Download or read book Essays on Value Distributions in All-pay Auctions written by Suat Akbulut and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three chapters. The first chapter studies the value distribution adoption choice of a player when she competes against an incumbent in an all-pay auction setting. The second chapter analyzes how much would a player like to learn about her own valuation in a similar setting. Lastly, the third chapter analyzes the best information disclosure policy that an auctioneer can adopt according to different performance measures in a two-player two-stage all-pay auction setting, where the players choose their value distributions in the first stage. The first chapter considers a two-player all-pay auction setting and modifies it by adding a technology-adoption stage at the beginning of the game. In a discrete valuations environment, assuming one player's valuation is common knowledge, we allow the other player (informed) to pick a distribution over the valuation space. Her opponent (uninformed) observes her choice of distribution. However, her valuation is privately drawn according to this distribution. The two players then play an asymmetric all-pay auction. We show that in such a setting, the informed player adopts a distribution that assigns positive probabilities to at most two elements; that will always contain the supremum, and sometimes, the infimum of the set of available values. She pools the extreme values in order to create an information asymmetry, which then would make the uninformed player bid less aggressively. We later impose a mean condition on the distribution that the informed player could pick and observe that she still prefers to split the probability mass on in-between values to the extreme ones. As a result, she picks the same support but arranges the probability mass on these values to meet the mean condition. In other words, the informed player is first interested in including only the extreme values in the support of her value distribution, and then the probabilities assigned to those values. The second chapter assumes that the informed player's value distribution is common knowledge and that she cannot observe her realized value. However, she can acquire additional information about her realized value by adopting a learning experiment. She picks such an experiment in the first stage. Even though her choice of experiment is observed by the uninformed player, she privately learns the realization of the experiment. Then, they play an all-pay auction in the second stage of the game. Every learning experiment induces a posterior probability distribution over the convex hull of the set of available values. The informed player bids as if her value is drawn from this posterior distribution, where she privately observes her value. Therefore, her problem boils down to choosing a posterior distribution that stochastically dominates the prior in the second-order sense. We show that the informed player's motivation to split the probability mass on in-between types to the extreme types is still present. However, due to the distributional constraints, she will pick a fully informative experiment to learn her value as long as it does not result in her two lowest values bidding zero with a positive probability in the equilibrium of the all-pay auction stage. If that is the case, she would try to mimic the prior distribution for the high types, who will never bid zero, and allocate the remaining probability to only one type to meet the constraint. One natural extension of our analysis is studying the equilibrium value distribution profiles when both players are choosing their own value distribution. When the possible values are only high and low, we show that the profile in which one player picks the high value with probability one while the other player assigns probability half to each values is the unique (up to symmetry) value distribution profile. Moreover, when we consider any set of values, we show that the profile in which one player picks the highest value with probability one, while the other player assigns probability half to the highest and the lowest values each is an equilibrium value distribution profile. Due to the lack of an analytical approach to the equilibrium bidding distributions of the all-pay auctions in an asymmetric information environment, checking whether this equilibrium is unique is left as future work. The last chapter analyzes the best information disclosure policy that an auctioneer can adopt according to different performance measures, namely players' payoff, prize allocation efficiency, and aggregate effort. The significant contribution of the analysis is that players have the ability to choose the distribution from which their own types are drawn. Using a two-player all-pay auction with the two-type setting, we show that the optimal disclosure policy depends on the ratio of the value of winning for a low type to the value of winning for a high type.