game theory

Computer Go

Go is an ancient Chinese game that originated some 4000 years ago and has still great popularity nowadays. Computer Go on the other hand has made little progress in these 4000 years: best go programs are rated like middle-to-weak amateur human players. We will discuss one recent approach to computer go [ยน], based on a mixture of two relatively well known strategies: the UCT algorithm and Monte Carlo, which happens to be the most successful one to date.

[1] Modification of UCT with Patterns in Monte-Carlo Go, S. Gerlly, Y. Wang, R. Munos and O.Teytaud, INRIA Technical Report, 2006.

Wed, 04/02/2009 - 12:30
Alfredo Braunstein

Approximation Algorithms for Budget-Constrained Auctions

Recently there has been a surge of interest in auctions research triggered on the one hand by auctions of bandwidth and other public assets and on the other by the popularity of Internet auctions and the possibility of new auction formats enabled by e-commerce. Simultaneous auction of items is a popular auction format. We consider the problem of maximizing total revenue in the simultaneous auction of a set of items where the bidders have individual budget constraints. Each bidder is permitted to bid on all the items of his choice and specifies his budget constraint to the auctioneer, who must select bids to maximize the revenue while ensuring that no budget constraints are violated. We show that the problem of maximizing revenue is such a setting is NP-hard, and present a factor-1.62 approximation algorithm for it. We formulate the problem as an integer program and solve a linear relaxation to obtain a fractional optimal solution, which is then deterministically rounded to obtain an integer solution. We argue that the loss in revenue incurred by the rounding procedure is bounded by a factor of 1.62.

[1] R. Garg, V. Kumar and V. Pandit.

Tue, 07/10/2008 - 14:30
John Realpe
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