First-price Auction Research Articles

Bidding mechanisms in graph games

A graph game proceeds as follows: two players move a token through a graph to produce a finite or infinite path, which determines the payoff of the game. We study bidding games in which in each turn, an auction determines which player moves the token. Bidding games were largely studied in combination with two variants of first-price auctions called “Richman” and “poorman” bidding. We study taxman bidding, which span the spectrum between the two. The game is parameterized by a constant τ∈[0,1]: portion τ of the winning bid is paid to the other player, and portion 1−τ to the bank. While finite-duration (reachability) taxman games have been studied before, we present, for the first time, results on infinite-duration taxman games: we unify, generalize, and simplify previous equivalences between bidding games and a class of stochastic games called random-turn games.

Effects of competition in first-price auctions

This paper analyzes the effects of industrial concentration on bidding behavior and expected revenues. These effects are studied under the CIAPI model, an affiliated value set-up that nests a variety of valuation and information environments. We formally decompose the revenue effects coming from less competition into five types. The properties of these effects are discussed and conditions for (non)monotonicity of both the equilibrium bid and revenue are stated. Our results suggest that it is more likely that the seller benefits from less competition in markets with more complete valuation and information structures.

Ranking reversals in asymmetric auctions

This paper compares the first-price auction and the second-price auction with several asymmetric bidders who are either weak or strong. The ranking of these auctions in terms of profit may flip as the exogenous reserve price or the number of weak or strong bidders change. Similarly, with endogenous reserve prices the ranking may depend on the seller’s own-use valuation. In other words, the ranking may be fragile to changes along these dimensions. Existing models rule out such ranking reversals by imposing substantial structure on type distributions. The current paper relies on simple mechanism design arguments that require less structure.

All-pay auctions with private signals about opponents’ values

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.

Cross-Game Learning and Cognitive Ability in Auctions

Overbidding in 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 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 has the potential to benefit bidders with lower cognitive ability whereas it has little or even adverse effects for higher ability bidders.

Strategic Leaks in First-Price Auctions and Tacit Collusion: The Case of Spying and Counter-Spying

We analyze strategic leaks due to spying out a rival’s bid in a first-price auction. Such leaks induce sequential bidding, complicated by the fact that the spy may be a counterspy who serves the interests of the spied at bidder and reports strategically distorted information. This ambiguity about the type of spy gives rise to a non-standard signaling problem where both sender and receiver of messages have private information and the sender has a chance to make an unobserved move. Whereas spying without counterspy exclusively benefits the spying bidder, the potential presence of a counterspy yields a collusive outcome, even if the likelihood that the spy is a counterspy is arbitrarily small. That collusive impact shows up in all equilibria and is strongest in the unique pooling equilibrium which is also the payoff dominant equilibrium.

Auction Design with Ambiguity: Optimality of the First-Price and All-Pay Auctions

We study the optimal auction design problem when bidders' preferences follow the maxmin expected utility model. We suppose that each bidder's set of priors consists of beliefs close to the seller's belief, where closeness is defined by a divergence. For a given allocation rule, we identify a class of optimal transfer candidates, named the win-lose dependent transfers, with the following property: each type of bidder's transfer conditional on winning or losing is independent of the competitor's type report. Our result reduces the infinite-dimensional optimal transfer problem to a two-dimensional optimization problem. By solving the reduced problem, we find that: (i) among efficient mechanisms with no premiums for losers, the first-price auction is optimal; and, (ii) among efficient winner-favored mechanisms where each bidder pays smaller amounts when she wins than loses: the all-pay auction is optimal. Under a simplifying assumption, these two auctions remain optimal under the endogenous allocation rule.

