remaining two unchosen doors will be opened and you will receive whats behind

# Remaining two unchosen doors will be opened and you

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remaining two unchosen doors will be opened (and you will receive what’s behind it) ifthe coin comes up “heads” or (2) the other remaining unchosen door will be opened (andyou will receive what’s behind it) if the coin comes up “tails.”(a) Suppose that your payoff from winning the prize is 1 and the payoff from not winningthe prize is 0 (i.e., you don’t care how you win or lose the prize, just whether youwin it). Suppose that the payoff of the host is 0 if he opens a door with the prizebehind it and 1 otherwise.Draw this as an extensive form game, supposing that the prize is equally likely to bebehind doorsA,B,C, andD.(b) What is the optimal strategy (i.e., should you flip the coin or not)? (This might bea function ofp.)(c) Supposing that you are risk-neutral and you have a linear payoff from “money,” whatis the maximum that you would be willing to pay for the optimal strategy (i.e., ifflipping the coin is not optimal, how much would you be willing to pay to see what’sbehind doorAinstead of the host flipping the coin, or vice-versa)? 2