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The Locker Problem with Empty Lockers
David Avis, Luc Devroye and Kazuo Iwama
AbstractWe consider a cooperative game played by n players
against a referee. The players names are randomly distributed among
n lockers, with one name per locker. Each player can open up to half
the lockers and each player must find his name. Once the game starts
the players may not communicate. It has been previously shown that,
quite surprisingly, an optimal strategy exists for which the success
probability is never worse than 1  ln 2 0.306. In this paper we
consider an extension where the number of lockers is greater than
the number of players, so that some lockers are empty. We show that
the players may still win with positive probability even if there are
a constant k number of empty lockers. We show that for each fixed
probability p, there is a constant c so that the players can win with
probability at least p if they are allowed to open cn lockers.
KeywordsLocker problem, pointerfollowing algorithms.
I. INTRODUCTION
The locker problem is a cooperative game between a team
of n players numbered 1, 2, . . . , n and a referee. In the initial
