Bayes-Nash Equilibria of the Generalized Second-Price Auction

Bayes-Nash Equilibria of the Generalized Second-Price Auction
Renato Gomes
Abstract

We develop a Bayes–Nash analysis of the generalized second-price (GSP) auction, the multi-unit auction used by search engines to sell sponsored advertising positions. Our main result characterizes the efficient Bayes–Nash equilibrium of the GSP and provides a necessary

and sufficient condition that guarantees existence of such an equilibrium. With only two positions, this condition requires that the click–through rate of the second position is sufficiently smaller than that of the first.

When an efficient equilibrium exists, we provide a necessary and sufficient condition for the auction revenue to decrease as click–through rates increase. Interestingly, under optimal reserve prices, revenue increases with the click–through rates of all positions. Further, we prove that no inefficient equilibrium of the GSP can be symmetric.

Our results are in sharp contrast with the previous literature that studied the GSP under complete information.

Another publication from the same category: Machine Learning and Data Science

Washinton DC, 27-30 Oct. 2014

Astro: A Predictive Model for Anomaly Detection and Feedback-based Scheduling on Hadoop

Chaitali Gupta, Mayank Bansal, Tzu-Cheng Chuang, Ranjan Sinha, Sami Ben-romdhane

The sheer growth in data volume and Hadoop cluster size make it a significant challenge to diagnose and locate problems in a production-level cluster environment efficiently and within a short period of time. Often times, the distributed monitoring systems are not capable of detecting a problem well in advance when a large-scale Hadoop cluster starts to deteriorate i n performance or becomes unavailable. Thus, inc o m i n g workloads, scheduled between the time when cluster starts to deteriorate and the time when the problem is identified, suffer from longer execution times. As a result, both reliability and throughput of the cluster reduce significantly. In this paper, we address this problem by proposing a system called Astro, which consists of a predictive model and an extension to the Hadoop scheduler. The predictive model in Astro takes into account a rich set of cluster behavioral information that are collected by monitoring processes and model them using machine learning algorithms to predict future behavior of the cluster. The Astro predictive model detects anomalies in the cluster and also identifies a ranked set of metrics that have contributed the most towards the problem. The Astro scheduler uses the prediction outcome and the list of metrics to decide whether it needs to move and reduce workloads from the problematic cluster nodes or to prevent additional workload allocations to them, in order to improve both throughput and reliability of the cluster. The results demonstrate that the Astro scheduler improves usage of cluster compute resources significantly by 64.23% compared to traditional Hadoop. Furthermore, the runtime of the benchmark application reduced by 26.68% during the time of anomaly, thus improving the cluster throughput.

Keywords