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We explore the impact of private information in sealed-bid first-price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning-bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative auction mechanisms.

The authors link the rapid and dramatic move from second-price to first-price auction format in the display advertising market, on the one hand, to the move from the waterfalling mechanism employed by publishers for soliciting bids in a preordered cascade over exchanges to an alternate header bidding strategy that broadcasts the request for bid to all exchanges simultaneously, on the other. First, they argue that the move from waterfalling to header bidding was a revenue-improving move for publishers in the old regime when exchanges employed second-price auctions. Given the publisher move to header bidding, the authors show that exchanges move from second-price to first-price auctions to increase their expected clearing prices. Interestingly, when all exchanges move to first-price auctions, each exchange faces stronger competition from other exchanges, and some exchanges may end up with lower revenue than when all exchanges use second-price auctions; yet all exchanges move to first-price auctions in the unique equilibrium of the game. The authors show that the new regime hinders the exchanges' ability to differentiate in equilibrium. Furthermore, it allows the publishers to achieve the revenue of the optimal mechanism despite not having direct access to the advertisers.

Most assets clear independently rather than jointly. This paper presents a model based on the uniform-price double auction which accommodates arbitrary restrictions on market clearing, including independent clearing across assets (allowed when demand for each asset is contingent only on the price of that asset) and joint market clearing for all assets (required when demand for each asset is contingent on the prices of all assets). Additional trading protocols for traded assets—neutral when the market clears jointly—are generally not redundant innovations, even if all traders participate in all protocols. Multiple trading protocols that clear independently can be designed to be at least as efficient as joint market clearing for all assets. The change in price impact brought by independence in market clearing can overcome the loss of information, and enhance diversification and risk sharing. Except when the market is competitive, market characteristics should guide innovation in trading technology.

A marketable permit system (MPS) has been suggested as a solution to environmental problems. Although the properties of MPSs under non-trader settings, in which each player is exclusively either a seller or a buyer, are well documented, little research has explored how MPSs perform under trader settings, in which each player can be both a seller and a buyer. We institute two auctions of trader settings in MPS experiments: a double auction (DA) and a uniform price auction (UPA). We then evaluate and compare their performances both with each other and with those under non-trader settings. The main results are as follows: DAs under trader settings perform much worse than do DAs under non-trader settings, whereas UPAs perform well, regardless of the trader and non-trader settings. UPAs are more efficient and generate more stable prices than do DAs under trader settings, and a considerable proportion of trades in DAs under trader settings consist of “flips” that could be considered speculation or errors. Thus, UPAs are likely to work better than DAs under trader settings.

Government agencies often rely on repeated discriminatory price auctions to procure ecosystem services from private landowners despite limited evidence on this mechanism’s performance. This study presents an agent-based model of a repeated discriminatory price procurement auction in which the auctioneer informs bidders of their respective bid outcomes and the average price of successful bids after each round. The model introduces a new learning algorithm through which bidders adapt to these price signals. Simulations are used to compare the mechanism’s performance to an equivalent uniform (second) price auction, providing several findings. First, the performance of the discriminatory mechanism tends to deteriorate over time relative to the uniform mechanism as bidders learn. Second, minimal changes in bidders’ price expectations have a large influence on the relative performance of the mechanisms. Third, the discriminatory mechanism maintains high levels of efficiency and cost-effectiveness over time if bidders have highly heterogeneous opportunity costs and neutral or moderately low price expectations. Fourth, the system’s price paths have a high degree of stochasticity and path dependency, making it difficult to predict a single realisation’s trajectory. Based on these findings, we provide several suggestions regarding auction design.

If bidders are better informed than the seller about a common component of auction heterogeneity, the seller can allocate more efficiently by keeping her reserve price secret and revising it using submitted bids. We build a model of a first-price auction under unobserved auction heterogeneity-imperfectly observed by the seller-that captures this rationale and derive conditions for identification. An application to French timber auctions, where such revisions are widely used, shows that having perfect information about unobserved auction heterogeneity would increase surplus by 5.22%. Combining a secret reserve price with learning from submitted bids reduces this surplus gap by up to 84%.

We study all-pay auctions where each player observes her private value as well as a noisy private signal about the opponent’s value, following Fang and Morris’s (J Econ Theory 126(1):1–30, 2006) analysis of winner-pay auctions with multidimensional private signals. A unique symmetric monotonic equilibrium exists if the signal is not informative enough. When the signal is sufficiently informative, there exists a symmetric non-monotonic equilibrium in which all types of players randomize in overlapping supports. The revenue is lower than that in the standard independent private value setting. Fixing the signal’s informativeness, the all-pay auction raises lower revenue than the second-price auction, whereas the revenue ranking between the all-pay and the first-price auction is ambiguous.

Consider a first-price, sealed-bid auction with interdependent valuations and private budget constraints. Focusing on the two-bidder case, we identify new sufficient conditions for the existence of a symmetric equilibrium in pure strategies. In equilibrium, agents may adopt discontinuous bidding strategies resulting in a stratification of competition along the budget dimension. Private budgets can simultaneously lead to more aggressive bidding (a high-budget agent leverages his wealth to outbid rivals) and more subdued bidding (competition becomes less intense among bidders at distinct budget levels). The presence of budget constraints may lead to multiple symmetric equilibria in the first-price auction.

Overbidding in sealed-bid second-price auctions (SPAs) has been shown to be persistent and associated with cognitive ability. We study experimentally to what extent cross-game learning can reduce overbidding in SPAs, taking into account cognitive skills. Employing an order-balanced design, we use first-price auctions (FPAs) to expose participants to an auction format in which losses from high bids are more salient than in SPAs. Experience in FPAs causes substantial cross-game learning for cognitively less able participants but does not affect overbidding for the cognitively more able. Vice versa, experiencing SPAs before bidding in an FPA does not substantially affect bidding behavior by the cognitively less able but, somewhat surprisingly, reduces bid shading by cognitively more able participants, resulting in lower profits in FPAs. Thus, ‘cross-game learning’ may rather be understood as ‘cross-game transfer’, as it has the potential to benefit bidders with lower cognitive ability whereas it has little or even adverse effects for higher-ability bidders.

One of the most important results in auction theory is that when bidders are symmetric (homogeneous), then under quite general conditions, the seller's expected revenue is independent of the auction mechanism (Revenue Equivalence Theorem). More often than not, however, bidders are asymmetric, and so revenue equivalence is lost. Previously, it was shown that asymmetric auctions become revenue equivalent as n → ∞, where n is the number of bidders. In this paper, we go beyond the limiting behavior and explicitly calculate the revenue to O(1/n³) accuracy, essentially with no information on the auction payment rules or bidders' equilibrium strategies, for a large class of asymmetric auctions that includes first-price, second-price, and optimal auctions. These calculations show that the revenue differences among asymmetric auctions scale as ϵ²/n³, where e is the level of asymmetry (heterogeneity) among the bidders. Therefore, bidders' asymmetry has a negligible effect on revenue ranking of auctions with as few as n = 6 bidders.