How to Play the Majority Game with Liars

Authors:
Steve Butler;Jia Mao;Ron Graham
Affiliations:
Dept. of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112,;Dept. of Computer Science and Engineering, University of California, San Diego, La Jolla, CA 92093-0404,;Dept. of Computer Science and Engineering, University of California, San Diego, La Jolla, CA 92093-0404,
Venue:
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Year:
2007

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Abstract

The Majoritygame is a two player game with a questioner Qand an answerer A. The answerer holds nelements, each of which can be labeled as 0 or 1. The questioner can ask questions comparing whether two elements have the same or different label. The goal for the questioner is to ask as few questions as possible to be able to identify a single element which has a majority label, or in the case of a tie claim there is none. We denote the minimum number of questions Qneeds to make, regardless of A's answers, as q*. In this paper we consider a variation of the Majority game where Ais allowed to lie up to ttimes, i.e., Qneeds to find an error-tolerantstrategy. In this paper we will give upper and lower bounds for q*for an adaptive game (where questions are processed one at a time), and will find q*for an oblivious game (where questions are asked in one batch).