Sequential All-Pay Auctions with Head Starts and Noisy Outputs

We study a sequential (Stackelberg) all-pay auction with two contestants who are privately informed about a parameter (ability) that affects their cost of effort. Contestant 1 (the fi?rst mover) exerts an effort in the fi?rst period, while contestant 2 (the second mover) observes the effort of contestant 1 and then exerts an effort in the second period. Contestant 2 wins the contest if his effort is larger than or equal to the effort of contestant 1; otherwise, contestant 1 wins. We characterize the unique subgame perfect equilibrium of this sequential all-pay auction and analyze the use of head starts to improve the contestants' performances. We also study this model when contestant 1 exerts an effort in the fi?rst period which translates into an observable output but with some noise. We study two variations of this model where contestant 1 either knows or does not know the realization of the noise before she chooses her effort. Contestant 2 does not know the realization of the noise in both variations. For both variations, we characterize the subgame perfect equilibrium and investigate the effect of a random noise on the contestants' performance.Sequential all-pay auctions, head starts, noisy outputs.

Strategic Implications of Uncertainty Over One’s Own Private Value in Auctions

Suppose a bidder must decide whether and when to incur the cost of estimating his own private value in an auction. This can explain why a bidder might increase his bid ceiling in the course of an auction, and why a bidder would like to know the private values of other bidders. It also can explain sniping — flurries of bids at the end of auctions with deadlines — as the result of other bidders trying to avoid stimulating the uninformed bidder to examine his value.

Endogenous Competition Alters the Structure of Optimal Auctions

Potential bidders respond to a sellerfs choice of auction mechanism for a common-value or affiliated-values asset by endogenous decisions whether to incur an information-acquisition cost (and observe a private estimate), or forgo competing. Privately informed participants decide whether to incur a bid-preparation cost and pay an entry fee, or cease competing. Auction rules and information flows are quite general; participation decisions may be simultaneous or sequential. The resulting revenue identity for any auction mechanism implies that optimal auctions are allocatively efficient; a nontrivial reserve price is revenue-inferior. Optimal auctions are otherwise contentless: any auction that sells without reserve becomes optimal by adjusting any one of the continuous, spanning parameters, e.g., the entry fee. Sellerfs surplus-extracting tools are now substitutes, not complements. Many econometric studies of auction markets are seen to be flawed in their identification of the number of bidders.

Rational Participation Revolutionizes Auction Theory

Potential bidders respond to a seller's choice of auction mechanism for a common-value or affiliated-values asset by endogenous decisions whether to incur a participation cost (and observe a private signal), or forego competing. Privately informed participants decide whether to incur a bid-preparation cost and pay an entry fee, or cease competing. Auction rules and information flows are quite general; participation decisions may be simultaneous or sequential. The resulting revenue identity for any auction mechanism implies that optimal auctions are allocatively efficient; a nontrivial reserve price is revenue-inferior for any common-value auction. Characterization of optimal auctions is otherwise contentless, in that any auction that sells without reserve is within the setting of one continuous parameter of an optimal auction; seller's surplus-extracting tools are now substitutes, not complements. Revenue comparisons from the exogenous-bidders literature are upheld in a half-space of parameters, overturned in a half-space. Many econometric studies of auction markets are seen to be flawed in their identifcation of the number of bidders.optimal auctions, endegenous bidder participation, affiliated-values, common-value auctions, surplus-extracting devices

Rational Participation Revolutionizes Auction Theory

Potential bidders respond to a seller's choice of auction mechanism for a common-value or affiliated-values asset by endogenous decisions whether to incur a participation cost (and observe a private signal), or forego competing. Privately informed participants decide whether to incur a bid-preparation cost and pay an entry fee, or cease competing. Auction rules and information flows are quite general; participation decisions may be simultaneous or sequential. The resulting revenue identity for any auction mechanism implies that optimal auctions are allocatively efficient; a nontrivial reserve price is revenue-inferior for any common-value auction. Optimal auctions are otherwise contentless: any auction that sells without reserve becomes optimal by adjusting any one of the continuous, spanning parameters, e.g., the entry fee. Seller.s surplus-extracting tools are now substitutes, not complements. Many econometric studies of auction markets are seen to be flawed in their identification of the number of bidders.Optimal Auctions, Endegenous Bidder Participation, Affiliated-Values, Common-Value Auctions, Surplus-Extracting Devices

Competition amongst contests

This article analyses the allocation of prizes in contests. While existing models consider a single contest with an exogenously given set of players, in our model several contests compete for participants. As a consequence, prizes not only induce incentive effects but also participation effects. We show that contests that aim to maximize players’ aggregate effort will award their entire prize budget to the winner. In contrast, multiple prizes will be awarded in contests that aim to maximize participation and the share of the prize budget awarded to the winner increases in the contests’ randomness. We also provide empirical evidence for this relationship using data from professional road running. In addition, we show that prize structures might be used to screen between players of differing ability.Contests, allocation of prizes, participation

Learning users' interests by quality classification in market-based recommender systems

Recommender systems are widely used to cope with the problem of information overload and, to date, many recommendation methods have been developed. However, no one technique is best for all users in all situations. To combat this, we have previously developed a market-based recommender system that allows multiple agents (each representing a different recommendation method or system) to compete with one another to present their best recommendations to the user. In our system, the marketplace encourages good recommendations by rewarding the corresponding agents who supplied them according to the users’ ratings of their suggestions. Moreover, we have theoretically shown how our system incentivises the agents to bid in a manner that ensures only the best recommendations are presented. To do this effectively in practice, however, each agent needs to be able to classify its recommendations into different internal quality levels, learn the users’ interests for these different levels, and then adapt its bidding behaviour for the various levels accordingly. To this end, in this paper we develop a reinforcement learning and Boltzmann exploration strategy that the recommending agents can exploit for these tasks. We then demonstrate that this strategy does indeed help the agents to effectively obtain information about the users’ interests which, in turn, speeds up the market convergence and enables the system to rapidly highlight the best recommendations