Waiting in line. Two hundred people are willing to wait in line to see a movie at a theater whose capacity is one hundred. Denote person i’s valuation of the movie in excess of the price of admission, expressed in terms of the amount of time she is willing to wait, by vi . That is, person i’s payoff if she waits to ti units of time is vi −ti . Each person attaches no value to a second ticket, and cannot buy tickets for other people. Assume v1 > v2 > · · · > v200. Each person chooses an arrival time. If several people arrive at the same time, then their order in line is determined by their index with lower numbered people going first. If a person arrives to find 100 or more people in line, her payoff is zero. Model the situation as a variant of a discriminatory multi-unit auction, in which each person submits a bid for only one unit, and find its Nash equilibrium.1 (a) What would a supply and demand analysis suggest? (b) Will at least 100 people wait in line? (c) Will the highest value people wait in line? I.e., will anyone with an index greater than 100 see the movie? (d) Will people choose to wait different amounts of time? (e) Will anyone that sees the movie wait more than v100? (f) Will anyone that sees the movie wait less than v101?