Show that for player 1 the strategy with a maximum bid of $6,000 dominates a strategy with a maximum bid of $5,000. Repeat with an alternative maximum bid of $7,000. Do all this under the first tie-breaking rule in which player 1 gets the drawing when the maximum bids are identical.

a. Repeat the previous question, using a tie-breaking rule in which a coin toss decides the winner.

b. Explain why your arguments in the previous two questions would still be valid, even if player 1 had no idea about how much the drawing is worth to player 2.