par Buhler, Joe;Freiling, Chris;Graham, Ron;Kariv, Jonathan;Roche, James J.R.;Tiefenbruck, Mark;Van Alten, Clint;Yeroshkin, Dmytro
Référence Number Theory and Combinatorics: A Collection in Honor of the Mathematics of Ronald Graham, De Gruyter, page (115-165)
Publication Publié, 2022-04
Partie d'ouvrage collectif
Résumé : The Levine hat game requires n players, each wearing an infinite random stack of black and white hats, to guess the location of a black hat on their own head seeing only the hats worn by all the other players. They are allowed a strategy session before the game, but no further communication. The players collectively win if and only if all their guesses are correct. In this paper, we give an overview of what is known about strategies for this game, including an extended discussion of the case with n =2 players (and a conjecture for an optimal strategy in this case). We also prove that Vn, the optimal value of the joint success probability in the n-player game, is a strictly decreasing function of n.