Discrete convex analysis for analysis of iterative auctions

May 24, 2016, Tokyo Institute of Technology
Discrete convex analysis for analysis of iterative auctions
Figure 1. Behavior of the iterative auction algorithm

Researchers are investigating auction models where there are many different indivisible goods such as houses and cars. Notably, algorithms known as iterative auctions are often used to compute equilibrium prices of goods.

However, the theoretical behavior of iterative auction algorithms is not fully understood. In particular, there are only a few scattered results of research on the theoretical analysis for time bounds of iterative auctions to-date, even though the theoretical bounds on the number of iterations are interesting as research topics in their own right and important for practical applications.

Here, Akiyoshi Shioura at Tokyo Tech and colleagues at Tokyo Metropolitan University, and University of York, UK, describe a unified method of analysis for iterative auctions based on discrete convex analysis—a theory of discrete optimization problems. A key tool in the analysis is the concept of the Lyapunov function in auction theory. The researchers show that the Lyapunov function has a useful property called discrete convexity. By making use of this property, the team derived exact bounds on the number of iterations in terms of the distance between the initial price vector and the resulting equilibrium.

The results of this research extend and unify the iterative auction algorithms for a variety of auction models, offering computational complexity results for these algorithms, and reinforcing the connection between auction theory and discrete convex .

Explore further: How to digitally stoke that old-time auction fever

More information: Kazuo Murota et al. Time bounds for iterative auctions: A unified approach by discrete convex analysis, Discrete Optimization (2016). DOI: 10.1016/j.disopt.2016.01.001

Related Stories

How to digitally stoke that old-time auction fever

July 28, 2015

Whether online auctions are selling rare Pokemon cards or fine art, the science behind inciting the highest bids gets a boost from a paper to be published in the September issue of the Journal of Retailing. Researchers from ...

Real competitors enhance thrill of auctions

September 4, 2015

The thrill is part of the game—whoever waits for his bid to be accepted on online auction platforms, feels the excitement in the bidding war for the object of desire. The heart beats faster, palms start to sweat. Physiological ...

Recommended for you

Archaeologists discover Cornish barrow site

April 20, 2018

An Archaeologist at The Australian National University (ANU) has discovered a prehistoric Bronze-Age barrow, or burial mound, on a hill in Cornwall and is about to start excavating the untouched site which overlooks the English ...

New ancestor of modern sea turtles found in Alabama

April 18, 2018

A sea turtle discovered in Alabama is a new species from the Late Cretaceous epoch, according to a study published April 18, 2018 in the open-access journal PLOS ONE by Drew Gentry from the University of Alabama at Birmingham, ...

New study improves 'crowd wisdom' estimates

April 18, 2018

In 1907, a statistician named Francis Galton recorded the entries from a weight-judging competition as people guessed the weight of an ox. Galton analyzed hundreds of estimates and found that while individual guesses varied ...

0 comments

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.