Estimation and Inference of Seller’s Expected Revenue in First-Price Auctions

Estimation and Inference of Seller’s Expected Revenue in First-Price Auctions

Non-Bossiness and First-Price Auctions

Non-Bossiness and First-Price Auctions

Disentangling Risk-Aversion and Loss Aversion in First-Price Auctions: An Empirical Approach

Disentangling Risk-Aversion and Loss Aversion in First-Price Auctions: An Empirical Approach

Simultaneous auctions with budgets: Equilibrium existence and characterization

We study the sale of two units of a good through simultaneous sealed bid first-price auctions to bidders who have private types and multi-unit demand. Bidders are differentiated based on their valuations and budgets. Under a parametric restriction, we show that this auction game is better-reply secure and thus possesses a Nash equilibrium. In equilibrium, bidders expend their budgets. The equilibrium strategies are essentially pure in the sense that each bidder-type has a unique split (up to a permutation) of her budget between the two auctions. In equilibrium, there always exist bidder-types who submit unequal bids in equilibrium even though they have the same valuations for the units. In addition, the equilibrium is monotone in valuations and budgets: bidders with higher valuations (lower budgets) prefer more unequal splits of their budgets than bidders with lower valuations (higher budgets) and the same budget (valuation).

Procuring NGA infrastructure: The performance of EMAT auctions in Italy

Italy was a patent laggard in the market roll-out of NGA networks. In 2015, the Italian Government introduced the “ultrabroadband strategy”, an ambitious policy agenda addressing the NGA market failures. This paper assesses the procurement policy assigning public concessions to build and manage passive infrastructure in “NGA white areas”: in detail, the techno-economic properties and outcomes of the auctions are analyzed, both theoretically and empirically. Because the applicable procurement law was the EU one, the EMAT scoring rules were mandatory. Relevant findings stand out, which confirm the received wisdom on first-price auctions, and extend it to high-tech sectors, where EMAT remains under-researched. First, the concession auctions unleashed vibrant bidding competition in many white areas, which enabled substantial budget savings. Second, the quality scoring rules provided adequate flexibility to prioritize the procurement of the most innovative and pro-competitive architectures (FTTH/B/P), despite the presence of high uncertainty. Third, the EMAT framework catered for a multidimensional procurement agenda; the latter targeted efficient and innovative procurement, universal service and higher market competition, while accommodating the ambitious industrial policy of the Government. Evidence of a potential trade-off between the plan implementation delay and its innovativeness emerged; such a conflict was eventually exacerbated by the bandwidth shortages generated by the COVID-19 crisis. By providing the very first study on EMAT auctions for broadband, this work stimulates future comparative research on additional EU member States.

Auctions with an Invitation Cost

We consider an auction in which a seller invites potential buyers to a sealed-bid first-price auction, without disclosing to the buyers the number of extended invitations. In the presence of a fixed invitation cost for each invited bidder, the whole auction can be described as a game, where the set of players consists of all bidders together with the seller. In a setting with fully observable common values we show the existence of a Nash equilibrium in mixed strategies. In this equilibrium, the seller should invite precisely one or two potential buyers with certain probabilities, and each invited buyer should place a randomized bid according to a certain distribution.

A model of electoral alliances in highly fragmented party systems

Highly fragmented party systems are composed of a large number of political groups, many of which have negligible bargaining power when it comes to negotiations of electoral alliances. Inspired by the Brazilian system—one of the most fragmented in the world—we provide a stylized model of electoral alliances in which there is a competition for the support of the small parties. Two leading parties try to entice a small one by simultaneously offering transfers (e.g. government positions, support in other elections, prestige). Through a first-price sealed-bid auction approach, we can analyze the role of two particular factors in alliance formation, namely pragmatism and ideology. Our findings show that, in equilibrium, the favorite party tends to offer lower transfers than the underdog. Furthermore, the closer the leading and the small parties are in terms of ideology, the smaller the transferred amount. When the ideological closeness between the small party and the underdog is sufficiently large—relative to the favorite—the effect may be strong enough to overcome the electoral advantage of the favorite.

The beauty of Dutch: Bidding behavior in combinatorial first-price procurement auctions

Ex-post split-award auctions are a frequently used form of combinatorial auction mechanism in practice. The procurement quantity is split into several shares and suppliers can submit bids on separate shares as well as on the entire quantity. Markets with diseconomies of scale are wide-spread, but strategically challenging. In a game-theoretical equilibrium analysis, Kokott et al. (2019) have recently shown that in contrast to single-object auctions, there is no strategic equivalence between first-price sealed-bid (FPSB) and Dutch combinatorial auctions. The FPSB auctions are characterized by efficient and inefficient equilibria while the Dutch auctions only possess efficient equilibria. We report the results of extensive laboratory experiments and show that the theory explains the bid data surprisingly well. Importantly, a compound Dutch auction format weakly outperforms the wide-spread combinatorial first-price sealed-bid auction in efficiency and total procurement costs. The results provide guidance for procurement managers in the field.

