All-pay Auction Research Articles

Optimal Disclosure in All-pay Auctions with Interdependent Valuations

Optimal Disclosure in All-pay Auctions with Interdependent Valuations

Disclosure Policies in All-Pay Auctions with Affiliation

Disclosure Policies in All-Pay Auctions with Affiliation

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

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

Disclosure Policies in All-pay Auctions with Affiliation

Disclosure Policies in All-pay Auctions with Affiliation

The role of luck in political and economic competition: noisy all-pay auctions

The role of luck in political and economic competition: noisy all-pay auctions

Competition between and within universities: Theoretical and experimental investigation of group identity and the desire to win

We study how group identity, based on university affiliation, impacts competitive behavior. Our experiment employs a simple all-pay auction within and between two university subject pools. Students within the lower-tier university bid more aggressively against each other than students within the top-tier university against each other. Lower-tier students, particularly females, bid more aggressively when competing against top-tier students. Interpreted through a theoretical model which incorporates both group identity and differential valuation of winning, our data indicate that students at the lower-tier university have a stronger group identity as well as a higher desire to win.

Mis-judging merit: the effects of adjudication errors in contests

Within contests, adjudication errors imply at the same time the exclusion of a meritorious candidate and the inclusion of a non-meritorious one. We study theoretically how adjudication errors affect bids in all-pay auctions, by disentangling the respective effects of exclusion and inclusion errors, and showing how they interact with the framing of incentives (prize or penalty) under different assumptions on preferences. We test our theoretical predictions with an experiment where we manipulate the presence of exclusion errors, inclusion errors, and the framing of incentives. The experimental evidence indicates that errors of either exclusion or inclusion significantly decrease bids in all-pay auctions relative to a setting without errors, interacting negatively, with no significant difference in the size of their effects. Bid levels are significantly higher in a penalty framing relative to a prize framing, both in the absence of errors and in the presence of adjudication errors.

Designing contests between heterogeneous contestants: An experimental study of tie-breaks and bid-caps in all-pay auctions

A well-known theoretical result in the contest literature is that greater heterogeneity decreases investments of contestants because of the “discouragement effect.” Levelling the playing field by favouring weaker contestants through strict bid-caps and favourable tie-breaking rules can reduce discouragement and increase the designer's revenue. We test these predictions in a laboratory experiment. Our data confirm that placing bid-caps and using favourable tie-breaking rules significantly diminishes discouragement of weaker contestants. However, its impact on revenues is muted by the fact that the encouragement of weaker contestants is offset by stronger contestants competing less aggressively, even when not predicted by theory. We discuss deviations from the Nash predictions in light of different behavioural approaches.

Designing all-pay auctions using deep learning and multi-agent simulation

We propose a multi-agent learning approach for designing crowdsourcing contests and All-Pay auctions. Prizes in contests incentivise contestants to expend effort on their entries, with different prize allocations resulting in different incentives and bidding behaviors. In contrast to auctions designed manually by economists, our method searches the possible design space using a simulation of the multi-agent learning process, and can thus handle settings where a game-theoretic equilibrium analysis is not tractable. Our method simulates agent learning in contests and evaluates the utility of the resulting outcome for the auctioneer. Given a large contest design space, we assess through simulation many possible contest designs within the space, and fit a neural network to predict outcomes for previously untested contest designs. Finally, we apply mirror ascent to optimize the design so as to achieve more desirable outcomes. Our empirical analysis shows our approach closely matches the optimal outcomes in settings where the equilibrium is known, and can produce high quality designs in settings where the equilibrium strategies are not solvable analytically.

Nonparametric identification and estimation of all-pay auction and contest models

AbstractIn this paper, I study the nonparametric identification and estimation of multi-unit all-pay auctions of incomplete information. First, I consider the setting where multiple goods are allocated among several risk-neutral participants with independent private values (IPV). I prove the nonparametric identification of the model and derive two different consistent estimators of the distribution of bidder valuations. The first estimator is based on the classical structural approach similar to that of Guerre et al. (Econometrica 68(3):525–574, 2000). The second estimator, instead, allows estimation of the quantile function of the bidders’ valuations directly using the quantile density of the bids. Monte Carlo simulations show good small sample property under various assumptions of the number of players and goods. Next, I consider a variety of model extensions: the case of affiliated private values (APV), asymmetric players, the addition of random noise, as well as the case of risk-averse bidders. In contrast to all other scenarios, I prove that the general model with risk-averse bidders is not identified even in the semi-parametric case in which utility function is restricted to belong to the class of functions with constant absolute risk aversion (CARA). On the other hand, I show that the model with risk aversion can be identified if the distribution of valuations is restricted to having fixed support.

Equilibrium existence and expected payoffs in all-pay auctions with constraints

This paper introduces constraints on player choices in a broad class of all-pay auctions by allowing for upper bounds on players’ strategy sets. It proves the existence of equilibrium and derives simple closed-form formulae for players’ expected payoffs in any equilibrium. These formulae are straightforward to calculate in applications and do not require the derivation of the equilibrium or equilibria. This may be useful because: (i) In some applications players’ expected payoffs are the main item of interest. For example, one may be concerned about the effect of a policy on the market participants. In these cases the results can be used directly, bypassing the need for the full derivation of the equilibrium. (ii) In all-pay auctions, equilibrium is typically in mixed strategies. So in applications where the full characterization of the equilibrium is of interest, finding the players’ expected payoffs is a crucial first step in the derivation of the equilibrium.

