Publications Repository - Gdańsk University of Technology

The topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of a win. In this version every player can see everybody excluding himself. We consider such a problem on a graph, where vertices correspond to players, and a player can see each player to whom he is connected by an edge. The solution of the hat problem on a graph is known for trees and for cycles on four or at least nine vertices. We consider the problem on the cycle on seven vertices. We prove that if in a strategy for this graph some vertex guesses its color with probability at least one by two, then the chance of success is at most one by two.

Authors

• dr inż. Marcin Krzywkowski link open in new tab