Bidding in private-value auctions with uncertain values

Auctions are often used to sell idiosyncratic goods difficult for potential bidders to value ex ante. Laboratory auctions with uncertainty over final values in this experiment resulted in 18% and 27% of bids above the expected value of the item in private-value first-price and English auctions, respectively. Risk-seeking preferences as measured on an individual decision task cannot explain overbidding and the first-price auction results suggest that risk aversion may not be a good explanation for bidding behavior observed with certain values. Several candidate explanations fail to explain overbidding, rather it appears to stem from some bidders who are prone to overbidding. Relative to first-price auctions, the size and frequency of overbids are significantly larger in English auctions, while more English auctions are won by overbidders. Differences between the formats appear to be driven by the dynamic nature of English auctions which is consistent with popular notions of “auction fever.”     

Multi-unit demand auctions with synergies: behavior in sealed-bid versus ascending-bid uniform-price auctions

We construct a relatively simple model of bidding with synergies and solve it for both open outcry and sealed-bid uniform-price auctions. The essential behavioral forces involved in these auctions are: (1) A demand reduction force resulting from the monopsony power that bidders with multiple-unit demands have when synergies are relatively inconsequential, and (2) Bidding above stand-alone values in order to capture significant complementarities between units. The latter creates a potential “exposure problem,” as bidders may win only parts of a package and earn negative profits. Bidding outcomes are closer to equilibrium in clock compared to sealed-bid auctions. However, there are substantial and systematic deviations from equilibrium, with patterns of out-of-equilibrium play differing systematically between the two auction formats. These patterns of out-of-equilibrium play are analyzed, along with their effects on revenue and efficiency.     

Equilibrium selection in common-value second-price auctions

This note considers equilibrium selection in common-value second-price auctions with two bidders. We show that for each ex post equilibrium in continuous and undominated strategies, a sequence of “almost common-value” auctions can be constructed such that each of them possesses a unique undominated and continuous equilibrium and the corresponding sequence of equilibria converges to that ex post equilibrium. As an implication, no equilibrium selection of this model based on perturbations seems to be more convincing than others.     

Pure strategy equilibria of single and double auctions with interdependent values

We prove the existence of monotonic pure strategy equilibrium for many kinds of asymmetric auctions with n bidders and unitary demands, interdependent values and independent types. The assumptions require monotonicity only in the own bidder's type. The payments can be a function of all bids. Thus, we provide a new equilibrium existence result for asymmetrical double auctions and a small number of bidders. The generality of our setting requires the use of special tie-breaking rules. We present an example of a double auction with interdependent values where all equilibria are trivial, that is, they have zero probability of trade. This is related to Akerlof's “market for lemmons” example and to the “winner's curse,” establishing a connection between them. However, we are able to provide sufficient conditions for non-trivial equilibrium existence.     

Multi-unit auctions with budget limits

We study multi-unit auctions for bidders that have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there is no deterministic auction that (1) is individually rational and dominant-strategy incentive-compatible, (2) makes no positive transfers, and (3) always produces a Pareto optimal outcome. In contrast, we show that Ausubel?s “clinching auction” satisfies all these properties when the budgets are public knowledge. Moreover, we prove that the “clinching auction” is the unique auction that satisfies all these properties when there are two players. This uniqueness result is the cornerstone of the impossibility result. Few additional related results are given, including some results on the revenue of the clinching auction and on the case where the items are divisible.     

Optimal auctions with information acquisition

This paper studies optimal auction design in a private value setting with endogenous information gathering. We develop a general framework for modeling information acquisition when a seller wants to sell an object to one of several potential buyers, who can each gather information about their valuations prior to participation in the auction. We first demonstrate that the optimal monopoly price is always lower than the standard monopoly price. We then show that standard auctions with a reserve price remain optimal among symmetric mechanisms, but the optimal reserve price lies between the ex ante mean valuation of bidders and the standard reserve price in Myerson (1981). Finally, we show that the optimal asymmetric mechanism softens the price discrimination against “strong” bidders.     