All-pay auctions as models for military annexation

All-pay auctions as models for military annexation

Round-robin tournaments with limited resources

We propose a theoretical model of a round-robin tournament with limited resources motivated by the fact that in real-world sport round-robin tournaments, participating teams are sometimes forced to distribute their effort over multiple matches. We assume that participating teams have a limited amount of effort that must be distributed between all matches of the tournament. We model the outcome of each match as a first-price all-pay auction. The prizes are awarded according to the ranking at the end of the tournament, based on the number of wins. The tournament with three teams is solved. In the case of identical budgets and low first prize, we find two types of equilibria—‘effort-saving’ and ‘burning-out’—both leading to unequal payoffs; when the first prize is large, we find multiple families of equilibria with both equal and non-equal payoffs. In the case of non-identical budgets, we show that there exist equilibria where a team with a lower budget gets a higher payoff than a team with a larger budget.

Optimal Accuracy of Unbiased Tullock Contests with Two Heterogeneous Players

I characterize the optimal accuracy level r of an unbiased Tullock contest between two players with heterogeneous prize valuations. The designer maximizes the winning probability of the strong player or the winner’s expected valuation by choosing a contest with an all-pay auction equilibrium (r≥2). By contrast, if she aims at maximizing the expected aggregate effort or the winner’s expected effort, she will choose a contest with a pure-strategy equilibrium, and the optimal accuracy level r<2 decreases in the players’ heterogeneity. Finally, a contest designer who faces a tradeoff between selection quality and minimum (maximum) effort will never choose a contest with a semi-mixed equilibrium.

Information Sharing Decisions in All-Pay Auctions With Correlated Types

Information Sharing Decisions in All-Pay Auctions With Correlated Types

All-pay auctions versus lotteries as provisional fixed-prize fundraising mechanisms: Theory and evidence

We compare two fixed-prize mechanisms for funding public goods, an all-pay auction and a lottery, where public good provision can only occur if the participants’ contributions equal or exceed the fixed-prize value. We show that the provisional nature of the fixed-prize means that efficiency and endowment conditions must both be satisfied to assure positive public good provision. Our main finding is that provisional fixed-prize lotteries can outperform provisional fixed-prize all-pay auctions in terms of public good provision when endowments are large relative to prize values. We test these predictions in a laboratory experiment where we vary the number of participants, the marginal per capita return (mpcr) on the public good, and the mechanism for awarding the prize, either a lottery or an all-pay auction. Consistent with the theory, we find that the mpcr matters for contribution amounts under the lottery mechanism. However, inconsistent with the theory, bids are significantly higher than predicted and there is no significant difference in the level of public good provision under either provisional, fixed-prize mechanism. We consider several different modifications to our framework that might help to explain these departures from theoretical predictions.

Optimal favoritism and maximal revenue: A generalized result

A contest designer who maximizes revenue can secure almost the highest valuation of the contested prize. So far, under complete information, this has been shown assuming that the contest is based on a specific contest success function (CSF) and the designer resorts to two specific instruments of favoritism. This paper generalizes these results by establishing them for any regular CSF augmented with a differential taxation mechanism allowing the equilibrium conditions to exist. In contrast to the conclusions derived thus far, in our general setting, the maximal revenue can be achieved not only at corner but also at interior equilibria with full participation. Our study brings to a closure the longstanding effort to clarify the maximum attainable revenue and how it can be achieved within a very general framework. It explains, in particular, that neither an all-pay-auction (APA) nor any other particular CSF is superior for generating revenue based on favoritism and that a tradeoff between revenue and the extent of participation is avoidable.

Spite vs. risk: Explaining overbidding in the second-price all-pay auction: A theoretical and experimental investigation

We use an experiment to compare a theory of risk-aversion and a theory of spite as an explanation for overbidding in auctions. As a workhorse we use the second-price all-pay auction. Both risk and spite are used to rationalize deviations from risk-neutral equilibrium bids. We exploit that equilibrium predictions in the second-price all-pay auctions for spite are different than those for risk-aversion. We find that spite is a convincing explanation for bidding behavior for the second-price all-pay auction. Not only can spite rationalize observed bids, also our measure for spite is consistent with observed bids.

Charity auctions from an economic perspective — literature review

One of the most common means of raising funds is the charity auction. At charity auctions, money is collected for a good cause, and the products are purchased for private consumption — the bidders may achieve both public and private gains. The charitable nature of this type of auction makes them different from standard auctions. The paper aims to present the main characteristics of this fundraising strategy as well as make a comparison with other formats of raising money for a good cause, i.a. lotteries. Furthermore, the main differences between charity and non-charity auctions will be explained. The studies do not clearly demonstrate whether the charity auction is a more effective mechanism of raising funds than the lottery. However, there is evidence that both formats outperform voluntary contributions. From the perspective of charity organizations, the most effective charity auction format seems to be the all-pay auction. The studies have also revealed that revenues at charity auctions are higher than at standard auctions.

Incentives and Careers in Academia: Theory and Empirical Analysis

Abstract We study career concerns in italian academia. We mold our empirical analysis on the standard model of contests, formalized in the multiunit all-pay auction. The number of posts, the number of applicants, and the relative importance of the criteria for promotion determine academics' effort and output. In Italian universities, incentives operate only through promotion, and all appointment panels are drawn from strictly separated and relatively narrow scientific sectors. Thus, the parameters affecting payoffs can be measured quite precisely, and we take the model to a newly constructed data set that collects the journal publications of all Italian university professors. Our identification strategy is based on a reform introduced in 1999, parts of which affected different academics differently. We find that individual researchers respond to incentives in the manner described by the theoretical model: roughly, more capable researchers respond to increases in the importance of the publications for promotion and in the competitiveness of the scientific sector by exerting more effort; less able researchers are discouraged by competition and do the opposite.