The board of a company has to elect a new CEO. Three members are on the board, 1,2,3. After a first round of selection, three candidates are left: α, β and γ. Preferences are as followed:

• Board member 1 prefers α to β and β to γ;

• Board member 2 prefers β to γ and γ to α;

• Board member 1 prefers γ to α and α to β;

To decide on the new CEO, they vote (secret ballot, one member one vote). Member 1, the chair of the board, is the tie breaker: if the vote is tied, the winner will be the candidate for whom member 1 votes.

1. For each member, find their weakly or strictly dominated strategy.

2. Consider the game when all weakly or strictly dominated strategies have been eliminated. What is the outcome of this game?

3. Comment.