Causality between credit depth and economic growth: evidence from 24 OECD countries

Causality between the ratio of domestic private credit to GDP and growth in real GDP per capita is investigated in a country-by-country time-series framework for 24 OECD economies over the period 1980–2013. The proposed threefold methodology to test for causal linkages integrates (1) lag-augmented VAR Granger causality tests, (2) Breitung–Candelon causality tests in the frequency domain, and (3) testing for causal inference based on a fully modified OLS (FMOLS) approach. For 12 of 24 countries in the sample, the three tests yield uniform results in terms of causality presence (absence) and direction. Causality running from credit depth to economic growth is found for the UK, Australia, Switzerland, and Greece. The findings lend no support to the view that financial development shifts from a supply-leading to demand-following pattern as economic development proceeds. The aggregate results mesh well with the current discussion on “too much finance” and disintermediation effects. However, idiosyncratic country determinants also appear significant.     

Spectrum auction designs and revenue variations

This study examines a sample of 93 national 3G spectrum auctions for the period 2000–2011 to identify the sources of substantial revenue variations. An implied reduced-form econometric model that recognises the censored nature of the sample relates per capita winning bid (per Mhz, per million populations) values to regulator-determined auction design characteristics, auction competitiveness, mobile wireless market conditions and spectrum package attributes identified from tender documents. The analysis reveals that among other factors, all auction design characteristics independently impact on realized 3G spectrum auction revenues.     

Mixed bundling auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling.     

Asymmetric common-value auctions with applications to private-value auctions with resale

We study a model of common-value auctions with two bidders in which bidders’ private information are independently and asymmetrically distributed. We present sufficient and necessary conditions, respectively, under which the expected revenues from first-price and second-price auctions can be ranked. Using these conditions and a bid-equivalence between common-value auctions and private-value auctions with resale, we extend the revenue-ranking result of Hafalir and Krishna [Am Econ Rev 98, 2008a] and provide necessary conditions for their ranking to hold. In addition, we provide sufficient and necessary conditions for the opposite ranking of revenues, respectively. Our analysis helps clarify the roles of two forms of regularity assumptions (buyer-regularity and seller-regularity) in ranking revenues and illustrates how revenue ranking is linked to submodularity and supermodularity of the common-value function and to a single-crossing property of a function derived from the monopoly or monopsony pricing function in the resale stage.     

Competitive auctions

We study a class of single-round, sealed-bid auctions for an item in unlimited supply, such as a digital good. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e. encourages bidders to bid their true valuations) and on all inputs yields profit that is within a constant factor of the profit of the optimal single sale price. We justify the use of optimal single price profit as a benchmark for evaluating a competitive auctions profit. We exhibit several randomized competitive auctions and show that there is no symmetric deterministic competitive auction. Our results extend to bounded supply markets, for which we also give competitive auctions.     

Does environmental quality influence health expenditures? Empirical evidence from a panel of selected OECD countries

In this paper we examine the role of environmental quality in determining per capita health expenditures. We take a panel cointegration approach in order to explore the possibility of estimating both short-run and long-run impacts of environmental quality. Our empirical analysis is based on eight OECD countries, namely Austria, Denmark, Iceland, Ireland, Norway, Spain, Switzerland, and the UK for the period 1980-1999. We find that per capita health expenditure, per capita income, carbon monoxide emissions, sulphur oxide emissions and nitrogen oxide emissions are panel cointegrated. While short-run elasticities reveal that income and carbon monoxide emissions exert a statistically significant positive effect on health expenditures, in the long-run in addition to income and carbon monoxide, we find that sulphur oxide emissions have a statistically significant positive impact on health expenditures.     

Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints

We show that all-pay auctions dominate first-price sealed-bid auctions when bidders face budget constraints. This ranking is explained by the fact that budget constraints bind less frequently in the all-pay auctions, which leads to more aggressive bidding in that format.     

Asymmetric Nash equilibrium in emission rights auctions

This paper studies the problems of emission rights auctions, and presents a uniform price auction mechanism based on three assumptions, i.e., all buyers are asymmetric, every buyer submits a nonincreasing continuous demand function, and every buyer's valuation to per unit of the emission rights is common value information. It focuses on solving the asymmetric Nash equilibrium for this auction mechanism. It concludes that there exist multiple Nash equilibria in our auction mechanism, but the arbitrary low equilibrium prices cannot emerge. We also give several suggestions on how to induce the auction to a desired ideal equilibrium state in mechanism design of emission rights auctions.     

