I started learning game theory and I'm trying to understand better things.
I came across this problem, but sadly there is not solution to it :
Three players must choose between two options X and Y. They voting system win by majority vote. Each player must vote for each of the alternatives and the one that gets the most votes wins (ie 2 out of 3). All players strictly prefer X to Y. Which of the statements are true:
A-In equilibrium X must always win.
B-Voting for X is strictly dominant strategy for the players.
C-Voting for X is a weakly dominant strategy for the players.
D-Voting for Y is never best response
E-There exists an equilibrium where Y wins.
My answer would be that all of these are correct expect E. This is because All of the players strictly prefer X to Y, and for this reason Y is never a best response, Y is a dominated strategy, hence does not win at equilibrium.
Is my reasoning correct? Any help/tips is appreciated.
Many thanks :)