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Register a new userPrice of Privacy in the Keynesian Beauty Contest
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Added by
Zachary Schutzman
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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The Keynesian Beauty Contest is a classical game in which strategic agents seek to both accurately guess the true state of the world as well as the average action of all agents. We study an augmentation of this game where agents are concerned about revealing their private information and additionally suffer a loss based on how well an observer can infer their private signals. We solve for an equilibrium of this augmented game and quantify the loss of social welfare as a result of agents acting to obscure their private information, which we call the price of privacy. We analyze t
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We present the results of the fifth Interferometric Imaging Beauty Contest. The contest consists in blind imaging of test data sets derived from model sources and distributed in the OIFITS format. Two scenarios of imaging with CHARA/MIRC-6T were offered for reconstruction: imaging a T Tauri disc and imaging a spotted red supergiant. There were eight different teams competing this time: Monnier with the software package MACIM; Hofmann, Schertl and Weigelt with IRS; Thiebaut and Soulez with MiRA ; Young with BSMEM; Mary and Vannier with MIROIRS; Millour and Vannier with independent BSMEM and MiRA entries; Rengaswamy with an original method; and Elias with the radio-astronomy package CASA. The contest model images, the data delivered to the contestants and the rules are described as well as the results of the image reconstruction obtained by each method. These results are discussed as well as the strengths and limitations of each algorithm.
We study contests where the designers objective is an extension of the widely studied objective of maximizing the total output: The designer gets zero marginal utility from a players output if the output of the player is very low or very high. We model this using two objective functions: binary threshold, where a players contribution to the designers utility is 1 if her output is above a certain threshold, and 0 otherwise; and linear threshold, where a players contribution is linear if her output is between a lower and an upper threshold, and becomes constant below the lower and above the upper threshold. For both of these objectives, we study (1) rank-order allocation contests that use only the ranking of the players to assign prizes and (2) general contests that may use the numerical values of the players outputs to assign prizes. We characterize the optimal contests that maximize the designers objective and indicate techniques to efficiently compute them. We also prove that for the linear threshold objective, a contest that distributes the prize equally among a fixed number of top-ranked players offers a factor-2 approximation to the optimal rank-order allocation contest.
Setting an effective reserve price for strategic bidders in repeated auctions is a central question in online advertising. In this paper, we investigate how to set an anonymous reserve price in repeated auctions based on historical bids in a way that balances revenue and incentives to misreport. We propose two simple and computationally efficient methods to set reserve prices based on the notion of a clearing price and make them robust to bidder misreports. The first approach adds random noise to the reserve price, drawing on techniques from differential privacy. The second method applies a smoothing technique by adding noise to the training bids used to compute the reserve price. We provide theoretical guarantees on the trade-offs between the revenue performance and bid-shading incentives of these two mechanisms. Finally, we empirically evaluate our mechanisms on synthetic data to validate our theoretical findings.
We study revenue maximization through sequential posted-price (SPP) mechanisms in single-dimensional settings with $n$ buyers and independent but not necessarily identical value distributions. We construct the SPP mechanisms by considering the best of two simple pricing rules: one that imitates the revenue optimal mchanism, namely the Myersonian mechanism, via the taxation principle and the other that posts a uniform price. Our pricing rules are rather generalizable and yield the first improvement over long-established approximation factors in several settings. We design factor-revealing mathematical programs that crisply capture the approximation factor of our SPP mechanism. In the single-unit setting, our SPP mechanism yields a better approximation factor than the state of the art prior to our work (Azar, Chiplunkar & Kaplan, 2018). In the multi-unit setting, our SPP mechanism yields the first improved approximation factor over the state of the art after over nine years (Yan, 2011 and Chakraborty et al., 2010). Our results on SPP mechanisms immediately imply improved performance guarantees for the equivalent free-order prophet inequality problem. In the position auction setting, our SPP mechanism yields the first higher-than $1-1/e$ approximation factor. In eager second-price (ESP) auctions, our two simple pricing rules lead to the first improved approximation factor that is strictly greater than what is obtained by the SPP mechanism in the single-unit setting.
The price of anarchy has become a standard measure of the efficiency of equilibria in games. Most of the literature in this area has focused on establishing worst-case bounds for specific classes of games, such as routing games or more general congestion games. Recently, the price of anarchy in routing games has been studied as a function of the traffic demand, providing asymptotic results in light and heavy traffic. The aim of this paper is to study the price of anarchy in nonatomic routing games in the intermediate region of the demand. To achieve this goal, we begin by establishing some smoothness properties of Wardrop equilibria and social optima for general smooth costs. In the case of affine costs we show that the equilibrium is piecewise linear, with break points at the demand levels at which the set of active paths changes. We prove that the number of such break points is finite, although it can be exponential in the size of the network. Exploiting a scaling law between the equilibrium and the social optimum, we derive a similar behavior for the optimal flows. We then prove that in any interval between break points the price of anarchy is smooth and it is either monotone (decreasing or increasing) over the full interval, or it decreases up to a certain minimum point in the interior of the interval and increases afterwards. We deduce that for affine costs the maximum of the price of anarchy can only occur at the break points. For general costs we provide counterexamples showing that the set of break points is not always finite.
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