Patience auctions: the impact of time vs. money bidding on elicited discount rates

We introduce, test, and compare two auction-based methods for eliciting discount rates. In these “patience auctions”, participants bid the smallest future sum they would prefer -or- the longest time they would wait for a reward, rather than receive a smaller, immediate payoff. The most patient bidder receives the delayed reward; all others receive the immediate payoff. These auctions allow us to compare discounting when participants’ attention is focused on the temporal versus monetary dimension of delayed rewards. We find that the estimated parameters in the three most commonly used discount functions (exponential, hyperbolic, and quasi-hyperbolic) differ across these two bidding methods (time-bids vs. money-bids). Specifically, our participants tend to show more impatience under time-bids. Furthermore, we find that people are more likely to exhibit exponential (as opposed to hyperbolic) discounting and exhibit less present bias under time-bids, compared to money-bids. To our knowledge, this paper is the first to directly compare time versus money preference elicitations, within the same subjects, using an incentive-compatible mechanism.     

Ascending price Vickrey auctions for general valuations

Ascending price auctions involving a single price path and buyers paying their final bid price cannot achieve the Vickrey-Clarke-Groves (VCG) outcome in the combinatorial auctions setting. Using a notion called universal competitive equilibrium prices, shown to be necessary and sufficient to achieve the VCG outcome using ascending price auctions, we define a class of ascending price auctions in which buyers bid on a single price path. Truthful bidding by buyers is an ex post Nash equilibrium in such auctions. By giving discounts to buyers from the final price, the VCG outcome is achieved for general valuations.     

An experimental investigation of the explosive effect in almost common value auctions

With only two bidders, a slight private value advantage in a common value auction is predicted to have an explosive effect on the allocation and revenue of the auction when using a second price and/or English clock mechanism. This paper uses the “wallet game” in an English clock mechanism with two players to test these predictions. The results show that the effect is proportional, not explosive, confirming the results of past experiments. A behavioral model with two types of players, naive and sophisticated, is developed and tested against the experimental data. In the model, naive players use a rule of thumb bidding function, while the sophisticated players are fully rational and, when forming their strategy (choosing the best response), correctly account for the probability that a rival is naive or sophisticated. We use cluster analysis to classify the players in the symmetric auctions as naive or sophisticated and a strict win/lose criteria to classify players in the asymmetric auctions. We find that those players classified as sophisticated are more aggressive in responding to high signals or advantaged status than their naive counterparts, but do not lower their bids relative to the naive players when receiving low signals or when regular.     

The determinants of price in 3G spectrum auctions

This article examined the empirical relationship between prices paid for national 3G wireless licenses when spectrums were sold by auction. The reduced-form modelling approach was based on the premise that auction design features can, and do, affect both final (revenue) and intermediate (viz., auction competitiveness and license assignment) auction outcomes. Importantly, the analysis recognizes, and explicitly allows for, the endogeneity of bidder entry and sample selection arising from an absence of bidding. Generally, these key features have only received attention in isolation. In particular, the study addressed the principal question of: which regulator chosen auction design variables determine prices paid in spectrum auctions? The analysis showed that flexible-package formats increased prices paid, and that higher reserve prices had a dampening effect. The article also showed that longer license terms and more competitive auctions (as measured by the bidders-to-licenses ratio) enhance prices paid.     

Bidding behavior in competing auctions: Evidence from eBay

Much of the existing auction literature treats auctions as running independently of one another, with each bidder choosing to participate in only one auction. However, in many online auctions, a number of substitutable goods are auctioned concurrently and bidders can bid on several auctions at the same time. Recent theoretical research shows how bidders can gain from the existence of competing auctions, the current paper providing the first empirical evidence in support of competing auctions theory using online auctions data from eBay. Our results indicate that a significant proportion of bidders do bid across competing auctions and that bidders tend to submit bids on auctions with the lowest standing bid, as the theory predicts. The paper also shows that winning bidders who cross-bid pay lower prices on average than winning bidders who do not.     

“Love of wealth” and economic growth

In a Ramsey–Cass–Koopmans growth framework it is shown that for an optimum a benevolent social planner cannot have an excessive “love of wealth”. With a “right” “love of wealth” an optimum exists and implies higher long‐run per‐capita capital, income, and consumption relative to the standard model. This has important implications for comparative development trajectories. The optimum implies dynamic efficiency with the possibility of getting arbitrarily close to the golden rule where long‐run per‐capita consumption is maximal. It is shown that the optimal path attains its steady state more slowly. Thus, the beneficial effects of love of wealth materialize later than in the standard model. Furthermore, the economy can be decentralized as a competitive private ownership economy. One can then identify “love of wealth” with the “spirit of capitalism.” The paper thus implies that one needs a “right” level of the “spirit of capitalism” to realize any beneficial effects for the long run.