Spectrum Fairly: Managing Spectrum Using Long-Term Nationwide and Short-Term Local Spectrum Licenses

A new method is proposed to divide upcoming spectrum band allocations into two different spectrum licence / management right types. The first, a spectrum license, would allow successful auction bidders to roll out mobile radio networks on a long-term nationwide scale as normal. The second is a new concept called a licensed spectrum park (LSP) and would allow smaller operators to roll out specialized mobile radio networks on a short-term local site by site basis. LSPs would be assigned by applying for a license based on a site specific, fixed base station location for a short timeframe that could be renewed periodically. It has been noted that the key purpose of spectrum management is to maximize the value that society gains from the radio spectrum by allowing as many efficient users as possible while ensuring that the interference between different users remains manageable. The creation of LSPs means there is a net social benefit or a fair allocation of spectrum for two reasons. The first is that the use of LSPs allows specialist networks to be formed, effectively opening up the spectrum to more users and to potentially create more competition in the mobile radio market. The second is the fact that an LSP is licensed which creates a method to control interference between different users and allows interference to be managed.A regulator faces the issue of whether to allocate a fixed amount of spectrum for LSP use before auctioning the remaining spectrum, or alternatively auctioning the total spectrum and allocating any unsold spectrum to LSPs, if any is available. An operator’s strategy when bidding in the spectrum auction in response to these two alternative strategies are analysed using non-cooperative game models. The equilibria from both strategies are compared and it is shown that in the case where spectrum for LSP use is assigned post auction, if any is available, then all bidders face a collective action problem in that they may find it attractive to exhaust the pool of offered spectrum in the action leaving none for LSPs. To demonstrate how this theory could work in practice, we discuss how LSP creation could have worked in recent 700 MHz spectrum auctions. In particular we look at the 700 MHz auction in New Zealand as an illustrative example, by describing the auction process and the hypothetical effect if spectrum was assigned for LSP use. In addition we propose how the LSP spectrum could be priced. The price considers the population covered by the proposed base station, the amount of spectrum requested and length of the management right, against the normalised cost of the spectrum, for a given population and bandwidth, under the spectrum license auctions.Our analysis offers an important contribution for both spectrum regulators and private spectrum managers, and provides the framework for spectrum allocation to new market entrants enabling more competition in the mobile radio market.

Pay-as-Bid: Selling Divisible Goods to Informed Bidders

Pay-as-bid is the most popular auction format for selling treasury securities. We prove the uniqueness of pure-strategy Bayesian-Nash equilibria in pay-as-bid auctions where symmetrically-informed bidders face uncertain supply, and we establish a tight sufficient condition for the existence of this equilibrium. Equilibrium bids have a convenient separable representation: the bid for any unit is a weighted average of marginal values for larger quantities. With optimal supply and reserve price, the pay-as-bid auction is revenue-equivalent to the uniform-price auction.

Identification and Estimation of First-Price Auctions Under Ambiguity

This paper studies identification and estimation of first-price auctions if the bidders face ambiguity about the distribution of valuations. Ambiguity is modeled using Gilboa and Schmeidler's (1989) Maxmin Expected Utility preferences. We exploit variation in the number of bidders to identify the essential primitives of the model. The identification result yields a closed form for the inverse bid function, which suggests a two-step estimation procedure. We study asymptotic and finite sample properties of the estimators. We find evidence of ambiguity in USFS timber auctions which leads to aggressive bidding for bidders with high valuations and has important implications for auction design.