Common Values, Unobserved Heterogeneity, and Endogenous Entry in US Offshore Oil Lease Auctions

Although an auction of drilling rights is often cited as an example of common values, formal evidence has been limited by the problem of auction-level unobserved heterogeneity. We develop an empirical approach for first-price sealed-bid auctions with affiliated values, unobserved heterogeneity, and endogenous bidder entry. We show that important features of the model are nonparametrically identified and apply a semiparametric estimation approach to data from US offshore oil and gas lease auctions. We find that common values, affiliated private information, and unobserved heterogeneity are all present. Failing to account for unobserved heterogeneity obscures the evidence of common values. We examine implications of our estimates for the interaction between affiliation, the winner’s curse, the auction rules, and the number of bidders in determining the aggressiveness of bidding and seller revenue.

Peaches, lemons, and cookies: Designing auction markets with dispersed information

We study how ex ante information asymmetries affect revenue in common-value second-price auctions, motivated by online advertising auctions where “cookies” inform individual advertisers about advertising opportunities. We distinguish information structures in which cookies identify “lemons” (low-value impressions) from those in which cookies identify “peaches” (high-value impressions). As this setting features multiple Nash equilibria, we introduce a new refinement, “tremble robust equilibrium” (TRE) and characterize the unique TRE in first-price and second-price common-value auctions with two bidders who each receive a binary signal. We find that common-value second-price auction revenues are vulnerable to ex ante information asymmetry if relatively rare cookies identify lemons, but not if they identify peaches. First-price auction revenues are substantially higher than second-price auction revenues under these conditions. Extensions show that these insights are robust.

Identification and Estimation in First-Price Auctions with Risk-Averse Bidders and Selective Entry

We study identification and estimation in first-price auctions with risk averse bidders and selective entry, building on a flexible entry and bidding framework we call the Affiliated Signal with Risk Aversion (AS-RA) model. This framework extends the AS model of Gentry and Li (2014) to accommodate arbitrary bidder risk aversion, thereby nesting a variety of standard models as special cases. It poses, however, a unique methodological challenge – existing results on identification with risk aversion fail in the presence of selection, while the selection-robust bounds of Gentry and Li (2014) fail in the presence of risk aversion. Motivated by this problem, we translate excludable variation in potential competition into identified sets for AS-RA primitives under various classes of restrictions on the model. We show that a single parametric restriction – on the copula governing selection into entry – is typically sufficient to restore point identification of all primitives. In contrast, a parametric form for utility yields point identification of the utility function but only partial identification of remaining primitives. Finally, we outline a simple semiparametric estimator combining Constant Relative Risk Aversion utility with a parametric signal-value copula. Simulation evidence suggests that this estimator performs very well even in small samples, underscoring the practical value of our identification results.

Reserve price signaling in first-price auctions with an uncertain number of bidders

We study first-price auctions in which the number of bidders is the seller’s private information, and investigate the use of a reserve price to signal this private information. We use the D1 criterion to refine the set of equilibria and characterize a symmetric separating equilibrium outcome, where the reserve price increases with the number of bidders. The key driving force is a certain form of single-crossing property. With more bidders, the seller can afford a high reserve price that discourages competition in the auction, for the winning bid is more likely to be higher.

Should Auctions Be Transparent?

We investigate the role of market transparency in repeated first-price auctions. We consider a setting with private and independent values across bidders. The values are assumed to be perfectly persistent over time.We analyze the first-price auction under three distinct disclosure regimes regarding the bid and award history. Of particular interest is the minimal disclosure regime, in which each bidder only learns privately whether he won or lost the auction at the end of each round. In equilibrium, the winner of the initial auction lowers his bids over time, while losers keep their bids constant, in anticipation of the winner’s lower future bids. This equilibrium is efficient, and all information is eventually revealed. Importantly, this disclosure regime does not give rise to pooling equilibria.We contrast the minimal disclosure setting with the case in which all bids are public, and the case in which only the winner’s bids are public. In these settings, an inefficient pooling equilibrium with low revenues always exists with a sufficiently large number of bidders.